Adaptively wavelet-based image denoising algorithm with edge preserving
NASA Astrophysics Data System (ADS)
Tan, Yihua; Tian, Jinwen; Liu, Jian
2006-02-01
A new wavelet-based image denoising algorithm, which exploits the edge information hidden in the corrupted image, is presented. Firstly, a canny-like edge detector identifies the edges in each subband. Secondly, multiplying the wavelet coefficients in neighboring scales is implemented to suppress the noise while magnifying the edge information, and the result is utilized to exclude the fake edges. The isolated edge pixel is also identified as noise. Unlike the thresholding method, after that we use local window filter in the wavelet domain to remove noise in which the variance estimation is elaborated to utilize the edge information. This method is adaptive to local image details, and can achieve better performance than the methods of state of the art.
NASA Astrophysics Data System (ADS)
Wang, Dong; Singh, Vijay P.; Shang, Xiaosan; Ding, Hao; Wu, Jichun; Wang, Lachun; Zou, Xinqing; Chen, Yuanfang; Chen, Xi; Wang, Shicheng; Wang, Zhenlong
2014-07-01
De-noising meteorologic and hydrologic time series is important to improve the accuracy and reliability of extraction, analysis, simulation, and forecasting. A hybrid approach, combining sample entropy and wavelet de-noising method, is developed to separate noise from original series and is named as AWDA-SE (adaptive wavelet de-noising approach using sample entropy). The AWDA-SE approach adaptively determines the threshold for wavelet analysis. Two kinds of meteorologic and hydrologic data sets, synthetic data set and 3 representative field measured data sets (one is the annual rainfall data of Jinan station and the other two are annual streamflow series from two typical stations in China, Yingluoxia station on the Heihe River, which is little affected by human activities, and Lijin station on the Yellow River, which is greatly affected by human activities), are used to illustrate the approach. The AWDA-SE approach is compared with three conventional de-noising methods, including fixed-form threshold algorithm, Stein unbiased risk estimation algorithm, and minimax algorithm. Results show that the AWDA-SE approach separates effectively the signal and noise of the data sets and is found to be better than the conventional methods. Measures of assessment standards show that the developed approach can be employed to investigate noisy and short time series and can also be applied to other areas.
Wavelet-Based Adaptive Denoising of Phonocardiographic Records
2007-11-02
the approximated signal, and d the signal details at the given scale; h and g are biorthogonal filters, corresponding to the selected mother wavelet ...dyadic scale can be written as: where is the orthogonal mother wavelet , and: The discrete version of the dyadic wavelet transform can be based on... wavelet with 4 moments equal to zero (Coiflet-2) as the mother wavelet . The two channels were wavelet decomposed up to the 9th order (i = 0, 1 ... 8
Birdsong Denoising Using Wavelets
Priyadarshani, Nirosha; Marsland, Stephen; Castro, Isabel; Punchihewa, Amal
2016-01-01
Automatic recording of birdsong is becoming the preferred way to monitor and quantify bird populations worldwide. Programmable recorders allow recordings to be obtained at all times of day and year for extended periods of time. Consequently, there is a critical need for robust automated birdsong recognition. One prominent obstacle to achieving this is low signal to noise ratio in unattended recordings. Field recordings are often very noisy: birdsong is only one component in a recording, which also includes noise from the environment (such as wind and rain), other animals (including insects), and human-related activities, as well as noise from the recorder itself. We describe a method of denoising using a combination of the wavelet packet decomposition and band-pass or low-pass filtering, and present experiments that demonstrate an order of magnitude improvement in noise reduction over natural noisy bird recordings. PMID:26812391
Enhancing P300 Wave of BCI Systems Via Negentropy in Adaptive Wavelet Denoising.
Vahabi, Z; Amirfattahi, R; Mirzaei, Ar
2011-07-01
Brian Computer Interface (BCI) is a direct communication pathway between the brain and an external device. BCIs are often aimed at assisting, augmenting or repairing human cognitive or sensory-motor functions. EEG separation into target and non-target ones based on presence of P300 signal is of difficult task mainly due to their natural low signal to noise ratio. In this paper a new algorithm is introduced to enhance EEG signals and improve their SNR. Our denoising method is based on multi-resolution analysis via Independent Component Analysis (ICA) Fundamentals. We have suggested combination of negentropy as a feature of signal and subband information from wavelet transform. The proposed method is finally tested with dataset from BCI Competition 2003 and gives results that compare favorably.
Optical Aperture Synthesis Object's Information Extracting Based on Wavelet Denoising
NASA Astrophysics Data System (ADS)
Fan, W. J.; Lu, Y.
2006-10-01
Wavelet denoising is studied to improve OAS(optical aperture synthesis) object's Fourier information extracting. Translation invariance wavelet denoising based on Donoho wavelet soft threshold denoising is researched to remove Pseudo-Gibbs in wavelet soft threshold image. OAS object's information extracting based on translation invariance wavelet denoising is studied. The study shows that wavelet threshold denoising can improve the precision and the repetition of object's information extracting from interferogram, and the translation invariance wavelet denoising information extracting is better than soft threshold wavelet denoising information extracting.
Nonlocal hierarchical dictionary learning using wavelets for image denoising.
Yan, Ruomei; Shao, Ling; Liu, Yan
2013-12-01
Exploiting the sparsity within representation models for images is critical for image denoising. The best currently available denoising methods take advantage of the sparsity from image self-similarity, pre-learned, and fixed representations. Most of these methods, however, still have difficulties in tackling high noise levels or noise models other than Gaussian. In this paper, the multiresolution structure and sparsity of wavelets are employed by nonlocal dictionary learning in each decomposition level of the wavelets. Experimental results show that our proposed method outperforms two state-of-the-art image denoising algorithms on higher noise levels. Furthermore, our approach is more adaptive to the less extensively researched uniform noise.
Time Difference of Arrival (TDOA) Estimation Using Wavelet Based Denoising
1999-03-01
NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS TIME DIFFERENCE OF ARRIVAL (TDOA) ESTIMATION USING WAVELET BASED DENOISING by Unal Aktas...4. TITLE AND SUBTITLE TIME DIFFERENCE OF ARRIVAL (TDOA) ESTIMATION USING WAVELET BASED DENOISING 6. AUTHOR(S) Unal Aktas 7...difference of arrival (TDOA) method. The wavelet transform is used to increase the accuracy of TDOA estimation. Several denoising techniques based on
Parallel object-oriented, denoising system using wavelet multiresolution analysis
Kamath, Chandrika; Baldwin, Chuck H.; Fodor, Imola K.; Tang, Nu A.
2005-04-12
The present invention provides a data de-noising system utilizing processors and wavelet denoising techniques. Data is read and displayed in different formats. The data is partitioned into regions and the regions are distributed onto the processors. Communication requirements are determined among the processors according to the wavelet denoising technique and the partitioning of the data. The data is transforming onto different multiresolution levels with the wavelet transform according to the wavelet denoising technique, the communication requirements, and the transformed data containing wavelet coefficients. The denoised data is then transformed into its original reading and displaying data format.
Oriented wavelet transform for image compression and denoising.
Chappelier, Vivien; Guillemot, Christine
2006-10-01
In this paper, we introduce a new transform for image processing, based on wavelets and the lifting paradigm. The lifting steps of a unidimensional wavelet are applied along a local orientation defined on a quincunx sampling grid. To maximize energy compaction, the orientation minimizing the prediction error is chosen adaptively. A fine-grained multiscale analysis is provided by iterating the decomposition on the low-frequency band. In the context of image compression, the multiresolution orientation map is coded using a quad tree. The rate allocation between the orientation map and wavelet coefficients is jointly optimized in a rate-distortion sense. For image denoising, a Markov model is used to extract the orientations from the noisy image. As long as the map is sufficiently homogeneous, interesting properties of the original wavelet are preserved such as regularity and orthogonality. Perfect reconstruction is ensured by the reversibility of the lifting scheme. The mutual information between the wavelet coefficients is studied and compared to the one observed with a separable wavelet transform. The rate-distortion performance of this new transform is evaluated for image coding using state-of-the-art subband coders. Its performance in a denoising application is also assessed against the performance obtained with other transforms or denoising methods.
Optimal wavelet denoising for smart biomonitor systems
NASA Astrophysics Data System (ADS)
Messer, Sheila R.; Agzarian, John; Abbott, Derek
2001-03-01
Future smart-systems promise many benefits for biomedical diagnostics. The ideal is for simple portable systems that display and interpret information from smart integrated probes or MEMS-based devices. In this paper, we will discuss a step towards this vision with a heart bio-monitor case study. An electronic stethoscope is used to record heart sounds and the problem of extracting noise from the signal is addressed via the use of wavelets and averaging. In our example of heartbeat analysis, phonocardiograms (PCGs) have many advantages in that they may be replayed and analysed for spectral and frequency information. Many sources of noise may pollute a PCG including foetal breath sounds if the subject is pregnant, lung and breath sounds, environmental noise and noise from contact between the recording device and the skin. Wavelets can be employed to denoise the PCG. The signal is decomposed by a discrete wavelet transform. Due to the efficient decomposition of heart signals, their wavelet coefficients tend to be much larger than those due to noise. Thus, coefficients below a certain level are regarded as noise and are thresholded out. The signal can then be reconstructed without significant loss of information in the signal. The questions that this study attempts to answer are which wavelet families, levels of decomposition, and thresholding techniques best remove the noise in a PCG. The use of averaging in combination with wavelet denoising is also addressed. Possible applications of the Hilbert Transform to heart sound analysis are discussed.
NASA Astrophysics Data System (ADS)
Ji, Yanju; Li, Dongsheng; Yu, Mingmei; Wang, Yuan; Wu, Qiong; Lin, Jun
2016-05-01
The ground electrical source airborne transient electromagnetic system (GREATEM) on an unmanned aircraft enjoys considerable prospecting depth, lateral resolution and detection efficiency, etc. In recent years it has become an important technical means of rapid resources exploration. However, GREATEM data are extremely vulnerable to stationary white noise and non-stationary electromagnetic noise (sferics noise, aircraft engine noise and other human electromagnetic noises). These noises will cause degradation of the imaging quality for data interpretation. Based on the characteristics of the GREATEM data and major noises, we propose a de-noising algorithm utilizing wavelet threshold method and exponential adaptive window width-fitting. Firstly, the white noise is filtered in the measured data using the wavelet threshold method. Then, the data are segmented using data window whose step length is even logarithmic intervals. The data polluted by electromagnetic noise are identified within each window based on the discriminating principle of energy detection, and the attenuation characteristics of the data slope are extracted. Eventually, an exponential fitting algorithm is adopted to fit the attenuation curve of each window, and the data polluted by non-stationary electromagnetic noise are replaced with their fitting results. Thus the non-stationary electromagnetic noise can be effectively removed. The proposed algorithm is verified by the synthetic and real GREATEM signals. The results show that in GREATEM signal, stationary white noise and non-stationary electromagnetic noise can be effectively filtered using the wavelet threshold-exponential adaptive window width-fitting algorithm, which enhances the imaging quality.
Adaptive Fourier decomposition based ECG denoising.
Wang, Ze; Wan, Feng; Wong, Chi Man; Zhang, Liming
2016-10-01
A novel ECG denoising method is proposed based on the adaptive Fourier decomposition (AFD). The AFD decomposes a signal according to its energy distribution, thereby making this algorithm suitable for separating pure ECG signal and noise with overlapping frequency ranges but different energy distributions. A stop criterion for the iterative decomposition process in the AFD is calculated on the basis of the estimated signal-to-noise ratio (SNR) of the noisy signal. The proposed AFD-based method is validated by the synthetic ECG signal using an ECG model and also real ECG signals from the MIT-BIH Arrhythmia Database both with additive Gaussian white noise. Simulation results of the proposed method show better performance on the denoising and the QRS detection in comparing with major ECG denoising schemes based on the wavelet transform, the Stockwell transform, the empirical mode decomposition, and the ensemble empirical mode decomposition.
Denoising solar radiation data using coiflet wavelets
Karim, Samsul Ariffin Abdul Janier, Josefina B. Muthuvalu, Mohana Sundaram; Hasan, Mohammad Khatim; Sulaiman, Jumat; Ismail, Mohd Tahir
2014-10-24
Signal denoising and smoothing plays an important role in processing the given signal either from experiment or data collection through observations. Data collection usually was mixed between true data and some error or noise. This noise might be coming from the apparatus to measure or collect the data or human error in handling the data. Normally before the data is use for further processing purposes, the unwanted noise need to be filtered out. One of the efficient methods that can be used to filter the data is wavelet transform. Due to the fact that the received solar radiation data fluctuates according to time, there exist few unwanted oscillation namely noise and it must be filtered out before the data is used for developing mathematical model. In order to apply denoising using wavelet transform (WT), the thresholding values need to be calculated. In this paper the new thresholding approach is proposed. The coiflet2 wavelet with variation diminishing 4 is utilized for our purpose. From numerical results it can be seen clearly that, the new thresholding approach give better results as compare with existing approach namely global thresholding value.
Musculoskeletal ultrasound image denoising using Daubechies wavelets
NASA Astrophysics Data System (ADS)
Gupta, Rishu; Elamvazuthi, I.; Vasant, P.
2012-11-01
Among various existing medical imaging modalities Ultrasound is providing promising future because of its ease availability and use of non-ionizing radiations. In this paper we have attempted to denoise ultrasound image using daubechies wavelet and analyze the results with peak signal to noise ratio and coefficient of correlation as performance measurement index. The different daubechies from 1 to 6 is used on four different ultrasound bone fracture images with three different levels from 1 to 3. The images for visual inspection and PSNR, Coefficient of correlation values are graphically shown for quantitaive analysis of resultant images.
Image denoising based on wavelet cone of influence analysis
NASA Astrophysics Data System (ADS)
Pang, Wei; Li, Yufeng
2009-11-01
Donoho et al have proposed a method for denoising by thresholding based on wavelet transform, and indeed, the application of their method to image denoising has been extremely successful. But this method is based on the assumption that the type of noise is only additive Gaussian white noise, which is not efficient to impulse noise. In this paper, a new image denoising algorithm based on wavelet cone of influence (COI) analyzing is proposed, and which can effectively remove the impulse noise and preserve the image edges via undecimated discrete wavelet transform (UDWT). Furthermore, combining with the traditional wavelet thresholding denoising method, it can be also used to restrain more widely type of noise such as Gaussian noise, impulse noise, poisson noise and other mixed noise. Experiment results illustrate the advantages of this method.
Terahertz digital holography image denoising using stationary wavelet transform
NASA Astrophysics Data System (ADS)
Cui, Shan-Shan; Li, Qi; Chen, Guanghao
2015-04-01
Terahertz (THz) holography is a frontier technology in terahertz imaging field. However, reconstructed images of holograms are inherently affected by speckle noise, on account of the coherent nature of light scattering. Stationary wavelet transform (SWT) is an effective tool in speckle noise removal. In this paper, two algorithms for despeckling SAR images are implemented to THz images based on SWT, which are threshold estimation and smoothing operation respectively. Denoised images are then quantitatively assessed by speckle index. Experimental results show that the stationary wavelet transform has superior denoising performance and image detail preservation to discrete wavelet transform. In terms of the threshold estimation, high levels of decomposing are needed for better denoising result. The smoothing operation combined with stationary wavelet transform manifests the optimal denoising effect at single decomposition level, with 5×5 average filtering.
Image denoising with the dual-tree complex wavelet transform
NASA Astrophysics Data System (ADS)
Yaseen, Alauldeen S.; Pavlova, Olga N.; Pavlov, Alexey N.; Hramov, Alexander E.
2016-04-01
The purpose of this study is to compare image denoising techniques based on real and complex wavelet-transforms. Possibilities provided by the classical discrete wavelet transform (DWT) with hard and soft thresholding are considered, and influences of the wavelet basis and image resizing are discussed. The quality of image denoising for the standard 2-D DWT and the dual-tree complex wavelet transform (DT-CWT) is studied. It is shown that DT-CWT outperforms 2-D DWT at the appropriate selection of the threshold level.
Undecimated Wavelet Transforms for Image De-noising
Gyaourova, A; Kamath, C; Fodor, I K
2002-11-19
A few different approaches exist for computing undecimated wavelet transform. In this work we construct three undecimated schemes and evaluate their performance for image noise reduction. We use standard wavelet based de-noising techniques and compare the performance of our algorithms with the original undecimated wavelet transform, as well as with the decimated wavelet transform. The experiments we have made show that our algorithms have better noise removal/blurring ratio.
Wavelet Denoising of Mobile Radiation Data
Campbell, D B
2008-10-31
The FY08 phase of this project investigated the merits of video fusion as a method for mitigating the false alarms encountered by vehicle borne detection systems in an effort to realize performance gains associated with wavelet denoising. The fusion strategy exploited the significant correlations which exist between data obtained from radiation detectors and video systems with coincident fields of view. The additional information provided by optical systems can greatly increase the capabilities of these detection systems by reducing the burden of false alarms and through the generation of actionable information. The investigation into the use of wavelet analysis techniques as a means of filtering the gross-counts signal obtained from moving radiation detectors showed promise for vehicle borne systems. However, the applicability of these techniques to man-portable systems is limited due to minimal gains in performance over the rapid feedback available to system operators under walking conditions. Furthermore, the fusion of video holds significant promise for systems operating from vehicles or systems organized into stationary arrays; however, the added complexity and hardware required by this technique renders it infeasible for man-portable systems.
Minimum risk wavelet shrinkage operator for Poisson image denoising.
Cheng, Wu; Hirakawa, Keigo
2015-05-01
The pixel values of images taken by an image sensor are said to be corrupted by Poisson noise. To date, multiscale Poisson image denoising techniques have processed Haar frame and wavelet coefficients--the modeling of coefficients is enabled by the Skellam distribution analysis. We extend these results by solving for shrinkage operators for Skellam that minimizes the risk functional in the multiscale Poisson image denoising setting. The minimum risk shrinkage operator of this kind effectively produces denoised wavelet coefficients with minimum attainable L2 error.
Szu, H.; Hsu, C.
1996-12-31
Human sensors systems (HSS) may be approximately described as an adaptive or self-learning version of the Wavelet Transforms (WT) that are capable to learn from several input-output associative pairs of suitable transform mother wavelets. Such an Adaptive WT (AWT) is a redundant combination of mother wavelets to either represent or classify inputs.
Image denoising based on wavelets and multifractals for singularity detection.
Zhong, Junmei; Ning, Ruola
2005-10-01
This paper presents a very efficient algorithm for image denoising based on wavelets and multifractals for singularity detection. A challenge of image denoising is how to preserve the edges of an image when reducing noise. By modeling the intensity surface of a noisy image as statistically self-similar multifractal processes and taking advantage of the multiresolution analysis with wavelet transform to exploit the local statistical self-similarity at different scales, the pointwise singularity strength value characterizing the local singularity at each scale was calculated. By thresholding the singularity strength, wavelet coefficients at each scale were classified into two categories: the edge-related and regular wavelet coefficients and the irregular coefficients. The irregular coefficients were denoised using an approximate minimum mean-squared error (MMSE) estimation method, while the edge-related and regular wavelet coefficients were smoothed using the fuzzy weighted mean (FWM) filter aiming at preserving the edges and details when reducing noise. Furthermore, to make the FWM-based filtering more efficient for noise reduction at the lowest decomposition level, the MMSE-based filtering was performed as the first pass of denoising followed by performing the FWM-based filtering. Experimental results demonstrated that this algorithm could achieve both good visual quality and high PSNR for the denoised images.
Zhang, Qiushi; Yang, Xueqian; Yao, Li; Zhao, Xiaojie
2017-03-27
Working memory (WM) refers to the holding and manipulation of information during cognitive tasks. Its underlying neural mechanisms have been explored through both functional magnetic resonance imaging (fMRI) and electroencephalography (EEG). Trial-by-trial coupling of simultaneously collected EEG and fMRI signals has become an important and promising approach to study the spatio-temporal dynamics of such cognitive processes. Previous studies have demonstrated a modulation effect of the WM load on both the BOLD response in certain brain areas and the amplitude of P3. However, much remains to be explored regarding the WM load-dependent relationship between the amplitude of ERP components and cortical activities, and the low signal-to-noise ratio (SNR) of the EEG signal still poses a challenge to performing single-trial analyses. In this paper, we investigated the spatio-temporal activities of P3 during an n-back verbal WM task by introducing an adaptive wavelet denoiser into the extraction of single-trial P3 features and using general linear model (GLM) to integrate simultaneously collected EEG and fMRI data. Our results replicated the modulation effect of the WM load on the P3 amplitude. Additionally, the activation of single-trial P3 amplitudes was detected in multiple brain regions, including the insula, the cuneus, the lingual gyrus (LG), and the middle occipital gyrus (MOG). Moreover, we found significant correlations between P3 features and behavioral performance. These findings suggest that the single-trial integration of simultaneous EEG and fMRI signals may provide new insights into classical cognitive functions.
Wavelet-based denoising using local Laplace prior
NASA Astrophysics Data System (ADS)
Rabbani, Hossein; Vafadust, Mansur; Selesnick, Ivan
2007-09-01
Although wavelet-based image denoising is a powerful tool for image processing applications, relatively few publications have addressed so far wavelet-based video denoising. The main reason is that the standard 3-D data transforms do not provide useful representations with good energy compaction property, for most video data. For example, the multi-dimensional standard separable discrete wavelet transform (M-D DWT) mixes orientations and motions in its subbands, and produces the checkerboard artifacts. So, instead of M-D DWT, usually oriented transforms suchas multi-dimensional complex wavelet transform (M-D DCWT) are proposed for video processing. In this paper we use a Laplace distribution with local variance to model the statistical properties of noise-free wavelet coefficients. This distribution is able to simultaneously model the heavy-tailed and intrascale dependency properties of wavelets. Using this model, simple shrinkage functions are obtained employing maximum a posteriori (MAP) and minimum mean squared error (MMSE) estimators. These shrinkage functions are proposed for video denoising in DCWT domain. The simulation results shows that this simple denoising method has impressive performance visually and quantitatively.
Obtaining single stimulus evoked potentials with wavelet denoising
NASA Astrophysics Data System (ADS)
Quian Quiroga, R.
2000-11-01
We present a method for the analysis of electroencephalograms (EEG). In particular, small signals due to stimulation, so-called evoked potentials (EPs), have to be detected in the background EEG. This is achieved by using a denoising implementation based on the wavelet decomposition. One recording of visual evoked potentials, and recordings of auditory evoked potentials from four subjects corresponding to different age groups are analyzed. We find higher variability in older individuals. Moreover, since the EPs are identified at the single stimulus level (without need of ensemble averaging), this will allow the calculation of better resolved averages. Since the method is parameter free (i.e. it does not need to be adapted to the particular characteristics of each recording), implementations in clinical settings are imaginable.
Adaptive Image Denoising by Mixture Adaptation
NASA Astrophysics Data System (ADS)
Luo, Enming; Chan, Stanley H.; Nguyen, Truong Q.
2016-10-01
We propose an adaptive learning procedure to learn patch-based image priors for image denoising. The new algorithm, called the Expectation-Maximization (EM) adaptation, takes a generic prior learned from a generic external database and adapts it to the noisy image to generate a specific prior. Different from existing methods that combine internal and external statistics in ad-hoc ways, the proposed algorithm is rigorously derived from a Bayesian hyper-prior perspective. There are two contributions of this paper: First, we provide full derivation of the EM adaptation algorithm and demonstrate methods to improve the computational complexity. Second, in the absence of the latent clean image, we show how EM adaptation can be modified based on pre-filtering. Experimental results show that the proposed adaptation algorithm yields consistently better denoising results than the one without adaptation and is superior to several state-of-the-art algorithms.
Adaptive Image Denoising by Mixture Adaptation.
Luo, Enming; Chan, Stanley H; Nguyen, Truong Q
2016-10-01
We propose an adaptive learning procedure to learn patch-based image priors for image denoising. The new algorithm, called the expectation-maximization (EM) adaptation, takes a generic prior learned from a generic external database and adapts it to the noisy image to generate a specific prior. Different from existing methods that combine internal and external statistics in ad hoc ways, the proposed algorithm is rigorously derived from a Bayesian hyper-prior perspective. There are two contributions of this paper. First, we provide full derivation of the EM adaptation algorithm and demonstrate methods to improve the computational complexity. Second, in the absence of the latent clean image, we show how EM adaptation can be modified based on pre-filtering. The experimental results show that the proposed adaptation algorithm yields consistently better denoising results than the one without adaptation and is superior to several state-of-the-art algorithms.
The Differential Pressure Signal De-noised by Domain Transform Combined with Wavelet Threshold
NASA Astrophysics Data System (ADS)
Zhang, Yuhao; Wang, Haihui; Li, Chao
2017-01-01
In the process of estimating the thrust of an aircraft engine, there is a big problem that the differential pressure signal has large fluctuation. To deal with this problem, we develop an effective and robust adaptive de-noising algorithm based on domain transform combined with wavelet transform (D-WT). First, we do the domain transform for the signal, then sample the transformed signal, and finally the wavelet threshold transform is performed for the signal. Compared with the traditional wavelet transforms, the D-WT method filters the noise effectively and keeps more details.
Impedance cardiography signal denoising using discrete wavelet transform.
Chabchoub, Souhir; Mansouri, Sofienne; Salah, Ridha Ben
2016-09-01
Impedance cardiography (ICG) is a non-invasive technique for diagnosing cardiovascular diseases. In the acquisition procedure, the ICG signal is often affected by several kinds of noise which distort the determination of the hemodynamic parameters. Therefore, doctors cannot recognize ICG waveform correctly and the diagnosis of cardiovascular diseases became inaccurate. The aim of this work is to choose the most suitable method for denoising the ICG signal. Indeed, different wavelet families are used to denoise the ICG signal. The Haar, Daubechies (db2, db4, db6, and db8), Symlet (sym2, sym4, sym6, sym8) and Coiflet (coif2, coif3, coif4, coif5) wavelet families are tested and evaluated in order to select the most suitable denoising method. The wavelet family with best performance is compared with two denoising methods: one based on Savitzky-Golay filtering and the other based on median filtering. Each method is evaluated by means of the signal to noise ratio (SNR), the root mean square error (RMSE) and the percent difference root mean square (PRD). The results show that the Daubechies wavelet family (db8) has superior performance on noise reduction in comparison to other methods.
Multitaper Spectral Analysis and Wavelet Denoising Applied to Helioseismic Data
NASA Technical Reports Server (NTRS)
Komm, R. W.; Gu, Y.; Hill, F.; Stark, P. B.; Fodor, I. K.
1999-01-01
Estimates of solar normal mode frequencies from helioseismic observations can be improved by using Multitaper Spectral Analysis (MTSA) to estimate spectra from the time series, then using wavelet denoising of the log spectra. MTSA leads to a power spectrum estimate with reduced variance and better leakage properties than the conventional periodogram. Under the assumption of stationarity and mild regularity conditions, the log multitaper spectrum has a statistical distribution that is approximately Gaussian, so wavelet denoising is asymptotically an optimal method to reduce the noise in the estimated spectra. We find that a single m-upsilon spectrum benefits greatly from MTSA followed by wavelet denoising, and that wavelet denoising by itself can be used to improve m-averaged spectra. We compare estimates using two different 5-taper estimates (Stepian and sine tapers) and the periodogram estimate, for GONG time series at selected angular degrees l. We compare those three spectra with and without wavelet-denoising, both visually, and in terms of the mode parameters estimated from the pre-processed spectra using the GONG peak-fitting algorithm. The two multitaper estimates give equivalent results. The number of modes fitted well by the GONG algorithm is 20% to 60% larger (depending on l and the temporal frequency) when applied to the multitaper estimates than when applied to the periodogram. The estimated mode parameters (frequency, amplitude and width) are comparable for the three power spectrum estimates, except for modes with very small mode widths (a few frequency bins), where the multitaper spectra broadened the modest compared with the periodogram. We tested the influence of the number of tapers used and found that narrow modes at low n values are broadened to the extent that they can no longer be fit if the number of tapers is too large. For helioseismic time series of this length and temporal resolution, the optimal number of tapers is less than 10.
Chen, Szi-Wen; Chen, Yuan-Ho
2015-01-01
In this paper, a discrete wavelet transform (DWT) based de-noising with its applications into the noise reduction for medical signal preprocessing is introduced. This work focuses on the hardware realization of a real-time wavelet de-noising procedure. The proposed de-noising circuit mainly consists of three modules: a DWT, a thresholding, and an inverse DWT (IDWT) modular circuits. We also proposed a novel adaptive thresholding scheme and incorporated it into our wavelet de-noising procedure. Performance was then evaluated on both the architectural designs of the software and. In addition, the de-noising circuit was also implemented by downloading the Verilog codes to a field programmable gate array (FPGA) based platform so that its ability in noise reduction may be further validated in actual practice. Simulation experiment results produced by applying a set of simulated noise-contaminated electrocardiogram (ECG) signals into the de-noising circuit showed that the circuit could not only desirably meet the requirement of real-time processing, but also achieve satisfactory performance for noise reduction, while the sharp features of the ECG signals can be well preserved. The proposed de-noising circuit was further synthesized using the Synopsys Design Compiler with an Artisan Taiwan Semiconductor Manufacturing Company (TSMC, Hsinchu, Taiwan) 40 nm standard cell library. The integrated circuit (IC) synthesis simulation results showed that the proposed design can achieve a clock frequency of 200 MHz and the power consumption was only 17.4 mW, when operated at 200 MHz. PMID:26501290
Chen, Szi-Wen; Chen, Yuan-Ho
2015-10-16
In this paper, a discrete wavelet transform (DWT) based de-noising with its applications into the noise reduction for medical signal preprocessing is introduced. This work focuses on the hardware realization of a real-time wavelet de-noising procedure. The proposed de-noising circuit mainly consists of three modules: a DWT, a thresholding, and an inverse DWT (IDWT) modular circuits. We also proposed a novel adaptive thresholding scheme and incorporated it into our wavelet de-noising procedure. Performance was then evaluated on both the architectural designs of the software and. In addition, the de-noising circuit was also implemented by downloading the Verilog codes to a field programmable gate array (FPGA) based platform so that its ability in noise reduction may be further validated in actual practice. Simulation experiment results produced by applying a set of simulated noise-contaminated electrocardiogram (ECG) signals into the de-noising circuit showed that the circuit could not only desirably meet the requirement of real-time processing, but also achieve satisfactory performance for noise reduction, while the sharp features of the ECG signals can be well preserved. The proposed de-noising circuit was further synthesized using the Synopsys Design Compiler with an Artisan Taiwan Semiconductor Manufacturing Company (TSMC, Hsinchu, Taiwan) 40 nm standard cell library. The integrated circuit (IC) synthesis simulation results showed that the proposed design can achieve a clock frequency of 200 MHz and the power consumption was only 17.4 mW, when operated at 200 MHz.
Denoising and robust nonlinear wavelet analysis
NASA Astrophysics Data System (ADS)
Bruce, Andrew G.; Donoho, David L.; Gao, Hong-Ye; Martin, R. D.
1994-03-01
In a series of papers, Donoho and Johnstone develop a powerful theory based on wavelets for extracting non-smooth signals from noisy data. Several nonlinear smoothing algorithms are presented which provide high performance for removing Gaussian noise from a wide range of spatially inhomogeneous signals. However, like other methods based on the linear wavelet transform, these algorithms are very sensitive to certain types of non-Gaussian noise, such as outliers. In this paper, we develop outlier resistant wavelet transforms. In these transforms, outliers and outlier patches are localized to just a few scales. By using the outlier resistant wavelet transform, we improve upon the Donoho and Johnstone nonlinear signal extraction methods. The outlier resistant wavelet algorithms are included with the 'S+WAVELETS' object-oriented toolkit for wavelet analysis.
Region-based image denoising through wavelet and fast discrete curvelet transform
NASA Astrophysics Data System (ADS)
Gu, Yanfeng; Guo, Yan; Liu, Xing; Zhang, Ye
2008-10-01
Image denoising always is one of important research topics in the image processing field. In this paper, fast discrete curvelet transform (FDCT) and undecimated wavelet transform (UDWT) are proposed for image denoising. A noisy image is first denoised by FDCT and UDWT separately. The whole image space is then divided into edge region and non-edge regions. After that, wavelet transform is performed on the images denoised by FDCT and UDWT respectively. Finally, the resultant image is fused through using both of edge region wavelet cofficients of the image denoised by FDCT and non-edge region wavelet cofficients of the image denoised by UDWT. The proposed method is validated through numerical experiments conducted on standard test images. The experimental results show that the proposed algorithm outperforms wavelet-based and curvelet-based image denoising methods and preserve linear features well.
Study on Underwater Image Denoising Algorithm Based on Wavelet Transform
NASA Astrophysics Data System (ADS)
Jian, Sun; Wen, Wang
2017-02-01
This paper analyzes the application of MATLAB in underwater image processing, the transmission characteristics of the underwater laser light signal and the kinds of underwater noise has been described, the common noise suppression algorithm: Wiener filter, median filter, average filter algorithm is brought out. Then the advantages and disadvantages of each algorithm in image sharpness and edge protection areas have been compared. A hybrid filter algorithm based on wavelet transform has been proposed which can be used for Color Image Denoising. At last the PSNR and NMSE of each algorithm has been given out, which compares the ability to de-noising
NASA Astrophysics Data System (ADS)
Ji, Yanju; Li, Dongsheng; Yuan, Guiyang; Lin, Jun; Du, Shangyu; Xie, Lijun; Wang, Yuan
2016-06-01
A denoising method based on wavelet analysis is presented for the removal of noise (background noise and random spike) from time domain electromagnetic (TEM) data. This method includes two signal processing technologies: wavelet threshold method and stationary wavelet transform. First, wavelet threshold method is used for the removal of background noise from TEM data. Then, the data are divided into a series of details and approximations by using stationary wavelet transform. The random spike in details is identified by zero reference data and adaptive energy detector. Next, the corresponding details are processed to suppress the random spike. The denoised TEM data are reconstructed via inverse stationary wavelet transform using the processed details at each level and the approximations at the highest level. The proposed method has been verified using a synthetic TEM data, the signal-to-noise ratio of synthetic TEM data is increased from 10.97 dB to 24.37 dB at last. This method is also applied to the noise suppression of the field data which were collected at Hengsha island, China. The section image results shown that the noise is suppressed effectively and the resolution of the deep anomaly is obviously improved.
Examining Alternatives to Wavelet Denoising for Astronomical Source Finding
NASA Astrophysics Data System (ADS)
Jurek, R.; Brown, S.
2012-08-01
The Square Kilometre Array and its pathfinders ASKAP and MeerKAT will produce prodigious amounts of data that necessitate automated source finding. The performance of automated source finders can be improved by pre-processing a dataset. In preparation for the WALLABY and DINGO surveys, we have used a test HI datacube constructed from actual Westerbork Telescope noise and WHISP HI galaxies to test the real world improvement of linear smoothing, the Duchamp source finder's wavelet denoising, iterative median smoothing and mathematical morphology subtraction, on intensity threshold source finding of spectral line datasets. To compare these pre-processing methods we have generated completeness-reliability performance curves for each method and a range of input parameters. We find that iterative median smoothing produces the best source finding results for ASKAP HI spectral line observations, but wavelet denoising is a safer pre-processing technique. In this paper we also present our implementations of iterative median smoothing and mathematical morphology subtraction.
Morphology of the Galaxy Distribution from Wavelet Denoising
NASA Astrophysics Data System (ADS)
Martínez, Vicent J.; Starck, Jean-Luc; Saar, Enn; Donoho, David L.; Reynolds, Simon C.; de la Cruz, Pablo; Paredes, Silvestre
2005-11-01
We have developed a method based on wavelets to obtain the true underlying smooth density from a point distribution. The goal has been to reconstruct the density field in an optimal way, ensuring that the morphology of the reconstructed field reflects the true underlying morphology of the point field, which, as the galaxy distribution, has a genuinely multiscale structure, with near-singular behavior on sheets, filaments, and hot spots. If the discrete distributions are smoothed using Gaussian filters, the morphological properties tend to be closer to those expected for a Gaussian field. The use of wavelet denoising provides us with a unique and more accurate morphological description.
Optimization of dynamic measurement of receptor kinetics by wavelet denoising.
Alpert, Nathaniel M; Reilhac, Anthonin; Chio, Tat C; Selesnick, Ivan
2006-04-01
The most important technical limitation affecting dynamic measurements with PET is low signal-to-noise ratio (SNR). Several reports have suggested that wavelet processing of receptor kinetic data in the human brain can improve the SNR of parametric images of binding potential (BP). However, it is difficult to fully assess these reports because objective standards have not been developed to measure the tradeoff between accuracy (e.g. degradation of resolution) and precision. This paper employs a realistic simulation method that includes all major elements affecting image formation. The simulation was used to derive an ensemble of dynamic PET ligand (11C-raclopride) experiments that was subjected to wavelet processing. A method for optimizing wavelet denoising is presented and used to analyze the simulated experiments. Using optimized wavelet denoising, SNR of the four-dimensional PET data increased by about a factor of two and SNR of three-dimensional BP maps increased by about a factor of 1.5. Analysis of the difference between the processed and unprocessed means for the 4D concentration data showed that more than 80% of voxels in the ensemble mean of the wavelet processed data deviated by less than 3%. These results show that a 1.5x increase in SNR can be achieved with little degradation of resolution. This corresponds to injecting about twice the radioactivity, a maneuver that is not possible in human studies without saturating the PET camera and/or exposing the subject to more than permitted radioactivity.
Electrocardiogram signal denoising based on a new improved wavelet thresholding
NASA Astrophysics Data System (ADS)
Han, Guoqiang; Xu, Zhijun
2016-08-01
Good quality electrocardiogram (ECG) is utilized by physicians for the interpretation and identification of physiological and pathological phenomena. In general, ECG signals may mix various noises such as baseline wander, power line interference, and electromagnetic interference in gathering and recording process. As ECG signals are non-stationary physiological signals, wavelet transform is investigated to be an effective tool to discard noises from corrupted signals. A new compromising threshold function called sigmoid function-based thresholding scheme is adopted in processing ECG signals. Compared with other methods such as hard/soft thresholding or other existing thresholding functions, the new algorithm has many advantages in the noise reduction of ECG signals. It perfectly overcomes the discontinuity at ±T of hard thresholding and reduces the fixed deviation of soft thresholding. The improved wavelet thresholding denoising can be proved to be more efficient than existing algorithms in ECG signal denoising. The signal to noise ratio, mean square error, and percent root mean square difference are calculated to verify the denoising performance as quantitative tools. The experimental results reveal that the waves including P, Q, R, and S waves of ECG signals after denoising coincide with the original ECG signals by employing the new proposed method.
NASA Astrophysics Data System (ADS)
Ren, Zhong; Liu, Guodong; Xiong, Zhihua
2016-10-01
The photoacoustic signals denoising of glucose is one of most important steps in the quality identification of the fruit because the real-time photoacoustic singals of glucose are easily interfered by all kinds of noises. To remove the noises and some useless information, an improved wavelet threshld function were proposed. Compared with the traditional wavelet hard and soft threshold functions, the improved wavelet threshold function can overcome the pseudo-oscillation effect of the denoised photoacoustic signals due to the continuity of the improved wavelet threshold function, and the error between the denoised signals and the original signals can be decreased. To validate the feasibility of the improved wavelet threshold function denoising, the denoising simulation experiments based on MATLAB programmimg were performed. In the simulation experiments, the standard test signal was used, and three different denoising methods were used and compared with the improved wavelet threshold function. The signal-to-noise ratio (SNR) and the root-mean-square error (RMSE) values were used to evaluate the performance of the improved wavelet threshold function denoising. The experimental results demonstrate that the SNR value of the improved wavelet threshold function is largest and the RMSE value is lest, which fully verifies that the improved wavelet threshold function denoising is feasible. Finally, the improved wavelet threshold function denoising was used to remove the noises of the photoacoustic signals of the glucose solutions. The denoising effect is also very good. Therefore, the improved wavelet threshold function denoising proposed by this paper, has a potential value in the field of denoising for the photoacoustic singals.
Energy-Based Wavelet De-Noising of Hydrologic Time Series
Sang, Yan-Fang; Liu, Changming; Wang, Zhonggen; Wen, Jun; Shang, Lunyu
2014-01-01
De-noising is a substantial issue in hydrologic time series analysis, but it is a difficult task due to the defect of methods. In this paper an energy-based wavelet de-noising method was proposed. It is to remove noise by comparing energy distribution of series with the background energy distribution, which is established from Monte-Carlo test. Differing from wavelet threshold de-noising (WTD) method with the basis of wavelet coefficient thresholding, the proposed method is based on energy distribution of series. It can distinguish noise from deterministic components in series, and uncertainty of de-noising result can be quantitatively estimated using proper confidence interval, but WTD method cannot do this. Analysis of both synthetic and observed series verified the comparable power of the proposed method and WTD, but de-noising process by the former is more easily operable. The results also indicate the influences of three key factors (wavelet choice, decomposition level choice and noise content) on wavelet de-noising. Wavelet should be carefully chosen when using the proposed method. The suitable decomposition level for wavelet de-noising should correspond to series' deterministic sub-signal which has the smallest temporal scale. If too much noise is included in a series, accurate de-noising result cannot be obtained by the proposed method or WTD, but the series would show pure random but not autocorrelation characters, so de-noising is no longer needed. PMID:25360533
Energy-based wavelet de-noising of hydrologic time series.
Sang, Yan-Fang; Liu, Changming; Wang, Zhonggen; Wen, Jun; Shang, Lunyu
2014-01-01
De-noising is a substantial issue in hydrologic time series analysis, but it is a difficult task due to the defect of methods. In this paper an energy-based wavelet de-noising method was proposed. It is to remove noise by comparing energy distribution of series with the background energy distribution, which is established from Monte-Carlo test. Differing from wavelet threshold de-noising (WTD) method with the basis of wavelet coefficient thresholding, the proposed method is based on energy distribution of series. It can distinguish noise from deterministic components in series, and uncertainty of de-noising result can be quantitatively estimated using proper confidence interval, but WTD method cannot do this. Analysis of both synthetic and observed series verified the comparable power of the proposed method and WTD, but de-noising process by the former is more easily operable. The results also indicate the influences of three key factors (wavelet choice, decomposition level choice and noise content) on wavelet de-noising. Wavelet should be carefully chosen when using the proposed method. The suitable decomposition level for wavelet de-noising should correspond to series' deterministic sub-signal which has the smallest temporal scale. If too much noise is included in a series, accurate de-noising result cannot be obtained by the proposed method or WTD, but the series would show pure random but not autocorrelation characters, so de-noising is no longer needed.
Denoising portal images by means of wavelet techniques
NASA Astrophysics Data System (ADS)
Gonzalez Lopez, Antonio Francisco
Portal images are used in radiotherapy for the verification of patient positioning. The distinguishing feature of this image type lies in its formation process: the same beam used for patient treatment is used for image formation. The high energy of the photons used in radiotherapy strongly limits the quality of portal images: Low contrast between tissues, low spatial resolution and low signal to noise ratio. This Thesis studies the enhancement of these images, in particular denoising of portal images. The statistical properties of portal images and noise are studied: power spectra, statistical dependencies between image and noise and marginal, joint and conditional distributions in the wavelet domain. Later, various denoising methods are applied to noisy portal images. Methods operating in the wavelet domain are the basis of this Thesis. In addition, the Wiener filter and the non local means filter (NLM), operating in the image domain, are used as a reference. Other topics studied in this Thesis are spatial resolution, wavelet processing and image processing in dosimetry in radiotherapy. In this regard, the spatial resolution of portal imaging systems is studied; a new method for determining the spatial resolution of the imaging equipments in digital radiology is presented; the calculation of the power spectrum in the wavelet domain is studied; reducing uncertainty in film dosimetry is investigated; a method for the dosimetry of small radiation fields with radiochromic film is presented; the optimal signal resolution is determined, as a function of the noise level and the quantization step, in the digitization process of films and the useful optical density range is set, as a function of the required uncertainty level, for a densitometric system. Marginal distributions of portal images are similar to those of natural images. This also applies to the statistical relationships between wavelet coefficients, intra-band and inter-band. These facts result in a better
Wavelet transform-based methods for denoising of Coulter counter signals
NASA Astrophysics Data System (ADS)
Jagtiani, Ashish V.; Sawant, Rupesh; Carletta, Joan; Zhe, Jiang
2008-06-01
A process based on discrete wavelet transforms is developed for denoising and baseline correction of measured signals from Coulter counters. Given signals from a particular Coulter counting experiment, which detect passage of particles through a fluid-filled microchannel, the process uses a cross-validation procedure to pick appropriate parameters for signal denoising; these parameters include the choice of the particular wavelet, the number of levels of decomposition, the threshold value and the threshold strategy. The process is demonstrated on simulated and experimental single channel data obtained from a particular multi-channel Coulter counter processing. For these example experimental signals from 20 µm polymethacrylate and Cottonwood/Eastern Deltoid pollen particles and the simulated signals, denoising is aimed at removing Gaussian white noise, 60 Hz power line interference and low frequency baseline drift. The process can be easily adapted for other Coulter counters and other sources of noise. Overall, wavelets are presented as a tool to aid in accurate detection of particles in Coulter counters.
ECG signal denoising via empirical wavelet transform.
Singh, Omkar; Sunkaria, Ramesh Kumar
2016-12-29
This paper presents new methods for baseline wander correction and powerline interference reduction in electrocardiogram (ECG) signals using empirical wavelet transform (EWT). During data acquisition of ECG signal, various noise sources such as powerline interference, baseline wander and muscle artifacts contaminate the information bearing ECG signal. For better analysis and interpretation, the ECG signal must be free of noise. In the present work, a new approach is used to filter baseline wander and power line interference from the ECG signal. The technique utilized is the empirical wavelet transform, which is a new method used to compute the building modes of a given signal. Its performance as a filter is compared to the standard linear filters and empirical mode decomposition.The results show that EWT delivers a better performance.
Improved deadzone modeling for bivariate wavelet shrinkage-based image denoising
NASA Astrophysics Data System (ADS)
DelMarco, Stephen
2016-05-01
Modern image processing performed on-board low Size, Weight, and Power (SWaP) platforms, must provide high- performance while simultaneously reducing memory footprint, power consumption, and computational complexity. Image preprocessing, along with downstream image exploitation algorithms such as object detection and recognition, and georegistration, place a heavy burden on power and processing resources. Image preprocessing often includes image denoising to improve data quality for downstream exploitation algorithms. High-performance image denoising is typically performed in the wavelet domain, where noise generally spreads and the wavelet transform compactly captures high information-bearing image characteristics. In this paper, we improve modeling fidelity of a previously-developed, computationally-efficient wavelet-based denoising algorithm. The modeling improvements enhance denoising performance without significantly increasing computational cost, thus making the approach suitable for low-SWAP platforms. Specifically, this paper presents modeling improvements to the Sendur-Selesnick model (SSM) which implements a bivariate wavelet shrinkage denoising algorithm that exploits interscale dependency between wavelet coefficients. We formulate optimization problems for parameters controlling deadzone size which leads to improved denoising performance. Two formulations are provided; one with a simple, closed form solution which we use for numerical result generation, and the second as an integral equation formulation involving elliptic integrals. We generate image denoising performance results over different image sets drawn from public domain imagery, and investigate the effect of wavelet filter tap length on denoising performance. We demonstrate denoising performance improvement when using the enhanced modeling over performance obtained with the baseline SSM model.
Denoising method of heart sound signals based on self-construct heart sound wavelet
NASA Astrophysics Data System (ADS)
Cheng, Xiefeng; Zhang, Zheng
2014-08-01
In the field of heart sound signal denoising, the wavelet transform has become one of the most effective measures. The selective wavelet basis is based on the well-known orthogonal db series or biorthogonal bior series wavelet. In this paper we present a self-construct wavelet basis which is suitable for the heart sound denoising and analyze its constructor method and features in detail according to the characteristics of heart sound and evaluation criterion of signal denoising. The experimental results show that the heart sound wavelet can effectively filter out the noise of the heart sound signals, reserve the main characteristics of the signal. Compared with the traditional wavelets, it has a higher signal-to-noise ratio, lower mean square error and better denoising effect.
Image denoising using principal component analysis in the wavelet domain
NASA Astrophysics Data System (ADS)
Bacchelli, Silvia; Papi, Serena
2006-05-01
In this work we describe a method for removing Gaussian noise from digital images, based on the combination of the wavelet packet transform and the principal component analysis. In particular, since the aim of denoising is to retain the energy of the signal while discarding the energy of the noise, our basic idea is to construct powerful tailored filters by applying the Karhunen-Loeve transform in the wavelet packet domain, thus obtaining a compaction of the signal energy into a few principal components, while the noise is spread over all the transformed coefficients. This allows us to act with a suitable shrinkage function on these new coefficients, removing the noise without blurring the edges and the important characteristics of the images. The results of a large numerical experimentation encourage us to keep going in this direction with our studies.
Wavelet denoising of multiframe optical coherence tomography data
Mayer, Markus A.; Borsdorf, Anja; Wagner, Martin; Hornegger, Joachim; Mardin, Christian Y.; Tornow, Ralf P.
2012-01-01
We introduce a novel speckle noise reduction algorithm for OCT images. Contrary to present approaches, the algorithm does not rely on simple averaging of multiple image frames or denoising on the final averaged image. Instead it uses wavelet decompositions of the single frames for a local noise and structure estimation. Based on this analysis, the wavelet detail coefficients are weighted, averaged and reconstructed. At a signal-to-noise gain at about 100% we observe only a minor sharpness decrease, as measured by a full-width-half-maximum reduction of 10.5%. While a similar signal-to-noise gain would require averaging of 29 frames, we achieve this result using only 8 frames as input to the algorithm. A possible application of the proposed algorithm is preprocessing in retinal structure segmentation algorithms, to allow a better differentiation between real tissue information and unwanted speckle noise. PMID:22435103
Chitchian, Shahab; Mayer, Markus A; Boretsky, Adam R; van Kuijk, Frederik J; Motamedi, Massoud
2012-11-01
ABSTRACT. Image enhancement of retinal structures, in optical coherence tomography (OCT) scans through denoising, has the potential to aid in the diagnosis of several eye diseases. In this paper, a locally adaptive denoising algorithm using double-density dual-tree complex wavelet transform, a combination of the double-density wavelet transform and the dual-tree complex wavelet transform, is applied to reduce speckle noise in OCT images of the retina. The algorithm overcomes the limitations of commonly used multiple frame averaging technique, namely the limited number of frames that can be recorded due to eye movements, by providing a comparable image quality in significantly less acquisition time equal to an order of magnitude less time compared to the averaging method. In addition, improvements of image quality metrics and 5 dB increase in the signal-to-noise ratio are attained.
Mayer, Markus A.; Boretsky, Adam R.; van Kuijk, Frederik J.; Motamedi, Massoud
2012-01-01
Abstract. Image enhancement of retinal structures, in optical coherence tomography (OCT) scans through denoising, has the potential to aid in the diagnosis of several eye diseases. In this paper, a locally adaptive denoising algorithm using double-density dual-tree complex wavelet transform, a combination of the double-density wavelet transform and the dual-tree complex wavelet transform, is applied to reduce speckle noise in OCT images of the retina. The algorithm overcomes the limitations of commonly used multiple frame averaging technique, namely the limited number of frames that can be recorded due to eye movements, by providing a comparable image quality in significantly less acquisition time equal to an order of magnitude less time compared to the averaging method. In addition, improvements of image quality metrics and 5 dB increase in the signal-to-noise ratio are attained. PMID:23117804
Denoising of X-ray pulsar observed profile in the undecimated wavelet domain
NASA Astrophysics Data System (ADS)
Xue, Meng-fan; Li, Xiao-ping; Fu, Ling-zhong; Liu, Xiu-ping; Sun, Hai-feng; Shen, Li-rong
2016-01-01
The low intensity of the X-ray pulsar signal and the strong X-ray background radiation lead to low signal-to-noise ratio (SNR) of the X-ray pulsar observed profile obtained through epoch folding, especially when the observation time is not long enough. This signifies the necessity of denoising of the observed profile. In this paper, the statistical characteristics of the X-ray pulsar signal are studied, and a signal-dependent noise model is established for the observed profile. Based on this, a profile noise reduction method by performing a local linear minimum mean square error filtering in the un-decimated wavelet domain is developed. The detail wavelet coefficients are rescaled by multiplying their amplitudes by a locally adaptive factor, which is the local variance ratio of the noiseless coefficients to the noisy ones. All the nonstationary statistics needed in the algorithm are calculated from the observed profile, without a priori information. The results of experim! ents, carried out on simulated data obtained by the ground-based simulation system and real data obtained by Rossi X-Ray Timing Explorer satellite, indicate that the proposed method is excellent in both noise suppression and preservation of peak sharpness, and it also clearly outperforms four widely accepted and used wavelet denoising methods, in terms of SNR, Pearson correlation coefficient and root mean square error.
Image-Specific Prior Adaptation for Denoising.
Lu, Xin; Lin, Zhe; Jin, Hailin; Yang, Jianchao; Wang, James Z
2015-12-01
Image priors are essential to many image restoration applications, including denoising, deblurring, and inpainting. Existing methods use either priors from the given image (internal) or priors from a separate collection of images (external). We find through statistical analysis that unifying the internal and external patch priors may yield a better patch prior. We propose a novel prior learning algorithm that combines the strength of both internal and external priors. In particular, we first learn a generic Gaussian mixture model from a collection of training images and then adapt the model to the given image by simultaneously adding additional components and refining the component parameters. We apply this image-specific prior to image denoising. The experimental results show that our approach yields better or competitive denoising results in terms of both the peak signal-to-noise ratio and structural similarity.
NASA Astrophysics Data System (ADS)
Ren, Zhong; Liu, Guodong
2016-11-01
To improve the denoising effect of the glucose photoacoustic signals, a modified wavelet thresholding combined shift-invariance algorithm was used in this paper. In addition, the shift-invariance method was added into the improved algorithm. To verify the feasibility of modified wavelet shift-invariance threshold denoising algorithm, the simulation experiments were performed. Results show that the denoising effect of modified wavelet shift-invariance thresholding algorithm is better than that of others because its signal-to-noise ratio is largest and the root-mean-square error is lest. Finally, the modified wavelet shift-invariance threshold denoising was used to remove the noises of the photoacoustic signals of glucose aqueous solutions.
Dual tree complex wavelet transform based denoising of optical microscopy images.
Bal, Ufuk
2012-12-01
Photon shot noise is the main noise source of optical microscopy images and can be modeled by a Poisson process. Several discrete wavelet transform based methods have been proposed in the literature for denoising images corrupted by Poisson noise. However, the discrete wavelet transform (DWT) has disadvantages such as shift variance, aliasing, and lack of directional selectivity. To overcome these problems, a dual tree complex wavelet transform is used in our proposed denoising algorithm. Our denoising algorithm is based on the assumption that for the Poisson noise case threshold values for wavelet coefficients can be estimated from the approximation coefficients. Our proposed method was compared with one of the state of the art denoising algorithms. Better results were obtained by using the proposed algorithm in terms of image quality metrics. Furthermore, the contrast enhancement effect of the proposed method on collagen fıber images is examined. Our method allows fast and efficient enhancement of images obtained under low light intensity conditions.
Cannistraci, Carlo Vittorio; Abbas, Ahmed; Gao, Xin
2015-01-26
Denoising multidimensional NMR-spectra is a fundamental step in NMR protein structure determination. The state-of-the-art method uses wavelet-denoising, which may suffer when applied to non-stationary signals affected by Gaussian-white-noise mixed with strong impulsive artifacts, like those in multi-dimensional NMR-spectra. Regrettably, Wavelet's performance depends on a combinatorial search of wavelet shapes and parameters; and multi-dimensional extension of wavelet-denoising is highly non-trivial, which hampers its application to multidimensional NMR-spectra. Here, we endorse a diverse philosophy of denoising NMR-spectra: less is more! We consider spatial filters that have only one parameter to tune: the window-size. We propose, for the first time, the 3D extension of the median-modified-Wiener-filter (MMWF), an adaptive variant of the median-filter, and also its novel variation named MMWF*. We test the proposed filters and the Wiener-filter, an adaptive variant of the mean-filter, on a benchmark set that contains 16 two-dimensional and three-dimensional NMR-spectra extracted from eight proteins. Our results demonstrate that the adaptive spatial filters significantly outperform their non-adaptive versions. The performance of the new MMWF* on 2D/3D-spectra is even better than wavelet-denoising. Noticeably, MMWF* produces stable high performance almost invariant for diverse window-size settings: this signifies a consistent advantage in the implementation of automatic pipelines for protein NMR-spectra analysis.
Cannistraci, Carlo Vittorio; Abbas, Ahmed; Gao, Xin
2015-01-01
Denoising multidimensional NMR-spectra is a fundamental step in NMR protein structure determination. The state-of-the-art method uses wavelet-denoising, which may suffer when applied to non-stationary signals affected by Gaussian-white-noise mixed with strong impulsive artifacts, like those in multi-dimensional NMR-spectra. Regrettably, Wavelet's performance depends on a combinatorial search of wavelet shapes and parameters; and multi-dimensional extension of wavelet-denoising is highly non-trivial, which hampers its application to multidimensional NMR-spectra. Here, we endorse a diverse philosophy of denoising NMR-spectra: less is more! We consider spatial filters that have only one parameter to tune: the window-size. We propose, for the first time, the 3D extension of the median-modified-Wiener-filter (MMWF), an adaptive variant of the median-filter, and also its novel variation named MMWF*. We test the proposed filters and the Wiener-filter, an adaptive variant of the mean-filter, on a benchmark set that contains 16 two-dimensional and three-dimensional NMR-spectra extracted from eight proteins. Our results demonstrate that the adaptive spatial filters significantly outperform their non-adaptive versions. The performance of the new MMWF* on 2D/3D-spectra is even better than wavelet-denoising. Noticeably, MMWF* produces stable high performance almost invariant for diverse window-size settings: this signifies a consistent advantage in the implementation of automatic pipelines for protein NMR-spectra analysis. PMID:25619991
Application of the dual-tree complex wavelet transform in biomedical signal denoising.
Wang, Fang; Ji, Zhong
2014-01-01
In biomedical signal processing, Gibbs oscillation and severe frequency aliasing may occur when using the traditional discrete wavelet transform (DWT). Herein, a new denoising algorithm based on the dual-tree complex wavelet transform (DTCWT) is presented. Electrocardiogram (ECG) signals and heart sound signals are denoised based on the DTCWT. The results prove that the DTCWT is efficient. The signal-to-noise ratio (SNR) and the mean square error (MSE) are used to compare the denoising effect. Results of the paired samples t-test show that the new method can remove noise more thoroughly and better retain the boundary and texture of the signal.
De-noising of digital image correlation based on stationary wavelet transform
NASA Astrophysics Data System (ADS)
Guo, Xiang; Li, Yulong; Suo, Tao; Liang, Jin
2017-03-01
In this paper, a stationary wavelet transform (SWT) based method is proposed to de-noise the digital image with the light noise, and the SWT de-noise algorithm is presented after the analyzing of the light noise. By using the de-noise algorithm, the method was demonstrated to be capable of providing accurate DIC measurements in the light noise environment. The verification, comparative and realistic experiments were conducted using this method. The result indicate that the de-noise method can be applied to the full-field strain measurement under the light interference with a high accuracy and stability.
Biomedical image and signal de-noising using dual tree complex wavelet transform
NASA Astrophysics Data System (ADS)
Rizi, F. Yousefi; Noubari, H. Ahmadi; Setarehdan, S. K.
2011-10-01
Dual tree complex wavelet transform(DTCWT) is a form of discrete wavelet transform, which generates complex coefficients by using a dual tree of wavelet filters to obtain their real and imaginary parts. The purposes of de-noising are reducing noise level and improving signal to noise ratio (SNR) without distorting the signal or image. This paper proposes a method for removing white Gaussian noise from ECG signals and biomedical images. The discrete wavelet transform (DWT) is very valuable in a large scope of de-noising problems. However, it has limitations such as oscillations of the coefficients at a singularity, lack of directional selectivity in higher dimensions, aliasing and consequent shift variance. The complex wavelet transform CWT strategy that we focus on in this paper is Kingsbury's and Selesnick's dual tree CWT (DTCWT) which outperforms the critically decimated DWT in a range of applications, such as de-noising. Each complex wavelet is oriented along one of six possible directions, and the magnitude of each complex wavelet has a smooth bell-shape. In the final part of this paper, we present biomedical image and signal de-noising by the means of thresholding magnitude of the wavelet coefficients.
An NMR log echo data de-noising method based on the wavelet packet threshold algorithm
NASA Astrophysics Data System (ADS)
Meng, Xiangning; Xie, Ranhong; Li, Changxi; Hu, Falong; Li, Chaoliu; Zhou, Cancan
2015-12-01
To improve the de-noising effects of low signal-to-noise ratio (SNR) nuclear magnetic resonance (NMR) log echo data, this paper applies the wavelet packet threshold algorithm to the data. The principle of the algorithm is elaborated in detail. By comparing the properties of a series of wavelet packet bases and the relevance between them and the NMR log echo train signal, ‘sym7’ is found to be the optimal wavelet packet basis of the wavelet packet threshold algorithm to de-noise the NMR log echo train signal. A new method is presented to determine the optimal wavelet packet decomposition scale; this is within the scope of its maximum, using the modulus maxima and the Shannon entropy minimum standards to determine the global and local optimal wavelet packet decomposition scales, respectively. The results of applying the method to the simulated and actual NMR log echo data indicate that compared with the wavelet threshold algorithm, the wavelet packet threshold algorithm, which shows higher decomposition accuracy and better de-noising effect, is much more suitable for de-noising low SNR-NMR log echo data.
Wavelet-based fMRI analysis: 3-D denoising, signal separation, and validation metrics.
Khullar, Siddharth; Michael, Andrew; Correa, Nicolle; Adali, Tulay; Baum, Stefi A; Calhoun, Vince D
2011-02-14
We present a novel integrated wavelet-domain based framework (w-ICA) for 3-D denoising functional magnetic resonance imaging (fMRI) data followed by source separation analysis using independent component analysis (ICA) in the wavelet domain. We propose the idea of a 3-D wavelet-based multi-directional denoising scheme where each volume in a 4-D fMRI data set is sub-sampled using the axial, sagittal and coronal geometries to obtain three different slice-by-slice representations of the same data. The filtered intensity value of an arbitrary voxel is computed as an expected value of the denoised wavelet coefficients corresponding to the three viewing geometries for each sub-band. This results in a robust set of denoised wavelet coefficients for each voxel. Given the de-correlated nature of these denoised wavelet coefficients, it is possible to obtain more accurate source estimates using ICA in the wavelet domain. The contributions of this work can be realized as two modules: First, in the analysis module we combine a new 3-D wavelet denoising approach with signal separation properties of ICA in the wavelet domain. This step helps obtain an activation component that corresponds closely to the true underlying signal, which is maximally independent with respect to other components. Second, we propose and describe two novel shape metrics for post-ICA comparisons between activation regions obtained through different frameworks. We verified our method using simulated as well as real fMRI data and compared our results against the conventional scheme (Gaussian smoothing+spatial ICA: s-ICA). The results show significant improvements based on two important features: (1) preservation of shape of the activation region (shape metrics) and (2) receiver operating characteristic curves. It was observed that the proposed framework was able to preserve the actual activation shape in a consistent manner even for very high noise levels in addition to significant reduction in false
A new adaptive algorithm for image denoising based on curvelet transform
NASA Astrophysics Data System (ADS)
Chen, Musheng; Cai, Zhishan
2013-10-01
The purpose of this paper is to study a method of denoising images corrupted with additive white Gaussian noise. In this paper, the application of the time invariant discrete curvelet transform for noise reduction is considered. In curvelet transform, the frame elements are indexed by scale, orientation and location parameters. It is designed to represent edges and the singularities along curved paths more efficiently than the wavelet transform. Therefore, curvelet transform can get better results than wavelet method in image denoising. In general, image denoising imposes a compromise between noise reduction and preserving significant image details. To achieve a good performance in this respect, an efficient and adaptive image denoising method based on curvelet transform is presented in this paper. Firstly, the noisy image is decomposed into many levels to obtain different frequency sub-bands by curvelet transform. Secondly, efficient and adaptive threshold estimation based on generalized Gaussian distribution modeling of sub-band coefficients is used to remove the noisy coefficients. The choice of the threshold estimation is carried out by analyzing the standard deviation and threshold. Ultimately, invert the multi-scale decomposition to reconstruct the denoised image. Here, to prove the performance of the proposed method, the results are compared with other existent algorithms such as hard and soft threshold based on wavelet. The simulation results on several testing images indicate that the proposed method outperforms the other methods in peak signal to noise ratio and keeps better visual in edges information reservation as well. The results also suggest that curvelet transform can achieve a better performance than the wavelet transform in image denoising.
Le Pogam, A; Hanzouli, H; Hatt, M; Cheze Le Rest, C; Visvikis, D
2013-12-01
Denoising of Positron Emission Tomography (PET) images is a challenging task due to the inherent low signal-to-noise ratio (SNR) of the acquired data. A pre-processing denoising step may facilitate and improve the results of further steps such as segmentation, quantification or textural features characterization. Different recent denoising techniques have been introduced and most state-of-the-art methods are based on filtering in the wavelet domain. However, the wavelet transform suffers from some limitations due to its non-optimal processing of edge discontinuities. More recently, a new multi scale geometric approach has been proposed, namely the curvelet transform. It extends the wavelet transform to account for directional properties in the image. In order to address the issue of resolution loss associated with standard denoising, we considered a strategy combining the complementary wavelet and curvelet transforms. We compared different figures of merit (e.g. SNR increase, noise decrease in homogeneous regions, resolution loss, and intensity bias) on simulated and clinical datasets with the proposed combined approach and the wavelet-only and curvelet-only filtering techniques. The three methods led to an increase of the SNR. Regarding the quantitative accuracy however, the wavelet and curvelet only denoising approaches led to larger biases in the intensity and the contrast than the proposed combined algorithm. This approach could become an alternative solution to filters currently used after image reconstruction in clinical systems such as the Gaussian filter.
[Near infrared spectra (NIR) analysis of octane number by wavelet denoising-derivative method].
Tian, Gao-you; Yuan, Hong-fu; Chu, Xiao-li; Liu, Hui-ying; Lu, Wan-zhen
2005-04-01
Derivative can correct baseline effects and also increase the level of noise. Wavelet transform has been proven an efficient tool for de-noising. This paper is directed to the application of wavelet transfer and derivative in the NIR analysis of octane number (RON). The derivative parameters, as well as their effects on the noise level and analytic accuracy of RON, have been studied in detail. The results show that derivative can correct the baseline effects and increase the analytic accuracy. Noise from the derivative spectra has great detriment to the analysis of RON. De-noising of wavelet transform can increase the S/N and improve the analytical accuracy.
Serbes, Gorkem; Aydin, Nizamettin
2014-01-01
Quadrature signals are dual-channel signals obtained from the systems employing quadrature demodulation. Embolic Doppler ultrasound signals obtained from stroke-prone patients by using Doppler ultrasound systems are quadrature signals caused by emboli, which are particles bigger than red blood cells within circulatory system. Detection of emboli is an important step in diagnosing stroke. Most widely used parameter in detection of emboli is embolic signal-to-background signal ratio. Therefore, in order to increase this ratio, denoising techniques are employed in detection systems. Discrete wavelet transform has been used for denoising of embolic signals, but it lacks shift invariance property. Instead, dual-tree complex wavelet transform having near-shift invariance property can be used. However, it is computationally expensive as two wavelet trees are required. Recently proposed modified dual-tree complex wavelet transform, which reduces the computational complexity, can also be used. In this study, the denoising performance of this method is extensively evaluated and compared with the others by using simulated and real quadrature signals. The quantitative results demonstrated that the modified dual-tree-complex-wavelet-transform-based denoising outperforms the conventional discrete wavelet transform with the same level of computational complexity and exhibits almost equal performance to the dual-tree complex wavelet transform with almost half computational cost.
NASA Astrophysics Data System (ADS)
Wang, Zhengzi; Ren, Zhong; Liu, Guodong
2015-10-01
Noninvasive measurement of blood glucose concentration has become a hotspot research in the world due to its characteristic of convenient, rapid and non-destructive etc. The blood glucose concentration monitoring based on photoacoustic technique has attracted many attentions because the detected signal is ultrasonic signals rather than the photo signals. But during the acquisition of the photoacoustic signals of glucose, the photoacoustic signals are not avoid to be polluted by some factors, such as the pulsed laser, electronic noises and circumstance noises etc. These disturbances will impact the measurement accuracy of the glucose concentration, So, the denoising of the glucose photoacoustic signals is a key work. In this paper, a wavelet shift-invariant threshold denoising method is improved, and a novel wavelet threshold function is proposed. For the novel wavelet threshold function, two threshold values and two different factors are set, and the novel function is high order derivative and continuous, which can be looked as the compromise between the wavelet soft threshold denoising and hard threshold denoising. Simulation experimental results illustrate that, compared with other wavelet threshold denoising, this improved wavelet shift-invariant threshold denoising has higher signal-to-noise ratio(SNR) and smaller root mean-square error (RMSE) value. And this improved denoising also has better denoising effect than others. Therefore, this improved denoising has a certain of potential value in the denoising of glucose photoacoustic signals.
Adaptive boxcar/wavelet transform
NASA Astrophysics Data System (ADS)
Sezer, Osman G.; Altunbasak, Yucel
2009-01-01
This paper presents a new adaptive Boxcar/Wavelet transform for image compression. Boxcar/Wavelet decomposition emphasizes the idea of average-interpolation representation which uses dyadic averages and their interpolation to explain a special case of biorthogonal wavelet transforms (BWT). This perspective for image compression together with lifting scheme offers the ability to train an optimum 2-D filter set for nonlinear prediction (interpolation) that will adapt to the context around the low-pass wavelet coefficients for reducing energy in the high-pass bands. Moreover, the filters obtained after training is observed to posses directional information with some textural clues that can provide better prediction performance. This work addresses a firrst step towards obtaining this new set of training-based fillters in the context of Boxcar/Wavelet transform. Initial experimental results show better subjective quality performance compared to popular 9/7-tap and 5/3-tap BWTs with comparable results in objective quality.
Denoising embolic Doppler ultrasound signals using Dual Tree Complex Discrete Wavelet Transform.
Serbes, Gorkem; Aydin, Nizamettin
2010-01-01
Early and accurate detection of asymptomatic emboli is important for monitoring of preventive therapy in stroke-prone patients. One of the problems in detection of emboli is the identification of an embolic signal caused by very small emboli. The amplitude of the embolic signal may be so small that advanced processing methods are required to distinguish these signals from Doppler signals arising from red blood cells. In this study instead of conventional discrete wavelet transform, the Dual Tree Complex Discrete Wavelet Transform was used for denoising embolic signals. Performances of both approaches were compared. Unlike the conventional discrete wavelet transform discrete complex wavelet transform is a shift invariant transform with limited redundancy. Results demonstrate that the Dual Tree Complex Discrete Wavelet Transform based denoising outperforms conventional discrete wavelet denoising. Approximately 8 dB improvement is obtained by using the Dual Tree Complex Discrete Wavelet Transform compared to the improvement provided by the conventional Discrete Wavelet Transform (less than 5 dB).
NASA Astrophysics Data System (ADS)
Bitenc, M.; Kieffer, D. S.; Khoshelham, K.
2015-08-01
The precision of Terrestrial Laser Scanning (TLS) data depends mainly on the inherent random range error, which hinders extraction of small details from TLS measurements. New post processing algorithms have been developed that reduce or eliminate the noise and therefore enable modelling details at a smaller scale than one would traditionally expect. The aim of this research is to find the optimum denoising method such that the corrected TLS data provides a reliable estimation of small-scale rock joint roughness. Two wavelet-based denoising methods are considered, namely Discrete Wavelet Transform (DWT) and Stationary Wavelet Transform (SWT), in combination with different thresholding procedures. The question is, which technique provides a more accurate roughness estimates considering (i) wavelet transform (SWT or DWT), (ii) thresholding method (fixed-form or penalised low) and (iii) thresholding mode (soft or hard). The performance of denoising methods is tested by two analyses, namely method noise and method sensitivity to noise. The reference data are precise Advanced TOpometric Sensor (ATOS) measurements obtained on 20 × 30 cm rock joint sample, which are for the second analysis corrupted by different levels of noise. With such a controlled noise level experiments it is possible to evaluate the methods' performance for different amounts of noise, which might be present in TLS data. Qualitative visual checks of denoised surfaces and quantitative parameters such as grid height and roughness are considered in a comparative analysis of denoising methods. Results indicate that the preferred method for realistic roughness estimation is DWT with penalised low hard thresholding.
G. S., Vijay; H. S., Kumar; Pai P., Srinivasa; N. S., Sriram; Rao, Raj B. K. N.
2012-01-01
The wavelet based denoising has proven its ability to denoise the bearing vibration signals by improving the signal-to-noise ratio (SNR) and reducing the root-mean-square error (RMSE). In this paper seven wavelet based denoising schemes have been evaluated based on the performance of the Artificial Neural Network (ANN) and the Support Vector Machine (SVM), for the bearing condition classification. The work consists of two parts, the first part in which a synthetic signal simulating the defective bearing vibration signal with Gaussian noise was subjected to these denoising schemes. The best scheme based on the SNR and the RMSE was identified. In the second part, the vibration signals collected from a customized Rolling Element Bearing (REB) test rig for four bearing conditions were subjected to these denoising schemes. Several time and frequency domain features were extracted from the denoised signals, out of which a few sensitive features were selected using the Fisher's Criterion (FC). Extracted features were used to train and test the ANN and the SVM. The best denoising scheme identified, based on the classification performances of the ANN and the SVM, was found to be the same as the one obtained using the synthetic signal. PMID:23213323
Liu, Ryan Wen; Shi, Lin; Huang, Wenhua; Xu, Jing; Yu, Simon Chun Ho; Wang, Defeng
2014-07-01
Magnetic resonance imaging (MRI) is an outstanding medical imaging modality but the quality often suffers from noise pollution during image acquisition and transmission. The purpose of this study is to enhance image quality using feature-preserving denoising method. In current literature, most existing MRI denoising methods did not simultaneously take the global image prior and local image features into account. The denoising method proposed in this paper is implemented based on an assumption of spatially varying Rician noise map. A two-step wavelet-domain estimation method is developed to extract the noise map. Following a Bayesian modeling approach, a generalized total variation-based MRI denoising model is proposed based on global hyper-Laplacian prior and Rician noise assumption. The proposed model has the properties of backward diffusion in local normal directions and forward diffusion in local tangent directions. To further improve the denoising performance, a local variance estimator-based method is introduced to calculate the spatially adaptive regularization parameters related to local image features and spatially varying noise map. The main benefit of the proposed method is that it takes full advantage of the global MR image prior and local image features. Numerous experiments have been conducted on both synthetic and real MR data sets to compare our proposed model with some state-of-the-art denoising methods. The experimental results have demonstrated the superior performance of our proposed model in terms of quantitative and qualitative image quality evaluations.
Yu, Hancheng; Zhao, Li; Wang, Haixian
2009-10-01
This correspondence proposes an efficient algorithm for removing Gaussian noise from corrupted image by incorporating a wavelet-based trivariate shrinkage filter with a spatial-based joint bilateral filter. In the wavelet domain, the wavelet coefficients are modeled as trivariate Gaussian distribution, taking into account the statistical dependencies among intrascale wavelet coefficients, and then a trivariate shrinkage filter is derived by using the maximum a posteriori (MAP) estimator. Although wavelet-based methods are efficient in image denoising, they are prone to producing salient artifacts such as low-frequency noise and edge ringing which relate to the structure of the underlying wavelet. On the other hand, most spatial-based algorithms output much higher quality denoising image with less artifacts. However, they are usually too computationally demanding. In order to reduce the computational cost, we develop an efficient joint bilateral filter by using the wavelet denoising result rather than directly processing the noisy image in the spatial domain. This filter could suppress the noise while preserve image details with small computational cost. Extension to color image denoising is also presented. We compare our denoising algorithm with other denoising techniques in terms of PSNR and visual quality. The experimental results indicate that our algorithm is competitive with other denoising techniques.
Implemented Wavelet Packet Tree based Denoising Algorithm in Bus Signals of a Wearable Sensorarray
NASA Astrophysics Data System (ADS)
Schimmack, M.; Nguyen, S.; Mercorelli, P.
2015-11-01
This paper introduces a thermosensing embedded system with a sensor bus that uses wavelets for the purposes of noise location and denoising. From the principle of the filter bank the measured signal is separated in two bands, low and high frequency. The proposed algorithm identifies the defined noise in these two bands. With the Wavelet Packet Transform as a method of Discrete Wavelet Transform, it is able to decompose and reconstruct bus input signals of a sensor network. Using a seminorm, the noise of a sequence can be detected and located, so that the wavelet basis can be rearranged. This particularly allows for elimination of any incoherent parts that make up unavoidable measuring noise of bus signals. The proposed method was built based on wavelet algorithms from the WaveLab 850 library of the Stanford University (USA). This work gives an insight to the workings of Wavelet Transformation.
Boix, Macarena; Cantó, Begoña
2013-04-01
Accurate image segmentation is used in medical diagnosis since this technique is a noninvasive pre-processing step for biomedical treatment. In this work we present an efficient segmentation method for medical image analysis. In particular, with this method blood cells can be segmented. For that, we combine the wavelet transform with morphological operations. Moreover, the wavelet thresholding technique is used to eliminate the noise and prepare the image for suitable segmentation. In wavelet denoising we determine the best wavelet that shows a segmentation with the largest area in the cell. We study different wavelet families and we conclude that the wavelet db1 is the best and it can serve for posterior works on blood pathologies. The proposed method generates goods results when it is applied on several images. Finally, the proposed algorithm made in MatLab environment is verified for a selected blood cells.
Chang, Ching-Wei; Mycek, Mary-Ann
2012-05-01
We report the first application of wavelet-based denoising (noise removal) methods to time-domain box-car fluorescence lifetime imaging microscopy (FLIM) images and compare the results to novel total variation (TV) denoising methods. Methods were tested first on artificial images and then applied to low-light live-cell images. Relative to undenoised images, TV methods could improve lifetime precision up to 10-fold in artificial images, while preserving the overall accuracy of lifetime and amplitude values of a single-exponential decay model and improving local lifetime fitting in live-cell images. Wavelet-based methods were at least 4-fold faster than TV methods, but could introduce significant inaccuracies in recovered lifetime values. The denoising methods discussed can potentially enhance a variety of FLIM applications, including live-cell, in vivo animal, or endoscopic imaging studies, especially under challenging imaging conditions such as low-light or fast video-rate imaging.
Low-dose computed tomography image denoising based on joint wavelet and sparse representation.
Ghadrdan, Samira; Alirezaie, Javad; Dillenseger, Jean-Louis; Babyn, Paul
2014-01-01
Image denoising and signal enhancement are the most challenging issues in low dose computed tomography (CT) imaging. Sparse representational methods have shown initial promise for these applications. In this work we present a wavelet based sparse representation denoising technique utilizing dictionary learning and clustering. By using wavelets we extract the most suitable features in the images to obtain accurate dictionary atoms for the denoising algorithm. To achieve improved results we also lower the number of clusters which reduces computational complexity. In addition, a single image noise level estimation is developed to update the cluster centers in higher PSNRs. Our results along with the computational efficiency of the proposed algorithm clearly demonstrates the improvement of the proposed algorithm over other clustering based sparse representation (CSR) and K-SVD methods.
Gap Measurement of Point Machine Using Adaptive Wavelet Threshold and Mathematical Morphology
Xu, Tianhua; Wang, Guang; Wang, Haifeng; Yuan, Tangming; Zhong, Zhiwang
2016-01-01
A point machine’s gap is an important indication of its healthy status. An edge detection algorithm is proposed to measure and calculate a point machine’s gap from the gap image captured by CCD plane arrays. This algorithm integrates adaptive wavelet-based image denoising, locally adaptive image binarization, and mathematical morphology technologies. The adaptive wavelet-based image denoising obtains not only an optimal denoising threshold, but also unblurred edges. Locally adaptive image binarization has the advantage of overcoming the local intensity variation in gap images. Mathematical morphology may suppress speckle spots caused by reflective metal surfaces in point machines. The subjective and objective evaluations of the proposed method are presented by using point machine gap images from a railway corporation in China. The performance between the proposed method and conventional edge detection methods has also been compared, and the result shows that the former outperforms the latter. PMID:27898042
The Application of Wavelet-Domain Hidden Markov Tree Model in Diabetic Retinal Image Denoising.
Cui, Dong; Liu, Minmin; Hu, Lei; Liu, Keju; Guo, Yongxin; Jiao, Qing
2015-01-01
The wavelet-domain Hidden Markov Tree Model can properly describe the dependence and correlation of fundus angiographic images' wavelet coefficients among scales. Based on the construction of the fundus angiographic images Hidden Markov Tree Models and Gaussian Mixture Models, this paper applied expectation-maximum algorithm to estimate the wavelet coefficients of original fundus angiographic images and the Bayesian estimation to achieve the goal of fundus angiographic images denoising. As is shown in the experimental result, compared with the other algorithms as mean filter and median filter, this method effectively improved the peak signal to noise ratio of fundus angiographic images after denoising and preserved the details of vascular edge in fundus angiographic images.
NASA Astrophysics Data System (ADS)
Yaseen, Alauldeen S.; Pavlov, Alexey N.; Hramov, Alexander E.
2016-03-01
Speech signal processing is widely used to reduce noise impact in acquired data. During the last decades, wavelet-based filtering techniques are often applied in communication systems due to their advantages in signal denoising as compared with Fourier-based methods. In this study we consider applications of a 1-D double density complex wavelet transform (1D-DDCWT) and compare the results with the standard 1-D discrete wavelet-transform (1DDWT). The performances of the considered techniques are compared using the mean opinion score (MOS) being the primary metric for the quality of the processed signals. A two-dimensional extension of this approach can be used for effective image denoising.
Denoising and robust non-linear wavelet analysis
NASA Astrophysics Data System (ADS)
Bruce, Andrew G.; Donoho, David L.; Gao, Hong-Ye; Martin, R. D.
1994-04-01
In a series of papers, Donoho and Johnstone develop a powerful theory based on wavelets for extracting non-smooth signals from noisy data. Several nonlinear smoothing algorithms are presented which provide high performance for removing Gaussian noise from a wide range of spatially inhomogeneous signals. However, like other methods based on the linear wavelet transform, these algorithms are very sensitive to certain types of non-Gaussian noise, such as outliers. In this paper, we develop outlier resistance wavelet transforms. In these transforms, outliers and outlier patches are localized to just a few scales. By using the outlier resistant wavelet transforms, we improve upon the Donoho and Johnstone nonlinear signal extraction methods. The outlier resistant wavelet algorithms are included with the S+Wavelets object-oriented toolkit for wavelet analysis.
A study of infrared spectroscopy de-noising based on LMS adaptive filter
NASA Astrophysics Data System (ADS)
Mo, Jia-qing; Lv, Xiao-yi; Yu, Xiao
2015-12-01
Infrared spectroscopy has been widely used, but which often contains a lot of noise, so the spectral characteristic of the sample is seriously affected. Therefore the de-noising is very important in the spectrum analysis and processing. In the study of infrared spectroscopy, the least mean square (LMS) adaptive filter was applied in the field firstly. LMS adaptive filter algorithm can reserve the detail and envelope of the effective signal when the method was applied to infrared spectroscopy of breast cancer which signal-to-noise ratio (SNR) is lower than 10 dB, contrast and analysis the result with result of wavelet transform and ensemble empirical mode decomposition (EEMD). The three evaluation standards (SNR, root mean square error (RMSE) and the correlation coefficient (ρ)) fully proved de-noising advantages of LMS adaptive filter in infrared spectroscopy of breast cancer.
Automated wavelet denoising of photoacoustic signals for burn-depth image reconstruction
NASA Astrophysics Data System (ADS)
Holan, Scott H.; Viator, John A.
2007-02-01
Photoacoustic image reconstruction involves dozens or perhaps hundreds of point measurements, each of which contributes unique information about the subsurface absorbing structures under study. For backprojection imaging, two or more point measurements of photoacoustic waves induced by irradiating a sample with laser light are used to produce an image of the acoustic source. Each of these point measurements must undergo some signal processing, such as denoising and system deconvolution. In order to efficiently process the numerous signals acquired for photoacoustic imaging, we have developed an automated wavelet algorithm for processing signals generated in a burn injury phantom. We used the discrete wavelet transform to denoise photoacoustic signals generated in an optically turbid phantom containing whole blood. The denoising used universal level independent thresholding, as developed by Donoho and Johnstone. The entire signal processing technique was automated so that no user intervention was needed to reconstruct the images. The signals were backprojected using the automated wavelet processing software and showed reconstruction using denoised signals improved image quality by 21%, using a relative 2-norm difference scheme.
NASA Astrophysics Data System (ADS)
Quesada-Barriuso, Pablo; Heras, Dora B.; Argüello, Francisco
2016-10-01
The classification of remote sensing hyperspectral images for land cover applications is a very intensive topic. In the case of supervised classification, Support Vector Machines (SVMs) play a dominant role. Recently, the Extreme Learning Machine algorithm (ELM) has been extensively used. The classification scheme previously published by the authors, and called WT-EMP, introduces spatial information in the classification process by means of an Extended Morphological Profile (EMP) that is created from features extracted by wavelets. In addition, the hyperspectral image is denoised in the 2-D spatial domain, also using wavelets and it is joined to the EMP via a stacked vector. In this paper, the scheme is improved achieving two goals. The first one is to reduce the classification time while preserving the accuracy of the classification by using ELM instead of SVM. The second one is to improve the accuracy results by performing not only a 2-D denoising for every spectral band, but also a previous additional 1-D spectral signature denoising applied to each pixel vector of the image. For each denoising the image is transformed by applying a 1-D or 2-D wavelet transform, and then a NeighShrink thresholding is applied. Improvements in terms of classification accuracy are obtained, especially for images with close regions in the classification reference map, because in these cases the accuracy of the classification in the edges between classes is more relevant.
Improved 3D wavelet-based de-noising of fMRI data
NASA Astrophysics Data System (ADS)
Khullar, Siddharth; Michael, Andrew M.; Correa, Nicolle; Adali, Tulay; Baum, Stefi A.; Calhoun, Vince D.
2011-03-01
Functional MRI (fMRI) data analysis deals with the problem of detecting very weak signals in very noisy data. Smoothing with a Gaussian kernel is often used to decrease noise at the cost of losing spatial specificity. We present a novel wavelet-based 3-D technique to remove noise in fMRI data while preserving the spatial features in the component maps obtained through group independent component analysis (ICA). Each volume is decomposed into eight volumetric sub-bands using a separable 3-D stationary wavelet transform. Each of the detail sub-bands are then treated through the main denoising module. This module facilitates computation of shrinkage factors through a hierarchical framework. It utilizes information iteratively from the sub-band at next higher level to estimate denoised coefficients at the current level. These de-noised sub-bands are then reconstructed back to the spatial domain using an inverse wavelet transform. Finally, the denoised group fMRI data is analyzed using ICA where the data is decomposed in to clusters of functionally correlated voxels (spatial maps) as indicators of task-related neural activity. The proposed method enables the preservation of shape of the actual activation regions associated with the BOLD activity. In addition it is able to achieve high specificity as compared to the conventionally used FWHM (full width half maximum) Gaussian kernels for smoothing fMRI data.
Gearbox Fault Diagnosis Using Adaptive Wavelet Filter
NASA Astrophysics Data System (ADS)
LIN, J.; ZUO, M. J.
2003-11-01
Vibration signals from a gearbox are usually noisy. As a result, it is difficult to find early symptoms of a potential failure in a gearbox. Wavelet transform is a powerful tool to disclose transient information in signals. An adaptive wavelet filter based on Morlet wavelet is introduced in this paper. The parameters in the Morlet wavelet function are optimised based on the kurtosis maximisation principle. The wavelet used is adaptive because the parameters are not fixed. The adaptive wavelet filter is found to be very effective in detection of symptoms from vibration signals of a gearbox with early fatigue tooth crack. Two types of discrete wavelet transform (DWT), the decimated with DB4 wavelet and the undecimated with harmonic wavelet, are also used to analyse the same signals for comparison. No periodic impulses appear on any scale in either DWT decomposition.
NASA Astrophysics Data System (ADS)
Holan, Scott H.; Viator, John A.
2008-06-01
Photoacoustic image reconstruction may involve hundreds of point measurements, each of which contributes unique information about the subsurface absorbing structures under study. For backprojection imaging, two or more point measurements of photoacoustic waves induced by irradiating a biological sample with laser light are used to produce an image of the acoustic source. Each of these measurements must undergo some signal processing, such as denoising or system deconvolution. In order to process the numerous signals, we have developed an automated wavelet algorithm for denoising signals. We appeal to the discrete wavelet transform for denoising photoacoustic signals generated in a dilute melanoma cell suspension and in thermally coagulated blood. We used 5, 9, 45 and 270 melanoma cells in the laser beam path as test concentrations. For the burn phantom, we used coagulated blood in 1.6 mm silicon tube submerged in Intralipid. Although these two targets were chosen as typical applications for photoacoustic detection and imaging, they are of independent interest. The denoising employs level-independent universal thresholding. In order to accommodate nonradix-2 signals, we considered a maximal overlap discrete wavelet transform (MODWT). For the lower melanoma cell concentrations, as the signal-to-noise ratio approached 1, denoising allowed better peak finding. For coagulated blood, the signals were denoised to yield a clean photoacoustic resulting in an improvement of 22% in the reconstructed image. The entire signal processing technique was automated so that minimal user intervention was needed to reconstruct the images. Such an algorithm may be used for image reconstruction and signal extraction for applications such as burn depth imaging, depth profiling of vascular lesions in skin and the detection of single cancer cells in blood samples.
NASA Astrophysics Data System (ADS)
Wang, Xiaojun; Lai, Weidong
2011-08-01
In this paper, a combined method have been put forward for one ASTER detected image with the wavelet filter to attenuate the noise and the anisotropic diffusion PDE(Partial Differential Equation) for further recovering image contrast. The model is verified in different noising background, since the remote sensing image usually contains salt and pepper, Gaussian as well as speckle noise. Considered the features that noise existing in wavelet domain, the wavelet filter with Bayesian estimation threshold is applied for recovering image contrast from the blurring background. The proposed PDE are performing an anisotropic diffusion in the orthogonal direction, thus preserving the edges during further denoising process. Simulation indicates that the combined algorithm can more effectively recover the blurred image from speckle and Gauss noise background than the only wavelet denoising method, while the denoising effect is also distinct when the pepper-salt noise has low intensity. The combined algorithm proposed in this article can be integrated in remote sensing image analyzing to obtain higher accuracy for environmental interpretation and pattern recognition.
Adaptive denoising and multiscale detection of the V wave in brainstem auditory evoked potentials.
Popescu, M; Papadimitriou, S; Karamitsos, D; Bezerianos, A
1999-01-01
This paper describes a wavelet-transform-based system for the V wave identification in brainstem auditory evoked potentials (BAEP). The system combines signal denoising and rule-based localization modules. The signal denoising module has the potential of effective noise reduction after signal averaging. It analyses adaptively the evolution of the wavelet transform maxima across scales. The singularities of the signal create wavelet maxima with different properties from those of the induced noise. A non-linear filtering process implemented with a neural network extracts out the noise-induced maxima. The filtered wavelet details are subsequently analysed by the rule-based localization module for the automatic identification of the V wave. In the first phase, it implements a set of statistical observations as well as heuristic criteria used by human experts in order to classify the IV-V complex. At the second phase, using a multiscale focusing algorithm, the IV and V waves are positioned on the BAEP signal. Our experiments revealed that the system provides accurate results even for signals exhibiting unclear IV-V complexes.
NASA Astrophysics Data System (ADS)
Sarty, Gordon E.; Atkins, M. Stella; Olatunbosun, Femi; Chizen, Donna; Loewy, John; Kendall, Edward J.; Pierson, Roger A.
1999-10-01
A new numerical wavelet transform, the discrete torus wavelet transform, is described and an application is given to the denoising of abdominal magnetic resonance imaging (MRI) data. The discrete tori wavelet transform is an undecimated wavelet transform which is computed using a discrete Fourier transform and multiplication instead of by direct convolution in the image domain. This approach leads to a decomposition of the image onto frames in the space of square summable functions on the discrete torus, l2(T2). The new transform was compared to the traditional decimated wavelet transform in its ability to denoise MRI data. By using denoised images as the basis for the computation of a nuclear magnetic resonance spin-spin relaxation-time map through least squares curve fitting, an error map was generated that was used to assess the performance of the denoising algorithms. The discrete torus wavelet transform outperformed the traditional wavelet transform in 88% of the T2 error map denoising tests with phantoms and gynecologic MRI images.
A joint inter- and intrascale statistical model for Bayesian wavelet based image denoising.
Pizurica, Aleksandra; Philips, Wilfried; Lemahieu, Ignace; Acheroy, Marc
2002-01-01
This paper presents a new wavelet-based image denoising method, which extends a "geometrical" Bayesian framework. The new method combines three criteria for distinguishing supposedly useful coefficients from noise: coefficient magnitudes, their evolution across scales and spatial clustering of large coefficients near image edges. These three criteria are combined in a Bayesian framework. The spatial clustering properties are expressed in a prior model. The statistical properties concerning coefficient magnitudes and their evolution across scales are expressed in a joint conditional model. The three main novelties with respect to related approaches are (1) the interscale-ratios of wavelet coefficients are statistically characterized and different local criteria for distinguishing useful coefficients from noise are evaluated, (2) a joint conditional model is introduced, and (3) a novel anisotropic Markov random field prior model is proposed. The results demonstrate an improved denoising performance over related earlier techniques.
Adaptive image denoising by targeted databases.
Luo, Enming; Chan, Stanley H; Nguyen, Truong Q
2015-07-01
We propose a data-dependent denoising procedure to restore noisy images. Different from existing denoising algorithms which search for patches from either the noisy image or a generic database, the new algorithm finds patches from a database that contains relevant patches. We formulate the denoising problem as an optimal filter design problem and make two contributions. First, we determine the basis function of the denoising filter by solving a group sparsity minimization problem. The optimization formulation generalizes existing denoising algorithms and offers systematic analysis of the performance. Improvement methods are proposed to enhance the patch search process. Second, we determine the spectral coefficients of the denoising filter by considering a localized Bayesian prior. The localized prior leverages the similarity of the targeted database, alleviates the intensive Bayesian computation, and links the new method to the classical linear minimum mean squared error estimation. We demonstrate applications of the proposed method in a variety of scenarios, including text images, multiview images, and face images. Experimental results show the superiority of the new algorithm over existing methods.
Synergistic Effects of Phase Folding and Wavelet Denoising with Applications in Light Curve Analysis
2016-09-15
FOLDING AND WAVELET DENOISING WITH APPLICATIONS IN LIGHT CURVE ANALYSIS I. Introduction Moore’s law, and other exponential growth patterns in technology...that the universe underwent a period of exponential growth shortly after the big bang. The exponential growth of the universe can be accounted for in the...The second section discusses the exponential growth of the solution space which accompanies the linear growth of components. Inherent Error. In
NASA Astrophysics Data System (ADS)
Dolabdjian, Ch.; Fadili, J.; Huertas Leyva, E.
2002-11-01
We have implemented a real-time numerical denoising algorithm, using the Discrete Wavelet Transform (DWT), on a TMS320C3x Digital Signal Processor (DSP). We also compared from a theoretical and practical viewpoints this post-processing approach to a more classical low-pass filter. This comparison was carried out using an ECG-type signal (ElectroCardiogram). The denoising approach is an elegant and extremely fast alternative to the classical linear filters class. It is particularly adapted to non-stationary signals such as those encountered in biological applications. The denoising allows to substantially improve detection of such signals over Fourier-based techniques. This processing step is a vital element in our acquisition chain using high sensitivity magnetic sensors. It should enhance detection of cardiac-type magnetic signals or magnetic particles in movement.
Tokmakçi, Mahmut; Erdoğan, Nuri
2009-05-01
In this paper, the effects of a wavelet transform based denoising strategy on clinical Doppler parameters are analyzed. The study scheme included: (a) Acquisition of arterial and venous Doppler signals by sampling the audio output of an ultrasound scanner from 20 healthy volunteers, (b) Noise reduction via decomposition of the signals through discrete wavelet transform, (c) Spectral analysis of noisy and noise-free signals with short time Fourier transform, (d) Curve fitting to spectrograms, (e) Calculation of clinical Doppler parameters, (f) Statistical comparison of parameters obtained from noisy and noise-free signals. The decomposition level was selected as the highest level at which the maximum power spectral density and its corresponding frequency were preserved. In all subjects, noise-free spectrograms had smoother trace with less ripples. In both arterial and venous spectrograms, denoising resulted in a significant decrease in the maximum (systolic) and mean frequency, with no statistical difference in the minimum (diastolic) frequency. In arterial signals, this leads to a significant decrease in the calculated parameters such as Systolic/Diastolic Velocity Ratio, Resistivity Index, Pulsatility Index and Acceleration Time. Acceleration Index did not change significantly. Despite a successful denoising, the effects of wavelet decomposition on high frequency components in the Doppler signal should be challenged by comparison with reference data, or, through clinical investigations.
Denoising algorithm based on edge extraction and wavelet transform in digital holography
NASA Astrophysics Data System (ADS)
Zhang, Ming; Sang, Xin-zhu; Leng, Jun-min; Cao, Xue-mei
2013-08-01
Digital holography is a kind of coherent imaging method and inevitably affected by many factors in the process of recording. One of dominant problems is the speckle noise, which is essentially nonlinear multiplicative noise related to signals. So it is more difficult to remove than additive noise. Due to the noise pollution, the low resolution of image reconstructed is caused. A new solution for suppressing speckle noise in digital hologram is presented, which combines Canny filtering algorithm with wavelet threshold denoising algorithm. Canny filter is used to obtain the edge detail. Wavelet transformation performs denoising. In order to suppress speckle effectively and retain the image details as much as possible, Neyman-Pearson (N-P) criterion is introduced to estimate wavelet coefficient in every scale. An improved threshold function is proposed, whose curve is smoother. The reconstructed image is achieved by merging the denoised image with the edge details. Experimental results and performance parameters of the proposed algorithm are discussed and compared with other methods, which shows that the presented approach can not only effectively eliminate speckle noise, but also retain useful signals and edge information simultaneously.
Fault Detection of a Roller-Bearing System through the EMD of a Wavelet Denoised Signal
Ahn, Jong-Hyo; Kwak, Dae-Ho; Koh, Bong-Hwan
2014-01-01
This paper investigates fault detection of a roller bearing system using a wavelet denoising scheme and proper orthogonal value (POV) of an intrinsic mode function (IMF) covariance matrix. The IMF of the bearing vibration signal is obtained through empirical mode decomposition (EMD). The signal screening process in the wavelet domain eliminates noise-corrupted portions that may lead to inaccurate prognosis of bearing conditions. We segmented the denoised bearing signal into several intervals, and decomposed each of them into IMFs. The first IMF of each segment is collected to become a covariance matrix for calculating the POV. We show that covariance matrices from healthy and damaged bearings exhibit different POV profiles, which can be a damage-sensitive feature. We also illustrate the conventional approach of feature extraction, of observing the kurtosis value of the measured signal, to compare the functionality of the proposed technique. The study demonstrates the feasibility of wavelet-based de-noising, and shows through laboratory experiments that tracking the proper orthogonal values of the covariance matrix of the IMF can be an effective and reliable measure for monitoring bearing fault. PMID:25196008
Wavelet-Based Speech Enhancement Using Time-Frequency Adaptation
NASA Astrophysics Data System (ADS)
Wang, Kun-Ching
2003-12-01
Wavelet denoising is commonly used for speech enhancement because of the simplicity of its implementation. However, the conventional methods generate the presence of musical residual noise while thresholding the background noise. The unvoiced components of speech are often eliminated from this method. In this paper, a novel algorithm of wavelet coefficient threshold (WCT) based on time-frequency adaptation is proposed. In addition, an unvoiced speech enhancement algorithm is also integrated into the system to improve the intelligibility of speech. The wavelet coefficient threshold (WCT) of each subband is first temporally adjusted according to the value of a posterior signal-to-noise ratio (SNR). To prevent the degradation of unvoiced sounds during noise, the algorithm utilizes a simple speech/noise detector (SND) and further divides speech signal into unvoiced and voiced sounds. Then, we apply appropriate wavelet thresholding according to voiced/unvoiced (V/U) decision. Based on the masking properties of human auditory system, a perceptual gain factor is adopted into wavelet thresholding for suppressing musical residual noise. Simulation results show that the proposed method is capable of reducing noise with little speech degradation and the overall performance is superior to several competitive methods.
Adaptive 2-D wavelet transform based on the lifting scheme with preserved vanishing moments.
Vrankic, Miroslav; Sersic, Damir; Sucic, Victor
2010-08-01
In this paper, we propose novel adaptive wavelet filter bank structures based on the lifting scheme. The filter banks are nonseparable, based on quincunx sampling, with their properties being pixel-wise adapted according to the local image features. Despite being adaptive, the filter banks retain a desirable number of primal and dual vanishing moments. The adaptation is introduced in the predict stage of the filter bank with an adaptation region chosen independently for each pixel, based on the intersection of confidence intervals (ICI) rule. The image denoising results are presented for both synthetic and real-world images. It is shown that the obtained wavelet decompositions perform well, especially for synthetic images that contain periodic patterns, for which the proposed method outperforms the state of the art in image denoising.
An adaptive nonlocal means scheme for medical image denoising
NASA Astrophysics Data System (ADS)
Thaipanich, Tanaphol; Kuo, C.-C. Jay
2010-03-01
Medical images often consist of low-contrast objects corrupted by random noise arising in the image acquisition process. Thus, image denoising is one of the fundamental tasks required by medical imaging analysis. In this work, we investigate an adaptive denoising scheme based on the nonlocal (NL)-means algorithm for medical imaging applications. In contrast with the traditional NL-means algorithm, the proposed adaptive NL-means (ANL-means) denoising scheme has three unique features. First, it employs the singular value decomposition (SVD) method and the K-means clustering (K-means) technique for robust classification of blocks in noisy images. Second, the local window is adaptively adjusted to match the local property of a block. Finally, a rotated block matching algorithm is adopted for better similarity matching. Experimental results from both additive white Gaussian noise (AWGN) and Rician noise are given to demonstrate the superior performance of the proposed ANL denoising technique over various image denoising benchmarks in term of both PSNR and perceptual quality comparison.
The EM Method in a Probabilistic Wavelet-Based MRI Denoising
2015-01-01
Human body heat emission and others external causes can interfere in magnetic resonance image acquisition and produce noise. In this kind of images, the noise, when no signal is present, is Rayleigh distributed and its wavelet coefficients can be approximately modeled by a Gaussian distribution. Noiseless magnetic resonance images can be modeled by a Laplacian distribution in the wavelet domain. This paper proposes a new magnetic resonance image denoising method to solve this fact. This method performs shrinkage of wavelet coefficients based on the conditioned probability of being noise or detail. The parameters involved in this filtering approach are calculated by means of the expectation maximization (EM) method, which avoids the need to use an estimator of noise variance. The efficiency of the proposed filter is studied and compared with other important filtering techniques, such as Nowak's, Donoho-Johnstone's, Awate-Whitaker's, and nonlocal means filters, in different 2D and 3D images. PMID:26089959
The EM Method in a Probabilistic Wavelet-Based MRI Denoising.
Martin-Fernandez, Marcos; Villullas, Sergio
2015-01-01
Human body heat emission and others external causes can interfere in magnetic resonance image acquisition and produce noise. In this kind of images, the noise, when no signal is present, is Rayleigh distributed and its wavelet coefficients can be approximately modeled by a Gaussian distribution. Noiseless magnetic resonance images can be modeled by a Laplacian distribution in the wavelet domain. This paper proposes a new magnetic resonance image denoising method to solve this fact. This method performs shrinkage of wavelet coefficients based on the conditioned probability of being noise or detail. The parameters involved in this filtering approach are calculated by means of the expectation maximization (EM) method, which avoids the need to use an estimator of noise variance. The efficiency of the proposed filter is studied and compared with other important filtering techniques, such as Nowak's, Donoho-Johnstone's, Awate-Whitaker's, and nonlocal means filters, in different 2D and 3D images.
NASA Astrophysics Data System (ADS)
Ren, Zhong; Liu, Guodong; Huang, Zhen
2014-10-01
Real-time monitoring of blood glucose concentration (BGC) is a great important procedure in controlling diabetes mellitus and preventing the complication for diabetic patients. Noninvasive measurement of BGC has already become a research hotspot because it can overcome the physical and psychological harm. Photoacoustic spectroscopy is a well-established, hybrid and alternative technique used to determine the BGC. According to the theory of photoacoustic technique, the blood is irradiated by plused laser with nano-second repeation time and micro-joule power, the photoacoustic singals contained the information of BGC are generated due to the thermal-elastic mechanism, then the BGC level can be interpreted from photoacoustic signal via the data analysis. But in practice, the time-resolved photoacoustic signals of BGC are polluted by the varities of noises, e.g., the interference of background sounds and multi-component of blood. The quality of photoacoustic signal of BGC directly impacts the precision of BGC measurement. So, an improved wavelet denoising method was proposed to eliminate the noises contained in BGC photoacoustic signals. To overcome the shortcoming of traditional wavelet threshold denoising, an improved dual-threshold wavelet function was proposed in this paper. Simulation experimental results illustrated that the denoising result of this improved wavelet method was better than that of traditional soft and hard threshold function. To varify the feasibility of this improved function, the actual photoacoustic BGC signals were test, the test reslut demonstrated that the signal-to-noises ratio(SNR) of the improved function increases about 40-80%, and its root-mean-square error (RMSE) decreases about 38.7-52.8%.
Matsuyama, Eri; Tsai, Du-Yih; Lee, Yongbum; Takahashi, Noriyuki
2013-01-01
The purpose of this study was to evaluate the performance of a conventional discrete wavelet transform (DWT) method and a modified undecimated discrete wavelet transform (M-UDWT) method applied to mammographic image denoising. Mutual information, mean square error, and signal to noise ratio were used as image quality measures of images processed by the two methods. We examined the performance of the two methods with visual perceptual evaluation. A two-tailed F test was used to measure statistical significance. The difference between the M-UDWT processed images and the conventional DWT-method processed images was statistically significant (P<0.01). The authors confirmed the superiority and effectiveness of the M-UDWT method. The results of this study suggest the M-UDWT method may provide better image quality as compared to the conventional DWT.
Wavelet detection of weak far-magnetic signal based on adaptive ARMA model threshold
NASA Astrophysics Data System (ADS)
Zhang, Ning; Lin, Chun-sheng; Fang, Shi
2009-10-01
Based on Mallat algorithm, a de-noising algorithm of adaptive wavelet threshold is applied for weak magnetic signal detection of far moving target in complex magnetic environment. The choice of threshold is the key problem. With the spectrum analysis of the magnetic field target, a threshold algorithm on the basis of adaptive ARMA model filter is brought forward to improve the wavelet filtering performance. The simulation of this algorithm on measured data is carried out. Compared to Donoho threshold algorithm, it shows that adaptive ARMA model threshold algorithm significantly improved the capability of weak magnetic signal detection in complex magnetic environment.
Nonuniform spatially adaptive wavelet packets
NASA Astrophysics Data System (ADS)
Carre, Philippe; Fernandez-Maloigne, Christine
2000-12-01
In this paper, we propose a new decomposition scheme for spatially adaptive wavelet packets. Contrary to the double tree algorithm, our method is non-uniform and shift- invariant in the time and frequency domains, and is minimal for an information cost function. We prose some-restrictions to our algorithm to reduce the complexity and permitting us to provide some time-frequency partitions of the signal in agreement with its structure. This new 'totally' non-uniform transform, more adapted than Malvar, Packets or dyadic double-tree decomposition, allows the study of all possible time-frequency partitions with the only restriction that the blocks are rectangular. It permits one to obtain a satisfying Time-Frequency representation, and is applied for the study of EEG signals.
NASA Astrophysics Data System (ADS)
Tao, Yinghua; Brunner, Stephen; Tang, Jie; Speidel, Michael; Rowley, Howard; VanLysel, Michael; Chen, Guang-Hong
2011-03-01
Radiation dose reduction remains at the forefront of research in computed tomography. X-ray tube parameters such as tube current can be lowered to reduce dose; however, images become prohibitively noisy when the tube current is too low. Wavelet denoising is one of many noise reduction techniques. However, traditional wavelet techniques have the tendency to create an artificial noise texture, due to the nonuniform denoising across the image, which is undesirable from a diagnostic perspective. This work presents a new implementation of wavelet denoising that is able to achieve noise reduction, while still preserving spatial resolution. Further, the proposed method has the potential to improve those unnatural noise textures. The technique was tested on both phantom and animal datasets (Catphan phantom and timeresolved swine heart scan) acquired on a GE Discovery VCT scanner. A number of tube currents were used to investigate the potential for dose reduction.
Prognostics of Lithium-Ion Batteries Based on Wavelet Denoising and DE-RVM
Zhang, Chaolong; He, Yigang; Yuan, Lifeng; Xiang, Sheng; Wang, Jinping
2015-01-01
Lithium-ion batteries are widely used in many electronic systems. Therefore, it is significantly important to estimate the lithium-ion battery's remaining useful life (RUL), yet very difficult. One important reason is that the measured battery capacity data are often subject to the different levels of noise pollution. In this paper, a novel battery capacity prognostics approach is presented to estimate the RUL of lithium-ion batteries. Wavelet denoising is performed with different thresholds in order to weaken the strong noise and remove the weak noise. Relevance vector machine (RVM) improved by differential evolution (DE) algorithm is utilized to estimate the battery RUL based on the denoised data. An experiment including battery 5 capacity prognostics case and battery 18 capacity prognostics case is conducted and validated that the proposed approach can predict the trend of battery capacity trajectory closely and estimate the battery RUL accurately. PMID:26413090
Image denoising via adaptive eigenvectors of graph Laplacian
NASA Astrophysics Data System (ADS)
Chen, Ying; Tang, Yibin; Xu, Ning; Zhou, Lin; Zhao, Li
2016-07-01
An image denoising method via adaptive eigenvectors of graph Laplacian (EGL) is proposed. Unlike the trivial parameter setting of the used eigenvectors in the traditional EGL method, in our method, the eigenvectors are adaptively selected in the whole denoising procedure. In detail, a rough image is first built with the eigenvectors from the noisy image, where the eigenvectors are selected by using the deviation estimation of the clean image. Subsequently, a guided image is effectively restored with a weighted average of the noisy and rough images. In this operation, the average coefficient is adaptively obtained to set the deviation of the guided image to approximately that of the clean image. Finally, the denoised image is achieved by a group-sparse model with the pattern from the guided image, where the eigenvectors are chosen in the error control of the noise deviation. Moreover, a modified group orthogonal matching pursuit algorithm is developed to efficiently solve the above group sparse model. The experiments show that our method not only improves the practicality of the EGL methods with the dependence reduction of the parameter setting, but also can outperform some well-developed denoising methods, especially for noise with large deviations.
Wavelet-Based Speech Enhancement Using Time-Adapted Noise Estimation
NASA Astrophysics Data System (ADS)
Lei, Sheau-Fang; Tung, Ying-Kai
Spectral subtraction is commonly used for speech enhancement in a single channel system because of the simplicity of its implementation. However, this algorithm introduces perceptually musical noise while suppressing the background noise. We propose a wavelet-based approach in this paper for suppressing the background noise for speech enhancement in a single channel system. The wavelet packet transform, which emulates the human auditory system, is used to decompose the noisy signal into critical bands. Wavelet thresholding is then temporally adjusted with the noise power by time-adapted noise estimation. The proposed algorithm can efficiently suppress the noise while reducing speech distortion. Experimental results, including several objective measurements, show that the proposed wavelet-based algorithm outperforms spectral subtraction and other wavelet-based denoising approaches for speech enhancement for nonstationary noise environments.
Adaptive Bayesian-based speck-reduction in SAR images using complex wavelet transform
NASA Astrophysics Data System (ADS)
Ma, Ning; Yan, Wei; Zhang, Peng
2005-10-01
In this paper, an improved adaptive speckle reduction method is presented based on dual tree complex wavelet transform (CWT). It combines the characteristics of additive noise reduction of soft thresholding with the CWT's directional selectivity, being its main contribution to adapt the effective threshold to preserve the edge detail. A Bayesian estimator is applied to the decomposed data also to estimate the best value for the noise-free complex wavelet coefficients. This estimation is based on alpha-stable and Gaussian distribution hypotheses for complex wavelet coefficients of the signal and noise, respectively. Experimental results show that the denoising performance is among the state-of-the-art techniques based on real discrete wavelet transform (DWT).
Novel wavelet threshold denoising method in axle press-fit zone ultrasonic detection
NASA Astrophysics Data System (ADS)
Peng, Chaoyong; Gao, Xiaorong; Peng, Jianping; Wang, Ai
2017-02-01
Axles are important part of railway locomotives and vehicles. Periodic ultrasonic inspection of axles can effectively detect and monitor axle fatigue cracks. However, in the axle press-fit zone, the complex interface contact condition reduces the signal-noise ratio (SNR). Therefore, the probability of false positives and false negatives increases. In this work, a novel wavelet threshold function is created to remove noise and suppress press-fit interface echoes in axle ultrasonic defect detection. The novel wavelet threshold function with two variables is designed to ensure the precision of optimum searching process. Based on the positive correlation between the correlation coefficient and SNR and with the experiment phenomenon that the defect and the press-fit interface echo have different axle-circumferential correlation characteristics, a discrete optimum searching process for two undetermined variables in novel wavelet threshold function is conducted. The performance of the proposed method is assessed by comparing it with traditional threshold methods using real data. The statistic results of the amplitude and the peak SNR of defect echoes show that the proposed wavelet threshold denoising method not only maintains the amplitude of defect echoes but also has a higher peak SNR.
Zou, Ling; Zhang, Yingchun; Yang, Laurence T; Zhou, Renlai
2010-02-01
The authors have developed a new approach by combining the wavelet denoising and principal component analysis methods to reduce the number of required trials for efficient extraction of brain evoked-related potentials (ERPs). Evoked-related potentials were initially extracted using wavelet denoising to enhance the signal-to-noise ratio of raw EEG measurements. Principal components of ERPs accounting for 80% of the total variance were extracted as part of the subspace of the ERPs. Finally, the ERPs were reconstructed from the selected principal components. Computer simulation results showed that the combined approach provided estimations with higher signal-to-noise ratio and lower root mean squared error than each of them alone. The authors further tested this proposed approach in single-trial ERPs extraction during an emotional process and brain responses analysis to emotional stimuli. The experimental results also demonstrated the effectiveness of this combined approach in ERPs extraction and further supported the view that emotional stimuli are processed more intensely.
Ultrasound imaging and characterization of biofilms based on wavelet de-noised radiofrequency data.
Vaidya, Kunal; Osgood, Robert; Ren, Dabin; Pichichero, Michael E; Helguera, María
2014-03-01
The ability to non-invasively image and characterize bacterial biofilms in children during nasopharyngeal colonization with potential otopathogens and during acute otitis media would represent a significant advance. We sought to determine if quantitative high-frequency ultrasound techniques could be used to achieve that goal. Systematic time studies of bacterial biofilm formation were performed on three preparations of an isolated Haemophilus influenzae (NTHi) strain, a Streptococcus pneumoniae (Sp) strain and a combination of H. influenzae and S. pneumoniae (NTHi + Sp) in an in vitro environment. The process of characterization included conditioning of the acquired radiofrequency data obtained with a 15-MHz focused, piston transducer by using a seven-level wavelet decomposition scheme to de-noise the individual A-lines acquired. All subsequent spectral parameter estimations were done on the wavelet de-noised radiofrequency data. Various spectral parameters-peak frequency shift, bandwidth reduction and integrated backscatter coefficient-were recorded. These parameters were successfully used to map the progression of the biofilms in time and to differentiate between single- and multiple-species biofilms. Results were compared with those for confocal microscopy and theoretical evaluation of form factor. We conclude that high-frequency ultrasound may prove a useful modality to detect and characterize bacterial biofilms in humans as they form on tissues and plastic materials.
NASA Astrophysics Data System (ADS)
Evrendilek, F.; Karakaya, N.
2014-06-01
Continuous time-series measurements of diel dissolved oxygen (DO) through online sensors are vital to better understanding and management of metabolism of lake ecosystems, but are prone to noise. Discrete wavelet transforms (DWT) with the orthogonal Symmlet and the semiorthogonal Chui-Wang B-spline were compared in denoising diel, daytime and nighttime dynamics of DO, water temperature, pH, and chlorophyll-a. Predictive efficacies of multiple non-linear regression (MNLR) models of DO dynamics were evaluated with or without DWT denoising of either the response variable alone or all the response and explanatory variables. The combined use of the B-spline-based denoising of all the variables and the temporally partitioned data improved both the predictive power and the errors of the MNLR models better than the use of Symmlet DWT denoising of DO only or all the variables with or without the temporal partitioning.
Optimal rejection of multiplicative noise via adaptive shrinkage of undecimated wavelet coefficients
NASA Astrophysics Data System (ADS)
Alparone, Luciano; Anghele, Nicola; Argenti, Fabrizio
2001-12-01
In this paper speckle reduction is approached as a Wiener-like filtering performed in the wavelet domain by means of an adaptive shrinkage of the detail coefficients of an undecimated decomposition. The amplitude of each coefficient is divided by the variance ratio of the noisy coefficient to the noise-free one. All the above quantities are analytically calculated from the speckled image, the speckle variance, and the wavelet filters. On the test image Lenna corrupted by synthetic speckle, the proposed method outperforms Kuan's LLMMSE filtering by almost 3 dB SNR. Experiments carried out on true and synthetic speckled images demonstrate that the visual quality of the results is excellent in terms of both background smoothing and preservation of edge sharpness and textures. The absence of decimation in the wavelet decomposition avoids the typical ringing impairments produced by critically-subsampled wavelet-based denoising.
Streak image denoising and segmentation using adaptive Gaussian guided filter.
Jiang, Zhuocheng; Guo, Baoping
2014-09-10
In streak tube imaging lidar (STIL), streak images are obtained using a CCD camera. However, noise in the captured streak images can greatly affect the quality of reconstructed 3D contrast and range images. The greatest challenge for streak image denoising is reducing the noise while preserving details. In this paper, we propose an adaptive Gaussian guided filter (AGGF) for noise removal and detail enhancement of streak images. The proposed algorithm is based on a guided filter (GF) and part of an adaptive bilateral filter (ABF). In the AGGF, the details are enhanced by optimizing the offset parameter. AGGF-denoised streak images are significantly sharper than those denoised by the GF. Moreover, the AGGF is a fast linear time algorithm achieved by recursively implementing a Gaussian filter kernel. Experimentally, AGGF demonstrates its capacity to preserve edges and thin structures and outperforms the existing bilateral filter and domain transform filter in terms of both visual quality and peak signal-to-noise ratio performance.
Microseismic event denoising via adaptive directional vector median filters
NASA Astrophysics Data System (ADS)
Zheng, Jing; Lu, Ji-Ren; Jiang, Tian-Qi; Liang, Zhe
2017-01-01
We present a novel denoising scheme via Radon transform-based adaptive vector directional median filters named adaptive directional vector median filter (AD-VMF) to suppress noise for microseismic downhole dataset. AD-VMF contains three major steps for microseismic downhole data processing: (i) applying Radon transform on the microseismic data to obtain the parameters of the waves, (ii) performing S-transform to determine the parameters for filters, and (iii) applying the parameters for vector median filter (VMF) to denoise the data. The steps (i) and (ii) can realize the automatic direction detection. The proposed algorithm is tested with synthetic and field datasets that were recorded with a vertical array of receivers. The P-wave and S-wave direct arrivals are properly denoised for poor signal-to-noise ratio (SNR) records. In the simulation case, we also evaluate the performance with mean square error (MSE) in terms of signal-to-noise ratio (SNR). The result shows that the distortion of the proposed method is very low; the SNR is even less than 0 dB.
The application of wavelet shrinkage denoising to magnetic Barkhausen noise measurements
Thomas, James
2014-02-18
The application of Magnetic Barkhausen Noise (MBN) as a non-destructive method of defect detection has proliferated throughout the manufacturing community. Instrument technology and measurement methodology have matured commensurately as applications have moved from the R and D labs to the fully automated manufacturing environment. These new applications present a new set of challenges including a bevy of error sources. A significant obstacle in many industrial applications is a decrease in signal to noise ratio due to (i) environmental EMI and (II) compromises in sensor design for the purposes of automation. The stochastic nature of MBN presents a challenge to any method of noise reduction. An application of wavelet shrinkage denoising is proposed as a method of decreasing extraneous noise in MBN measurements. The method is tested and yields marked improvement on measurements subject to EMI, grounding noise, and even measurements in ideal conditions.
A cross-correlation based fiber optic white-light interferometry with wavelet transform denoising
NASA Astrophysics Data System (ADS)
Wang, Zhen; Jiang, Yi; Ding, Wenhui; Gao, Ran
2013-09-01
A fiber optic white-light interferometry based on cross-correlation calculation is presented. The detected white-light spectrum signal of fiber optic extrinsic Fabry-Perot interferometric (EFPI) sensor is firstly decomposed by discrete wavelet transform for denoising before interrogating the cavity length of the EFPI sensor. In measurement experiment, the cross-correlation algorithm with multiple-level calculations is performed both for achieving the high measurement resolution and for improving the efficiency of the measurement. The experimental results show that the variation range of the measurement results was 1.265 nm, and the standard deviation of the measurement results can reach 0.375 nm when an EFPI sensor with cavity length of 1500 μm was interrogated.
NASA Astrophysics Data System (ADS)
Li, Ruijie; Dang, Anhong
2015-10-01
This paper investigates a detection scheme without channel state information for wireless optical communication (WOC) systems in turbulence induced fading channel. The proposed scheme can effectively diminish the additive noise caused by background radiation and photodetector, as well as the intensity scintillation caused by turbulence. The additive noise can be mitigated significantly using the modified wavelet threshold denoising algorithm, and then, the intensity scintillation can be attenuated by exploiting the temporal correlation of the WOC channel. Moreover, to improve the performance beyond that of the maximum likelihood decision, the maximum a posteriori probability (MAP) criterion is considered. Compared with conventional blind detection algorithm, simulation results show that the proposed detection scheme can improve the signal-to-noise ratio (SNR) performance about 4.38 dB while the bit error rate and scintillation index (SI) are 1×10-6 and 0.02, respectively.
Soumia, Sid Ahmed; Messali, Zoubeida; Ouahabi, Abdeldjalil; Trepout, Sylvain E-mail: cedric.messaoudi@curie.fr Messaoudi, Cedric E-mail: cedric.messaoudi@curie.fr Marco, Sergio E-mail: cedric.messaoudi@curie.fr
2015-01-13
The 3D reconstruction of the Cryo-Transmission Electron Microscopy (Cryo-TEM) and Energy Filtering TEM images (EFTEM) hampered by the noisy nature of these images, so that their alignment becomes so difficult. This noise refers to the collision between the frozen hydrated biological samples and the electrons beam, where the specimen is exposed to the radiation with a high exposure time. This sensitivity to the electrons beam led specialists to obtain the specimen projection images at very low exposure time, which resulting the emergence of a new problem, an extremely low signal-to-noise ratio (SNR). This paper investigates the problem of TEM images denoising when they are acquired at very low exposure time. So, our main objective is to enhance the quality of TEM images to improve the alignment process which will in turn improve the three dimensional tomography reconstructions. We have done multiple tests on special TEM images acquired at different exposure time 0.5s, 0.2s, 0.1s and 1s (i.e. with different values of SNR)) and equipped by Golding beads for helping us in the assessment step. We herein, propose a structure to combine multiple noisy copies of the TEM images. The structure is based on four different denoising methods, to combine the multiple noisy TEM images copies. Namely, the four different methods are Soft, the Hard as Wavelet-Thresholding methods, Bilateral Filter as a non-linear technique able to maintain the edges neatly, and the Bayesian approach in the wavelet domain, in which context modeling is used to estimate the parameter for each coefficient. To ensure getting a high signal-to-noise ratio, we have guaranteed that we are using the appropriate wavelet family at the appropriate level. So we have chosen âĂIJsym8âĂİ wavelet at level 3 as the most appropriate parameter. Whereas, for the bilateral filtering many tests are done in order to determine the proper filter parameters represented by the size of the filter, the range parameter and the
NASA Astrophysics Data System (ADS)
Soumia, Sid Ahmed; Messali, Zoubeida; Ouahabi, Abdeldjalil; Trepout, Sylvain; Messaoudi, Cedric; Marco, Sergio
2015-01-01
The 3D reconstruction of the Cryo-Transmission Electron Microscopy (Cryo-TEM) and Energy Filtering TEM images (EFTEM) hampered by the noisy nature of these images, so that their alignment becomes so difficult. This noise refers to the collision between the frozen hydrated biological samples and the electrons beam, where the specimen is exposed to the radiation with a high exposure time. This sensitivity to the electrons beam led specialists to obtain the specimen projection images at very low exposure time, which resulting the emergence of a new problem, an extremely low signal-to-noise ratio (SNR). This paper investigates the problem of TEM images denoising when they are acquired at very low exposure time. So, our main objective is to enhance the quality of TEM images to improve the alignment process which will in turn improve the three dimensional tomography reconstructions. We have done multiple tests on special TEM images acquired at different exposure time 0.5s, 0.2s, 0.1s and 1s (i.e. with different values of SNR)) and equipped by Golding beads for helping us in the assessment step. We herein, propose a structure to combine multiple noisy copies of the TEM images. The structure is based on four different denoising methods, to combine the multiple noisy TEM images copies. Namely, the four different methods are Soft, the Hard as Wavelet-Thresholding methods, Bilateral Filter as a non-linear technique able to maintain the edges neatly, and the Bayesian approach in the wavelet domain, in which context modeling is used to estimate the parameter for each coefficient. To ensure getting a high signal-to-noise ratio, we have guaranteed that we are using the appropriate wavelet family at the appropriate level. So we have chosen âĂIJsym8âĂİ wavelet at level 3 as the most appropriate parameter. Whereas, for the bilateral filtering many tests are done in order to determine the proper filter parameters represented by the size of the filter, the range parameter and the
NASA Astrophysics Data System (ADS)
Wang, Yanxue; He, Zhengjia; Zi, Yanyang
2010-01-01
In order to enhance the desired features related to some special type of machine fault, a technique based on the dual-tree complex wavelet transform (DTCWT) is proposed in this paper. It is demonstrated that DTCWT enjoys better shift invariance and reduced spectral aliasing than second-generation wavelet transform (SGWT) and empirical mode decomposition by means of numerical simulations. These advantages of the DTCWT arise from the relationship between the two dual-tree wavelet basis functions, instead of the matching of the used single wavelet basis function to the signal being analyzed. Since noise inevitably exists in the measured signals, an enhanced vibration signals denoising algorithm incorporating DTCWT with NeighCoeff shrinkage is also developed. Denoising results of vibration signals resulting from a crack gear indicate the proposed denoising method can effectively remove noise and retain the valuable information as much as possible compared to those DWT- and SGWT-based NeighCoeff shrinkage denoising methods. As is well known, excavation of comprehensive signatures embedded in the vibration signals is of practical importance to clearly clarify the roots of the fault, especially the combined faults. In the case of multiple features detection, diagnosis results of rolling element bearings with combined faults and an actual industrial equipment confirm that the proposed DTCWT-based method is a powerful and versatile tool and consistently outperforms SGWT and fast kurtogram, which are widely used recently. Moreover, it must be noted, the proposed method is completely suitable for on-line surveillance and diagnosis due to its good robustness and efficient algorithm.
Parallel adaptive wavelet collocation method for PDEs
Nejadmalayeri, Alireza; Vezolainen, Alexei; Brown-Dymkoski, Eric; Vasilyev, Oleg V.
2015-10-01
A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution. The data are stored using tree-like structure with tree roots starting at a priori defined level of resolution. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quanta of data to be migrated between the processes. This allows fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process. The parallel efficiency of the approach is discussed based on parallel adaptive wavelet-based Coherent Vortex Simulations of homogeneous turbulence with linear forcing at effective non-adaptive resolutions up to 2048{sup 3} using as many as 2048 CPU cores.
Parallel adaptive wavelet collocation method for PDEs
NASA Astrophysics Data System (ADS)
Nejadmalayeri, Alireza; Vezolainen, Alexei; Brown-Dymkoski, Eric; Vasilyev, Oleg V.
2015-10-01
A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution. The data are stored using tree-like structure with tree roots starting at a priori defined level of resolution. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quanta of data to be migrated between the processes. This allows fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process. The parallel efficiency of the approach is discussed based on parallel adaptive wavelet-based Coherent Vortex Simulations of homogeneous turbulence with linear forcing at effective non-adaptive resolutions up to 20483 using as many as 2048 CPU cores.
Mathematical theorems of adaptive wavelet transform
NASA Astrophysics Data System (ADS)
Szu, Harold H.; Telfer, Brian A.
1994-03-01
The computational efficiency of the adaptive wavelet transform (AWT) is due both to the compact support closely matching with signal characteristics, and to a larger redundancy factor of the superposition-mother (s(x), or in short super-mother, created adaptively by a linear superposition of other admissible mother wavelets. We prove that the super-mother always forms a complete basis, but usually associated with a higher redundancy number than its constituent C.O.N. bases. Then, in terms of Daubechies frame redundancy, we prove that the robustness of super-mother in suffering less noise contamination (since noise is everywhere, and a redundant sampling by band-passings can suppress the noise and enhance the signal). Since the continuous function of super- mother has been created with least-mean-squares (LMS) off-line using neural nets and is formulated in discrete approximation in terms of high-pass and low-pass filter bank coefficients, then such a digital subband coding via QMF saves the in-situ computational time of AWT. Moreover, the power of such an adaptive wavelet transform is due to the potential of massive parallel real-time implementation by means of artificial neural networks, where each node is a daughter wavelet similar to a radial basis function using dyadic affine scaling.
Locally adaptive bilateral clustering for universal image denoising
NASA Astrophysics Data System (ADS)
Toh, K. K. V.; Mat Isa, N. A.
2012-12-01
This paper presents a novel and efficient locally adaptive denoising method based on clustering of pixels into regions of similar geometric and radiometric structures. Clustering is performed by adaptively segmenting pixels in the local kernel based on their augmented variational series. Then, noise pixels are restored by selectively considering the radiometric and spatial properties of every pixel in the formed clusters. The proposed method is exceedingly robust in conveying reliable local structural information even in the presence of noise. As a result, the proposed method substantially outperforms other state-of-the-art methods in terms of image restoration and computational cost. We support our claims with ample simulated and real data experiments. The relatively fast runtime from extensive simulations also suggests that the proposed method is suitable for a variety of image-based products — either embedded in image capturing devices or applied as image enhancement software.
Mouse EEG spike detection based on the adapted continuous wavelet transform
NASA Astrophysics Data System (ADS)
Tieng, Quang M.; Kharatishvili, Irina; Chen, Min; Reutens, David C.
2016-04-01
Objective. Electroencephalography (EEG) is an important tool in the diagnosis of epilepsy. Interictal spikes on EEG are used to monitor the development of epilepsy and the effects of drug therapy. EEG recordings are generally long and the data voluminous. Thus developing a sensitive and reliable automated algorithm for analyzing EEG data is necessary. Approach. A new algorithm for detecting and classifying interictal spikes in mouse EEG recordings is proposed, based on the adapted continuous wavelet transform (CWT). The construction of the adapted mother wavelet is founded on a template obtained from a sample comprising the first few minutes of an EEG data set. Main Result. The algorithm was tested with EEG data from a mouse model of epilepsy and experimental results showed that the algorithm could distinguish EEG spikes from other transient waveforms with a high degree of sensitivity and specificity. Significance. Differing from existing approaches, the proposed approach combines wavelet denoising, to isolate transient signals, with adapted CWT-based template matching, to detect true interictal spikes. Using the adapted wavelet constructed from a predefined template, the adapted CWT is calculated on small EEG segments to fit dynamical changes in the EEG recording.
Denoising of magnetotelluric signals by polarization analysis in the discrete wavelet domain
NASA Astrophysics Data System (ADS)
Carbonari, R.; D'Auria, L.; Di Maio, R.; Petrillo, Z.
2017-03-01
Magnetotellurics (MT) is one of the prominent geophysical methods for underground deep exploration and, thus, appropriate for applications to petroleum and geothermal research. However, it is not completely reliable when applied in areas characterized by intense urbanization, as the presence of cultural noise may significantly affect the MT impedance tensor estimates and, consequently, the apparent resistivity values that describe the electrical behaviour of the investigated buried structures. The development of denoising techniques of MT data is thus one of the main objectives to make magnetotellurics reliably even in urban or industrialized environments. In this work we propose an algorithm for filtering of MT data affected by temporally localized noise. It exploits the discrete wavelet transform (DWT) that, thanks to the possibility to operates in both time and frequency domain, allows to detect transient components of the MT signal, likely due to disturbances of anthropic nature. The implemented filter relies on the estimate of the ellipticity of the polarized MT wave. The application of the filter to synthetic and field MT data has proven its ability in detecting and removing cultural noise, thus providing apparent resistivity curves more smoothed than those obtained by using raw signals.
Image denoising using a directional adaptive diffusion filter
NASA Astrophysics Data System (ADS)
Zhao, Cuifang; Shi, Caicheng; He, Peikun
2006-11-01
Partial differential equations (PDEs) are well-known due to their good processing results which it can not only smooth the noise but also preserve the edges. But the shortcomings of these processes came to being noticed by people. In some sense, PDE filter is called "cartoon model" as it produces an approximation of the input image, use the same diffusion model and parameters to process noise and signal because it can not differentiate them, therefore, the image is naturally modified toward piecewise constant functions. A new method called a directional adaptive diffusion filter is proposed in the paper, which combines PDE mode with wavelet transform. The undecimated discrete wavelet transform (UDWT) is carried out to get different frequency bands which have obviously directional selectivity and more redundancy details. Experimental results show that the proposed method provides a performance better to preserve textures, small details and global information.
NASA Astrophysics Data System (ADS)
Shi, Fei; Wang, Beibei; Selesnick, Ivan W.; Wang, Yao
2006-01-01
This paper introduces an anisotropic decomposition structure of a recently introduced 3-D dual-tree discrete wavelet transform (DDWT), and explores the applications for video denoising and coding. The 3-D DDWT is an attractive video representation because it isolates motion along different directions in separate subbands, and thus leads to sparse video decompositions. Our previous investigation shows that the 3-D DDWT, compared to the standard discrete wavelet transform (DWT), complies better with the statistical models based on sparse presumptions, and gives better visual and numerical results when used for statistical denoising algorithms. Our research on video compression also shows that even with 4:1 redundancy, the 3-D DDWT needs fewer coefficients to achieve the same coding quality (in PSNR) by applying the iterative projection-based noise shaping scheme proposed by Kingsbury. The proposed anisotropic DDWT extends the superiority of isotropic DDWT with more directional subbands without adding to the redundancy. Unlike the original 3-D DDWT which applies dyadic decomposition along all three directions and produces isotropic frequency spacing, it has a non-uniform tiling of the frequency space. By applying this structure, we can improve the denoising results, and the number of significant coefficients can be reduced further, which is beneficial for video coding.
Liu, Zhiwen; He, Zhengjia; Guo, Wei; Tang, Zhangchun
2016-03-01
In order to extract fault features of large-scale power equipment from strong background noise, a hybrid fault diagnosis method based on the second generation wavelet de-noising (SGWD) and the local mean decomposition (LMD) is proposed in this paper. In this method, a de-noising algorithm of second generation wavelet transform (SGWT) using neighboring coefficients was employed as the pretreatment to remove noise in rotating machinery vibration signals by virtue of its good effect in enhancing the signal-noise ratio (SNR). Then, the LMD method is used to decompose the de-noised signals into several product functions (PFs). The PF corresponding to the faulty feature signal is selected according to the correlation coefficients criterion. Finally, the frequency spectrum is analyzed by applying the FFT to the selected PF. The proposed method is applied to analyze the vibration signals collected from an experimental gearbox and a real locomotive rolling bearing. The results demonstrate that the proposed method has better performances such as high SNR and fast convergence speed than the normal LMD method.
Singh, Omkar; Sunkaria, Ramesh Kumar
2015-01-01
Separating an information-bearing signal from the background noise is a general problem in signal processing. In a clinical environment during acquisition of an electrocardiogram (ECG) signal, The ECG signal is corrupted by various noise sources such as powerline interference (PLI), baseline wander and muscle artifacts. This paper presents novel methods for reduction of powerline interference in ECG signals using empirical wavelet transform (EWT) and adaptive filtering. The proposed methods are compared with the empirical mode decomposition (EMD) based PLI cancellation methods. A total of six methods for PLI reduction based on EMD and EWT are analysed and their results are presented in this paper. The EWT-based de-noising methods have less computational complexity and are more efficient as compared with the EMD-based de-noising methods.
Efficient architecture for adaptive directional lifting-based wavelet transform
NASA Astrophysics Data System (ADS)
Yin, Zan; Zhang, Li; Shi, Guangming
2010-07-01
Adaptive direction lifting-based wavelet transform (ADL) has better performance than conventional lifting both in image compression and de-noising. However, no architecture has been proposed to hardware implement it because of its high computational complexity and huge internal memory requirements. In this paper, we propose a four-stage pipelined architecture for 2 Dimensional (2D) ADL with fast computation and high data throughput. The proposed architecture comprises column direction estimation, column lifting, row direction estimation and row lifting which are performed in parallel in a pipeline mode. Since the column processed data is transposed, the row processor can reuse the column processor which can decrease the design complexity. In the lifting step, predict and update are also performed in parallel. For an 8×8 image sub-block, the proposed architecture can finish the ADL forward transform within 78 clock cycles. The architecture is implemented on Xilinx Virtex5 device on which the frequency can achieve 367 MHz. The processed time is 212.5 ns, which can meet the request of real-time system.
Self-adaptive image denoising based on bidimensional empirical mode decomposition (BEMD).
Guo, Song; Luan, Fangjun; Song, Xiaoyu; Li, Changyou
2014-01-01
To better analyze images with the Gaussian white noise, it is necessary to remove the noise before image processing. In this paper, we propose a self-adaptive image denoising method based on bidimensional empirical mode decomposition (BEMD). Firstly, normal probability plot confirms that 2D-IMF of Gaussian white noise images decomposed by BEMD follow the normal distribution. Secondly, energy estimation equation of the ith 2D-IMF (i=2,3,4,......) is proposed referencing that of ith IMF (i=2,3,4,......) obtained by empirical mode decomposition (EMD). Thirdly, the self-adaptive threshold of each 2D-IMF is calculated. Eventually, the algorithm of the self-adaptive image denoising method based on BEMD is described. From the practical perspective, this is applied for denoising of the magnetic resonance images (MRI) of the brain. And the results show it has a better denoising performance compared with other methods.
Hybrid regularizers-based adaptive anisotropic diffusion for image denoising.
Liu, Kui; Tan, Jieqing; Ai, Liefu
2016-01-01
To eliminate the staircasing effect for total variation filter and synchronously avoid the edges blurring for fourth-order PDE filter, a hybrid regularizers-based adaptive anisotropic diffusion is proposed for image denoising. In the proposed model, the [Formula: see text]-norm is considered as the fidelity term and the regularization term is composed of a total variation regularization and a fourth-order filter. The two filters can be adaptively selected according to the diffusion function. When the pixels locate at the edges, the total variation filter is selected to filter the image, which can preserve the edges. When the pixels belong to the flat regions, the fourth-order filter is adopted to smooth the image, which can eliminate the staircase artifacts. In addition, the split Bregman and relaxation approach are employed in our numerical algorithm to speed up the computation. Experimental results demonstrate that our proposed model outperforms the state-of-the-art models cited in the paper in both the qualitative and quantitative evaluations.
NASA Astrophysics Data System (ADS)
Goossens, Bart; Aelterman, Jan; Luong, Hiep; Pizurica, Aleksandra; Philips, Wilfried
2013-02-01
In digital cameras and mobile phones, there is an ongoing trend to increase the image resolution, decrease the sensor size and to use lower exposure times. Because smaller sensors inherently lead to more noise and a worse spatial resolution, digital post-processing techniques are required to resolve many of the artifacts. Color filter arrays (CFAs), which use alternating patterns of color filters, are very popular because of price and power consumption reasons. However, color filter arrays require the use of a post-processing technique such as demosaicing to recover full resolution RGB images. Recently, there has been some interest in techniques that jointly perform the demosaicing and denoising. This has the advantage that the demosaicing and denoising can be performed optimally (e.g. in the MSE sense) for the considered noise model, while avoiding artifacts introduced when using demosaicing and denoising sequentially. In this paper, we will continue the research line of the wavelet-based demosaicing techniques. These approaches are computationally simple and very suited for combination with denoising. Therefore, we will derive Bayesian Minimum Squared Error (MMSE) joint demosaicing and denoising rules in the complex wavelet packet domain, taking local adaptivity into account. As an image model, we will use Gaussian Scale Mixtures, thereby taking advantage of the directionality of the complex wavelets. Our results show that this technique is well capable of reconstructing fine details in the image, while removing all of the noise, at a relatively low computational cost. In particular, the complete reconstruction (including color correction, white balancing etc) of a 12 megapixel RAW image takes 3.5 sec on a recent mid-range GPU.
Na, Man Gyun; Oh, Seungrohk
2002-11-15
A neuro-fuzzy inference system combined with the wavelet denoising, principal component analysis (PCA), and sequential probability ratio test (SPRT) methods has been developed to monitor the relevant sensor using the information of other sensors. The parameters of the neuro-fuzzy inference system that estimates the relevant sensor signal are optimized by a genetic algorithm and a least-squares algorithm. The wavelet denoising technique was applied to remove noise components in input signals into the neuro-fuzzy system. By reducing the dimension of an input space into the neuro-fuzzy system without losing a significant amount of information, the PCA was used to reduce the time necessary to train the neuro-fuzzy system, simplify the structure of the neuro-fuzzy inference system, and also, make easy the selection of the input signals into the neuro-fuzzy system. By using the residual signals between the estimated signals and the measured signals, the SPRT is applied to detect whether the sensors are degraded or not. The proposed sensor-monitoring algorithm was verified through applications to the pressurizer water level, the pressurizer pressure, and the hot-leg temperature sensors in pressurized water reactors.
Zhang, Z; Tian, X
2005-01-01
The application of a recently proposed denoising implementation for obtaining cognitive evoked potentials (CEPs) at the single-trial level is shown. The aim of this investigation is to develop the technique of extracting CEPs by combining both the third-order correlation and the wavelet denoising methods. First, the noisy CEPs was passed through a finite impulse response filter whose impulse response is matched with the shape of the noise-free signal. It was shown that it is possible to estimate the filter impulse response on basis of a select third-order correlation slice (TOCS) of the input noisy CEPs. Second, the output from the third-order correlation filter is decomposed with bi-orthogonal splines at 5 levels. The CEPs is reconstructed by wavelet final approximation a
2016-01-01
The motivation behind this research is to innovatively combine new methods like wavelet, principal component analysis (PCA), and artificial neural network (ANN) approaches to analyze trade in today’s increasingly difficult and volatile financial futures markets. The main focus of this study is to facilitate forecasting by using an enhanced denoising process on market data, taken as a multivariate signal, in order to deduct the same noise from the open-high-low-close signal of a market. This research offers evidence on the predictive ability and the profitability of abnormal returns of a new hybrid forecasting model using Wavelet-PCA denoising and ANN (named WPCA-NN) on futures contracts of Hong Kong’s Hang Seng futures, Japan’s NIKKEI 225 futures, Singapore’s MSCI futures, South Korea’s KOSPI 200 futures, and Taiwan’s TAIEX futures from 2005 to 2014. Using a host of technical analysis indicators consisting of RSI, MACD, MACD Signal, Stochastic Fast %K, Stochastic Slow %K, Stochastic %D, and Ultimate Oscillator, empirical results show that the annual mean returns of WPCA-NN are more than the threshold buy-and-hold for the validation, test, and evaluation periods; this is inconsistent with the traditional random walk hypothesis, which insists that mechanical rules cannot outperform the threshold buy-and-hold. The findings, however, are consistent with literature that advocates technical analysis. PMID:27248692
Adaptive wavelet simulation of global ocean dynamics
NASA Astrophysics Data System (ADS)
Kevlahan, N. K.-R.; Dubos, T.; Aechtner, M.
2015-07-01
In order to easily enforce solid-wall boundary conditions in the presence of complex coastlines, we propose a new mass and energy conserving Brinkman penalization for the rotating shallow water equations. This penalization does not lead to higher wave speeds in the solid region. The error estimates for the penalization are derived analytically and verified numerically for linearized one dimensional equations. The penalization is implemented in a conservative dynamically adaptive wavelet method for the rotating shallow water equations on the sphere with bathymetry and coastline data from NOAA's ETOPO1 database. This code could form the dynamical core for a future global ocean model. The potential of the dynamically adaptive ocean model is illustrated by using it to simulate the 2004 Indonesian tsunami and wind-driven gyres.
NASA Astrophysics Data System (ADS)
Ren, Zhong; Liu, Guodong; Huang, Zhen
2012-11-01
The image reconstruction is a key step in medical imaging (MI) and its algorithm's performance determinates the quality and resolution of reconstructed image. Although some algorithms have been used, filter back-projection (FBP) algorithm is still the classical and commonly-used algorithm in clinical MI. In FBP algorithm, filtering of original projection data is a key step in order to overcome artifact of the reconstructed image. Since simple using of classical filters, such as Shepp-Logan (SL), Ram-Lak (RL) filter have some drawbacks and limitations in practice, especially for the projection data polluted by non-stationary random noises. So, an improved wavelet denoising combined with parallel-beam FBP algorithm is used to enhance the quality of reconstructed image in this paper. In the experiments, the reconstructed effects were compared between the improved wavelet denoising and others (directly FBP, mean filter combined FBP and median filter combined FBP method). To determine the optimum reconstruction effect, different algorithms, and different wavelet bases combined with three filters were respectively test. Experimental results show the reconstruction effect of improved FBP algorithm is better than that of others. Comparing the results of different algorithms based on two evaluation standards i.e. mean-square error (MSE), peak-to-peak signal-noise ratio (PSNR), it was found that the reconstructed effects of the improved FBP based on db2 and Hanning filter at decomposition scale 2 was best, its MSE value was less and the PSNR value was higher than others. Therefore, this improved FBP algorithm has potential value in the medical imaging.
Adaptively Tuned Iterative Low Dose CT Image Denoising
Hashemi, SayedMasoud; Paul, Narinder S.; Beheshti, Soosan; Cobbold, Richard S. C.
2015-01-01
Improving image quality is a critical objective in low dose computed tomography (CT) imaging and is the primary focus of CT image denoising. State-of-the-art CT denoising algorithms are mainly based on iterative minimization of an objective function, in which the performance is controlled by regularization parameters. To achieve the best results, these should be chosen carefully. However, the parameter selection is typically performed in an ad hoc manner, which can cause the algorithms to converge slowly or become trapped in a local minimum. To overcome these issues a noise confidence region evaluation (NCRE) method is used, which evaluates the denoising residuals iteratively and compares their statistics with those produced by additive noise. It then updates the parameters at the end of each iteration to achieve a better match to the noise statistics. By combining NCRE with the fundamentals of block matching and 3D filtering (BM3D) approach, a new iterative CT image denoising method is proposed. It is shown that this new denoising method improves the BM3D performance in terms of both the mean square error and a structural similarity index. Moreover, simulations and patient results show that this method preserves the clinically important details of low dose CT images together with a substantial noise reduction. PMID:26089972
Adaptively Tuned Iterative Low Dose CT Image Denoising.
Hashemi, SayedMasoud; Paul, Narinder S; Beheshti, Soosan; Cobbold, Richard S C
2015-01-01
Improving image quality is a critical objective in low dose computed tomography (CT) imaging and is the primary focus of CT image denoising. State-of-the-art CT denoising algorithms are mainly based on iterative minimization of an objective function, in which the performance is controlled by regularization parameters. To achieve the best results, these should be chosen carefully. However, the parameter selection is typically performed in an ad hoc manner, which can cause the algorithms to converge slowly or become trapped in a local minimum. To overcome these issues a noise confidence region evaluation (NCRE) method is used, which evaluates the denoising residuals iteratively and compares their statistics with those produced by additive noise. It then updates the parameters at the end of each iteration to achieve a better match to the noise statistics. By combining NCRE with the fundamentals of block matching and 3D filtering (BM3D) approach, a new iterative CT image denoising method is proposed. It is shown that this new denoising method improves the BM3D performance in terms of both the mean square error and a structural similarity index. Moreover, simulations and patient results show that this method preserves the clinically important details of low dose CT images together with a substantial noise reduction.
Paul, Sabyasachi; Suman, V; Sarkar, P K; Ranade, A K; Pulhani, V; Dafauti, S; Datta, D
2013-08-01
A wavelet transform based denoising methodology has been applied to detect the presence of any discernable trend in (137)Cs and (90)Sr activity levels in bore-hole water samples collected four times a year over a period of eight years, from 2002 to 2009, in the vicinity of typical nuclear facilities inside the restricted access zones. The conventional non-parametric methods viz., Mann-Kendall and Spearman rho, along with linear regression when applied for detecting the linear trend in the time series data do not yield results conclusive for trend detection with a confidence of 95% for most of the samples. The stationary wavelet based hard thresholding data pruning method with Haar as the analyzing wavelet was applied to remove the noise present in the same data. Results indicate that confidence interval of the established trend has significantly improved after pre-processing to more than 98% compared to the conventional non-parametric methods when applied to direct measurements.
Adaptive regularization of the NL-means: application to image and video denoising.
Sutour, Camille; Deledalle, Charles-Alban; Aujol, Jean-François
2014-08-01
Image denoising is a central problem in image processing and it is often a necessary step prior to higher level analysis such as segmentation, reconstruction, or super-resolution. The nonlocal means (NL-means) perform denoising by exploiting the natural redundancy of patterns inside an image; they perform a weighted average of pixels whose neighborhoods (patches) are close to each other. This reduces significantly the noise while preserving most of the image content. While it performs well on flat areas and textures, it suffers from two opposite drawbacks: it might over-smooth low-contrasted areas or leave a residual noise around edges and singular structures. Denoising can also be performed by total variation minimization-the Rudin, Osher and Fatemi model-which leads to restore regular images, but it is prone to over-smooth textures, staircasing effects, and contrast losses. We introduce in this paper a variational approach that corrects the over-smoothing and reduces the residual noise of the NL-means by adaptively regularizing nonlocal methods with the total variation. The proposed regularized NL-means algorithm combines these methods and reduces both of their respective defaults by minimizing an adaptive total variation with a nonlocal data fidelity term. Besides, this model adapts to different noise statistics and a fast solution can be obtained in the general case of the exponential family. We develop this model for image denoising and we adapt it to video denoising with 3D patches.
A New Adaptive Mother Wavelet for Electromagnetic Transient Analysis
NASA Astrophysics Data System (ADS)
Guillén, Daniel; Idárraga-Ospina, Gina; Cortes, Camilo
2016-01-01
Wavelet Transform (WT) is a powerful technique of signal processing, its applications in power systems have been increasing to evaluate power system conditions, such as faults, switching transients, power quality issues, among others. Electromagnetic transients in power systems are due to changes in the network configuration, producing non-periodic signals, which have to be identified to avoid power outages in normal operation or transient conditions. In this paper a methodology to develop a new adaptive mother wavelet for electromagnetic transient analysis is proposed. Classification is carried out with an innovative technique based on adaptive wavelets, where filter bank coefficients will be adapted until a discriminant criterion is optimized. Then, its corresponding filter coefficients will be used to get the new mother wavelet, named wavelet ET, which allowed to identify and to distinguish the high frequency information produced by different electromagnetic transients.
WAKES: Wavelet Adaptive Kinetic Evolution Solvers
NASA Astrophysics Data System (ADS)
Mardirian, Marine; Afeyan, Bedros; Larson, David
2016-10-01
We are developing a general capability to adaptively solve phase space evolution equations mixing particle and continuum techniques in an adaptive manner. The multi-scale approach is achieved using wavelet decompositions which allow phase space density estimation to occur with scale dependent increased accuracy and variable time stepping. Possible improvements on the SFK method of Larson are discussed, including the use of multiresolution analysis based Richardson-Lucy Iteration, adaptive step size control in explicit vs implicit approaches. Examples will be shown with KEEN waves and KEEPN (Kinetic Electrostatic Electron Positron Nonlinear) waves, which are the pair plasma generalization of the former, and have a much richer span of dynamical behavior. WAKES techniques are well suited for the study of driven and released nonlinear, non-stationary, self-organized structures in phase space which have no fluid, limit nor a linear limit, and yet remain undamped and coherent well past the drive period. The work reported here is based on the Vlasov-Poisson model of plasma dynamics. Work supported by a Grant from the AFOSR.
Identification of Infinite Dimensional Systems via Adaptive Wavelet Neural Networks
1993-01-01
We consider identification of distributed systems via adaptive wavelet neural networks (AWNNs). We take advantage of the multiresolution property of...wavelet systems and the computational structure of neural networks to approximate the unknown plant successively. A systematic approach is developed
[Curvelet denoising algorithm for medical ultrasound image based on adaptive threshold].
Zhuang, Zhemin; Yao, Weike; Yang, Jinyao; Li, FenLan; Yuan, Ye
2014-11-01
The traditional denoising algorithm for ultrasound images would lost a lot of details and weak edge information when suppressing speckle noise. A new denoising algorithm of adaptive threshold based on curvelet transform is proposed in this paper. The algorithm utilizes differences of coefficients' local variance between texture and smooth region in each layer of ultrasound image to define fuzzy regions and membership functions. In the end, using the adaptive threshold that determine by the membership function to denoise the ultrasound image. The experimental text shows that the algorithm can reduce the speckle noise effectively and retain the detail information of original image at the same time, thus it can greatly enhance the performance of B ultrasound instrument.
Adaptive Filtering in the Wavelet Transform Domain via Genetic Algorithms
2004-08-06
identification. Figure 1 shows a very basic example of this type of system . x(n) Figure 1. Basic system identification using adaptive filters block diagram...block diagram of adaptive wavelet filtering system . The main objective of the system shown in Figure 2 is to minimize the error signal, e(k), which is...in Table 1. Daub4 wavelets use filter banks (Vaidyanathan 1992) containing exactly four elements. 5 Figure 4. Time-Domain Representation of
NASA Astrophysics Data System (ADS)
Tehrani, Kayvan Forouhesh; Mortensen, Luke J.; Kner, Peter
2016-03-01
Wavefront sensorless schemes for correction of aberrations induced by biological specimens require a time invariant property of an image as a measure of fitness. Image intensity cannot be used as a metric for Single Molecule Localization (SML) microscopy because the intensity of blinking fluorophores follows exponential statistics. Therefore a robust intensity-independent metric is required. We previously reported a Fourier Metric (FM) that is relatively intensity independent. The Fourier metric has been successfully tested on two machine learning algorithms, a Genetic Algorithm and Particle Swarm Optimization, for wavefront correction about 50 μm deep inside the Central Nervous System (CNS) of Drosophila. However, since the spatial frequencies that need to be optimized fall into regions of the Optical Transfer Function (OTF) that are more susceptible to noise, adding a level of denoising can improve performance. Here we present wavelet-based approaches to lower the noise level and produce a more consistent metric. We compare performance of different wavelets such as Daubechies, Bi-Orthogonal, and reverse Bi-orthogonal of different degrees and orders for pre-processing of images.
Adaptive Denoising Technique for Robust Analysis of Functional Magnetic Resonance Imaging Data
2007-11-02
or receive while t fMRI o versatil of epoc method ER-fM to the studies comes intra-su functioADAPTIVE DENOISING TECHNIQUE FOR ROBUST ANALYSIS OF...supported in part by the Center for Advanced Software and Biomedical Engineering Consultations (CASBEC), Cairo University, and IBE Technologies , Egypt
Edge-preserving image compression using adaptive lifting wavelet transform
NASA Astrophysics Data System (ADS)
Zhang, Libao; Qiu, Bingchang
2015-07-01
In this paper, a novel 2-D adaptive lifting wavelet transform is presented. The proposed algorithm is designed to further reduce the high-frequency energy of wavelet transform, improve the image compression efficiency and preserve the edge or texture of original images more effectively. In this paper, a new optional direction set, covering the surrounding integer pixels and sub-pixels, is designed. Hence, our algorithm adapts far better to the image orientation features in local image blocks. To obtain the computationally efficient and coding performance, the complete processes of 2-D adaptive lifting wavelet transform is introduced and implemented. Compared with the traditional lifting-based wavelet transform, the adaptive directional lifting and the direction-adaptive discrete wavelet transform, the new structure reduces the high-frequency wavelet coefficients more effectively, and the texture structures of the reconstructed images are more refined and clear than that of the other methods. The peak signal-to-noise ratio and the subjective quality of the reconstructed images are significantly improved.
Adaptive Tensor-Based Principal Component Analysis for Low-Dose CT Image Denoising.
Ai, Danni; Yang, Jian; Fan, Jingfan; Cong, Weijian; Wang, Yongtian
2015-01-01
Computed tomography (CT) has a revolutionized diagnostic radiology but involves large radiation doses that directly impact image quality. In this paper, we propose adaptive tensor-based principal component analysis (AT-PCA) algorithm for low-dose CT image denoising. Pixels in the image are presented by their nearby neighbors, and are modeled as a patch. Adaptive searching windows are calculated to find similar patches as training groups for further processing. Tensor-based PCA is used to obtain transformation matrices, and coefficients are sequentially shrunk by the linear minimum mean square error. Reconstructed patches are obtained, and a denoised image is finally achieved by aggregating all of these patches. The experimental results of the standard test image show that the best results are obtained with two denoising rounds according to six quantitative measures. For the experiment on the clinical images, the proposed AT-PCA method can suppress the noise, enhance the edge, and improve the image quality more effectively than NLM and KSVD denoising methods.
Adaptive Tensor-Based Principal Component Analysis for Low-Dose CT Image Denoising
Ai, Danni; Yang, Jian; Fan, Jingfan; Cong, Weijian; Wang, Yongtian
2015-01-01
Computed tomography (CT) has a revolutionized diagnostic radiology but involves large radiation doses that directly impact image quality. In this paper, we propose adaptive tensor-based principal component analysis (AT-PCA) algorithm for low-dose CT image denoising. Pixels in the image are presented by their nearby neighbors, and are modeled as a patch. Adaptive searching windows are calculated to find similar patches as training groups for further processing. Tensor-based PCA is used to obtain transformation matrices, and coefficients are sequentially shrunk by the linear minimum mean square error. Reconstructed patches are obtained, and a denoised image is finally achieved by aggregating all of these patches. The experimental results of the standard test image show that the best results are obtained with two denoising rounds according to six quantitative measures. For the experiment on the clinical images, the proposed AT-PCA method can suppress the noise, enhance the edge, and improve the image quality more effectively than NLM and KSVD denoising methods. PMID:25993566
Patel, Ameera X; Bullmore, Edward T
2016-11-15
Connectome mapping using techniques such as functional magnetic resonance imaging (fMRI) has become a focus of systems neuroscience. There remain many statistical challenges in analysis of functional connectivity and network architecture from BOLD fMRI multivariate time series. One key statistic for any time series is its (effective) degrees of freedom, df, which will generally be less than the number of time points (or nominal degrees of freedom, N). If we know the df, then probabilistic inference on other fMRI statistics, such as the correlation between two voxel or regional time series, is feasible. However, we currently lack good estimators of df in fMRI time series, especially after the degrees of freedom of the "raw" data have been modified substantially by denoising algorithms for head movement. Here, we used a wavelet-based method both to denoise fMRI data and to estimate the (effective) df of the denoised process. We show that seed voxel correlations corrected for locally variable df could be tested for false positive connectivity with better control over Type I error and greater specificity of anatomical mapping than probabilistic connectivity maps using the nominal degrees of freedom. We also show that wavelet despiked statistics can be used to estimate all pairwise correlations between a set of regional nodes, assign a P value to each edge, and then iteratively add edges to the graph in order of increasing P. These probabilistically thresholded graphs are likely more robust to regional variation in head movement effects than comparable graphs constructed by thresholding correlations. Finally, we show that time-windowed estimates of df can be used for probabilistic connectivity testing or dynamic network analysis so that apparent changes in the functional connectome are appropriately corrected for the effects of transient noise bursts. Wavelet despiking is both an algorithm for fMRI time series denoising and an estimator of the (effective) df of denoised
Adaptive wavelet transform algorithm for lossy image compression
NASA Astrophysics Data System (ADS)
Pogrebnyak, Oleksiy B.; Ramirez, Pablo M.; Acevedo Mosqueda, Marco Antonio
2004-11-01
A new algorithm of locally adaptive wavelet transform based on the modified lifting scheme is presented. It performs an adaptation of the wavelet high-pass filter at the prediction stage to the local image data activity. The proposed algorithm uses the generalized framework for the lifting scheme that permits to obtain easily different wavelet filter coefficients in the case of the (~N, N) lifting. Changing wavelet filter order and different control parameters, one can obtain the desired filter frequency response. It is proposed to perform the hard switching between different wavelet lifting filter outputs according to the local data activity estimate. The proposed adaptive transform possesses a good energy compaction. The designed algorithm was tested on different images. The obtained simulation results show that the visual and quantitative quality of the restored images is high. The distortions are less in the vicinity of high spatial activity details comparing to the non-adaptive transform, which introduces ringing artifacts. The designed algorithm can be used for lossy image compression and in the noise suppression applications.
Adaptive zero-tree structure for curved wavelet image coding
NASA Astrophysics Data System (ADS)
Zhang, Liang; Wang, Demin; Vincent, André
2006-02-01
We investigate the issue of efficient data organization and representation of the curved wavelet coefficients [curved wavelet transform (WT)]. We present an adaptive zero-tree structure that exploits the cross-subband similarity of the curved wavelet transform. In the embedded zero-tree wavelet (EZW) and the set partitioning in hierarchical trees (SPIHT), the parent-child relationship is defined in such a way that a parent has four children, restricted to a square of 2×2 pixels, the parent-child relationship in the adaptive zero-tree structure varies according to the curves along which the curved WT is performed. Five child patterns were determined based on different combinations of curve orientation. A new image coder was then developed based on this adaptive zero-tree structure and the set-partitioning technique. Experimental results using synthetic and natural images showed the effectiveness of the proposed adaptive zero-tree structure for encoding of the curved wavelet coefficients. The coding gain of the proposed coder can be up to 1.2 dB in terms of peak SNR (PSNR) compared to the SPIHT coder. Subjective evaluation shows that the proposed coder preserves lines and edges better than the SPIHT coder.
Steady-state sweep visual evoked potential processing denoised by wavelet transform
NASA Astrophysics Data System (ADS)
Weiderpass, Heinar A.; Yamamoto, Jorge F.; Salomão, Solange R.; Berezovsky, Adriana; Pereira, Josenilson M.; Sacai, Paula Y.; de Oliveira, José P.; Costa, Marcio A.; Burattini, Marcelo N.
2008-03-01
Visually evoked potential (VEP) is a very small electrical signal originated in the visual cortex in response to periodic visual stimulation. Sweep-VEP is a modified VEP procedure used to measure grating visual acuity in non-verbal and preverbal patients. This biopotential is buried in a large amount of electroencephalographic (EEG) noise and movement related artifact. The signal-to-noise ratio (SNR) plays a dominant role in determining both systematic and statistic errors. The purpose of this study is to present a method based on wavelet transform technique for filtering and extracting steady-state sweep-VEP. Counter-phase sine-wave luminance gratings modulated at 6 Hz were used as stimuli to determine sweep-VEP grating acuity thresholds. The amplitude and phase of the second-harmonic (12 Hz) pattern reversal response were analyzed using the fast Fourier transform after the wavelet filtering. The wavelet transform method was used to decompose the VEP signal into wavelet coefficients by a discrete wavelet analysis to determine which coefficients yield significant activity at the corresponding frequency. In a subsequent step only significant coefficients were considered and the remaining was set to zero allowing a reconstruction of the VEP signal. This procedure resulted in filtering out other frequencies that were considered noise. Numerical simulations and analyses of human VEP data showed that this method has provided higher SNR when compared with the classical recursive least squares (RLS) method. An additional advantage was a more appropriate phase analysis showing more realistic second-harmonic amplitude value during phase brake.
Motion-compensated wavelet video coding using adaptive mode selection
NASA Astrophysics Data System (ADS)
Zhai, Fan; Pappas, Thrasyvoulos N.
2004-01-01
A motion-compensated wavelet video coder is presented that uses adaptive mode selection (AMS) for each macroblock (MB). The block-based motion estimation is performed in the spatial domain, and an embedded zerotree wavelet coder (EZW) is employed to encode the residue frame. In contrast to other motion-compensated wavelet video coders, where all the MBs are forced to be in INTER mode, we construct the residue frame by combining the prediction residual of the INTER MBs with the coding residual of the INTRA and INTER_ENCODE MBs. Different from INTER MBs that are not coded, the INTRA and INTER_ENCODE MBs are encoded separately by a DCT coder. By adaptively selecting the quantizers of the INTRA and INTER_ENCODE coded MBs, our goal is to equalize the characteristics of the residue frame in order to improve the overall coding efficiency of the wavelet coder. The mode selection is based on the variance of the MB, the variance of the prediction error, and the variance of the neighboring MBs' residual. Simulations show that the proposed motion-compensated wavelet video coder achieves a gain of around 0.7-0.8dB PSNR over MPEG-2 TM5, and a comparable PSNR to other 2D motion-compensated wavelet-based video codecs. It also provides potential visual quality improvement.
AMA- and RWE- Based Adaptive Kalman Filter for Denoising Fiber Optic Gyroscope Drift Signal
Yang, Gongliu; Liu, Yuanyuan; Li, Ming; Song, Shunguang
2015-01-01
An improved double-factor adaptive Kalman filter called AMA-RWE-DFAKF is proposed to denoise fiber optic gyroscope (FOG) drift signal in both static and dynamic conditions. The first factor is Kalman gain updated by random weighting estimation (RWE) of the covariance matrix of innovation sequence at any time to ensure the lowest noise level of output, but the inertia of KF response increases in dynamic condition. To decrease the inertia, the second factor is the covariance matrix of predicted state vector adjusted by RWE only when discontinuities are detected by adaptive moving average (AMA).The AMA-RWE-DFAKF is applied for denoising FOG static and dynamic signals, its performance is compared with conventional KF (CKF), RWE-based adaptive KF with gain correction (RWE-AKFG), AMA- and RWE- based dual mode adaptive KF (AMA-RWE-DMAKF). Results of Allan variance on static signal and root mean square error (RMSE) on dynamic signal show that this proposed algorithm outperforms all the considered methods in denoising FOG signal. PMID:26512665
AMA- and RWE- Based Adaptive Kalman Filter for Denoising Fiber Optic Gyroscope Drift Signal.
Yang, Gongliu; Liu, Yuanyuan; Li, Ming; Song, Shunguang
2015-10-23
An improved double-factor adaptive Kalman filter called AMA-RWE-DFAKF is proposed to denoise fiber optic gyroscope (FOG) drift signal in both static and dynamic conditions. The first factor is Kalman gain updated by random weighting estimation (RWE) of the covariance matrix of innovation sequence at any time to ensure the lowest noise level of output, but the inertia of KF response increases in dynamic condition. To decrease the inertia, the second factor is the covariance matrix of predicted state vector adjusted by RWE only when discontinuities are detected by adaptive moving average (AMA).The AMA-RWE-DFAKF is applied for denoising FOG static and dynamic signals, its performance is compared with conventional KF (CKF), RWE-based adaptive KF with gain correction (RWE-AKFG), AMA- and RWE- based dual mode adaptive KF (AMA-RWE-DMAKF). Results of Allan variance on static signal and root mean square error (RMSE) on dynamic signal show that this proposed algorithm outperforms all the considered methods in denoising FOG signal.
NASA Astrophysics Data System (ADS)
Peña, M.
2016-10-01
Achieving acceptable signal-to-noise ratio (SNR) can be difficult when working in sparsely populated waters and/or when species have low scattering such as fluid filled animals. The increasing use of higher frequencies and the study of deeper depths in fisheries acoustics, as well as the use of commercial vessels, is raising the need to employ good denoising algorithms. The use of a lower Sv threshold to remove noise or unwanted targets is not suitable in many cases and increases the relative background noise component in the echogram, demanding more effectiveness from denoising algorithms. The Adaptive Wiener Filter (AWF) denoising algorithm is presented in this study. The technique is based on the AWF commonly used in digital photography and video enhancement. The algorithm firstly increments the quality of the data with a variance-dependent smoothing, before estimating the noise level as the envelope of the Sv minima. The AWF denoising algorithm outperforms existing algorithms in the presence of gaussian, speckle and salt & pepper noise, although impulse noise needs to be previously removed. Cleaned echograms present homogenous echotraces with outlined edges.
Digel, S.W.; Zhang, B.; Chiang, J.; Fadili, J.M.; Starck, J.-L.; /Saclay /Stanford U., Statistics Dept.
2005-12-02
Zhang, Fadili, & Starck have recently developed a denoising procedure for Poisson data that offers advantages over other methods of intensity estimation in multiple dimensions. Their procedure, which is nonparametric, is based on thresholding wavelet coefficients. The restoration algorithm applied after thresholding provides good conservation of source flux. We present an investigation of the procedure of Zhang et al. for the detection and characterization of astrophysical sources of high-energy gamma rays, using realistic simulated observations with the Large Area Telescope (LAT). The LAT is to be launched in late 2007 on the Gamma-ray Large Area Space Telescope mission. Source detection in the LAT data is complicated by the low fluxes of point sources relative to the diffuse celestial background, the limited angular resolution, and the tremendous variation of that resolution with energy (from tens of degrees at {approx}30 MeV to 0.1{sup o} at 10 GeV). The algorithm is very fast relative to traditional likelihood model fitting, and permits immediate estimation of spectral properties. Astrophysical sources of gamma rays, especially active galaxies, are typically quite variable, and our current work may lead to a reliable method to quickly characterize the flaring properties of newly-detected sources.
NASA Astrophysics Data System (ADS)
Mishra, C.; Samantaray, A. K.; Chakraborty, G.
2016-05-01
Rolling element bearings are widely used in rotating machines and their faults can lead to excessive vibration levels and/or complete seizure of the machine. Under special operating conditions such as non-uniform or low speed shaft rotation, the available fault diagnosis methods cannot be applied for bearing fault diagnosis with full confidence. Fault symptoms in such operating conditions cannot be easily extracted through usual measurement and signal processing techniques. A typical example is a bearing in heavy rolling mill with variable load and disturbance from other sources. In extremely slow speed operation, variation in speed due to speed controller transients or external disturbances (e.g., varying load) can be relatively high. To account for speed variation, instantaneous angular position instead of time is used as the base variable of signals for signal processing purposes. Even with time synchronous averaging (TSA) and well-established methods like envelope order analysis, rolling element faults in rolling element bearings cannot be easily identified during such operating conditions. In this article we propose to use order tracking on the envelope of the wavelet de-noised estimate of the short-duration angle synchronous averaged signal to diagnose faults in rolling element bearing operating under the stated special conditions. The proposed four-stage sequential signal processing method eliminates uncorrelated content, avoids signal smearing and exposes only the fault frequencies and its harmonics in the spectrum. We use experimental data1
De-striping hyperspectral imagery using wavelet transform and adaptive frequency domain filtering
NASA Astrophysics Data System (ADS)
Pande-Chhetri, Roshan; Abd-Elrahman, Amr
2011-09-01
Hyperspectral imagers are built line-by-line similar to images acquired by pushbroom sensors. They can experience striping artifacts due to variations in detector response to incident imagery. In this research, a method for hyperspectral image de-striping based on wavelet analysis and adaptive Fourier zero-frequency amplitude normalization has been developed. The algorithm was tested against three other de-striping algorithms. Hyperspectral image bands of different scenes with significant striping and random noise, as well as an image with simulated noise, were used in the testing. The results were assessed visually and quantitatively using frequency domain Signal-to-Noise Ratio (SNR), Root Mean Square Error (RMSE) and/or Peak Signal-to-Ratio (PSNR). The results demonstrated the superiority of our proposed algorithm in de-striping hyperspectral images without introducing unwanted artifacts, yet preserving image details. In the noise-induced image results, the proposed method reduced RMSE error and improved PSNR by 3.5 dB which is better than other tested methods. A Combined method, integrating the proposed algorithm with a generic wavelet-based de-noising algorithm, showed significant random noise suppression in addition to stripe reduction with a PSNR value of 4.3 dB. These findings make the algorithm a candidate for practical implementation on remote sensing images including high resolution hyperspectral images contaminated with stripe and random noise.
Adaptive kernel-based image denoising employing semi-parametric regularization.
Bouboulis, Pantelis; Slavakis, Konstantinos; Theodoridis, Sergios
2010-06-01
The main contribution of this paper is the development of a novel approach, based on the theory of Reproducing Kernel Hilbert Spaces (RKHS), for the problem of noise removal in the spatial domain. The proposed methodology has the advantage that it is able to remove any kind of additive noise (impulse, gaussian, uniform, etc.) from any digital image, in contrast to the most commonly used denoising techniques, which are noise dependent. The problem is cast as an optimization task in a RKHS, by taking advantage of the celebrated Representer Theorem in its semi-parametric formulation. The semi-parametric formulation, although known in theory, has so far found limited, to our knowledge, application. However, in the image denoising problem, its use is dictated by the nature of the problem itself. The need for edge preservation naturally leads to such a modeling. Examples verify that in the presence of gaussian noise the proposed methodology performs well compared to wavelet based technics and outperforms them significantly in the presence of impulse or mixed noise.
Adaptive wavelet-based recognition of oscillatory patterns on electroencephalograms
NASA Astrophysics Data System (ADS)
Nazimov, Alexey I.; Pavlov, Alexey N.; Hramov, Alexander E.; Grubov, Vadim V.; Koronovskii, Alexey A.; Sitnikova, Evgenija Y.
2013-02-01
The problem of automatic recognition of specific oscillatory patterns on electroencephalograms (EEG) is addressed using the continuous wavelet-transform (CWT). A possibility of improving the quality of recognition by optimizing the choice of CWT parameters is discussed. An adaptive approach is proposed to identify sleep spindles (SS) and spike wave discharges (SWD) that assumes automatic selection of CWT-parameters reflecting the most informative features of the analyzed time-frequency structures. Advantages of the proposed technique over the standard wavelet-based approaches are considered.
NASA Astrophysics Data System (ADS)
Bitenc, M.; Kieffer, D. S.; Khoshelham, K.
2016-06-01
Terrestrial Laser Scanning (TLS) is a well-known remote sensing tool that enables precise 3D acquisition of surface morphology from distances of a few meters to a few kilometres. The morphological representations obtained are important in engineering geology and rock mechanics, where surface morphology details are of particular interest in rock stability problems and engineering construction. The actual size of the discernible surface detail depends on the instrument range error (noise effect) and effective data resolution (smoothing effect). Range error can be (partly) removed by applying a denoising method. Based on the positive results from previous studies, two denoising methods, namely 2D wavelet transform (WT) and non-local mean (NLM), are tested here, with the goal of obtaining roughness estimations that are suitable in the context of rock engineering practice. Both methods are applied in two variants: conventional Discrete WT (DWT) and Stationary WT (SWT), classic NLM (NLM) and probabilistic NLM (PNLM). The noise effect and denoising performance are studied in relation to the TLS effective data resolution. Analyses are performed on the reference data acquired by a highly precise Advanced TOpometric Sensor (ATOS) on a 20x30 cm rock joint sample. Roughness ratio is computed by comparing the noisy and denoised surfaces to the original ATOS surface. The roughness ratio indicates the success of all denoising methods. Besides, it shows that SWT oversmoothes the surface and the performance of the DWT, NLM and PNLM vary with the noise level and data resolution. The noise effect becomes less prominent when data resolution decreases.
Improving the performance of the prony method using a wavelet domain filter for MRI denoising.
Jaramillo, Rodney; Lentini, Marianela; Paluszny, Marco
2014-01-01
The Prony methods are used for exponential fitting. We use a variant of the Prony method for abnormal brain tissue detection in sequences of T 2 weighted magnetic resonance images. Here, MR images are considered to be affected only by Rician noise, and a new wavelet domain bilateral filtering process is implemented to reduce the noise in the images. This filter is a modification of Kazubek's algorithm and we use synthetic images to show the ability of the new procedure to suppress noise and compare its performance with respect to the original filter, using quantitative and qualitative criteria. The tissue classification process is illustrated using a real sequence of T 2 MR images, and the filter is applied to each image before using the variant of the Prony method.
Wavelet De-noising of GNSS Based Bridge Health Monitoring Data
NASA Astrophysics Data System (ADS)
Ogundipe, Oluropo; Lee, Jae Kang; Roberts, Gethin Wyn
2014-11-01
GNSS signal multipath occurs when the GNSS signal reflects of objects in the antenna environment and arrives at the antenna via multiple paths. A bridge environment is one that is prone to multipath with the bridge structure, as well as passing vehicles providing static and dynamic sources of multipath. In this paper, the Wavelet Transform (WT) is applied to bridge data collected on the Machang cable stayed bridge in Korea. The WT algorithm was applied to the GNSS derived bridge defection data at the mid-span. Up to 41% improvement in RMS was observed afterwavelet shrinkage de-noisingwas applied.Application of this algorithm to the torsion data showed significant improvement with the residual average and RMS decreased by 40% and 45% respectively. This method enabled the generation of more accurate information for bridge health monitoring systems in terms of the analysis of frequency, mode shape and three dimensional defections.
Improving the Performance of the Prony Method Using a Wavelet Domain Filter for MRI Denoising
Lentini, Marianela; Paluszny, Marco
2014-01-01
The Prony methods are used for exponential fitting. We use a variant of the Prony method for abnormal brain tissue detection in sequences of T2 weighted magnetic resonance images. Here, MR images are considered to be affected only by Rician noise, and a new wavelet domain bilateral filtering process is implemented to reduce the noise in the images. This filter is a modification of Kazubek's algorithm and we use synthetic images to show the ability of the new procedure to suppress noise and compare its performance with respect to the original filter, using quantitative and qualitative criteria. The tissue classification process is illustrated using a real sequence of T2 MR images, and the filter is applied to each image before using the variant of the Prony method. PMID:24834108
Adaptive solution of the biharmonic problem with shortly supported cubic spline-wavelets
NASA Astrophysics Data System (ADS)
Černá, Dana; Finěk, Václav
2012-09-01
In our contribution, we design a cubic spline-wavelet basis on the interval. The basis functions have small support and wavelets have vanishing moments. We show that stiffness matrices arising from discretization of the two-dimensional biharmonic problem using a constructed wavelet basis have uniformly bounded condition numbers and these condition numbers are very small. We compare quantitative behavior of adaptive wavelet method with a constructed basis and other cubic spline-wavelet bases, and show the superiority of our construction.
Image Denoising via Bandwise Adaptive Modeling and Regularization Exploiting Nonlocal Similarity.
Xiong, Ruiqin; Liu, Hangfan; Zhang, Xinfeng; Zhang, Jian; Ma, Siwei; Wu, Feng; Gao, Wen
2016-09-27
This paper proposes a new image denoising algorithm based on adaptive signal modeling and regularization. It improves the quality of images by regularizing each image patch using bandwise distribution modeling in transform domain. Instead of using a global model for all the patches in an image, it employs content-dependent adaptive models to address the non-stationarity of image signals and also the diversity among different transform bands. The distribution model is adaptively estimated for each patch individually. It varies from one patch location to another and also varies for different bands. In particular, we consider the estimated distribution to have non-zero expectation. To estimate the expectation and variance parameters for every band of a particular patch, we exploit the nonlocal correlation in image to collect a set of highly similar patches as the data samples to form the distribution. Irrelevant patches are excluded so that such adaptively-learned model is more accurate than a global one. The image is ultimately restored via bandwise adaptive soft-thresholding, based on a Laplacian approximation of the distribution of similar-patch group transform coefficients. Experimental results demonstrate that the proposed scheme outperforms several state-of-the-art denoising methods in both the objective and the perceptual qualities.
Adaptive nonlocal means filtering based on local noise level for CT denoising
Li, Zhoubo; Trzasko, Joshua D.; Lake, David S.; Blezek, Daniel J.; Manduca, Armando; Yu, Lifeng; Fletcher, Joel G.; McCollough, Cynthia H.
2014-01-15
Purpose: To develop and evaluate an image-domain noise reduction method based on a modified nonlocal means (NLM) algorithm that is adaptive to local noise level of CT images and to implement this method in a time frame consistent with clinical workflow. Methods: A computationally efficient technique for local noise estimation directly from CT images was developed. A forward projection, based on a 2D fan-beam approximation, was used to generate the projection data, with a noise model incorporating the effects of the bowtie filter and automatic exposure control. The noise propagation from projection data to images was analytically derived. The analytical noise map was validated using repeated scans of a phantom. A 3D NLM denoising algorithm was modified to adapt its denoising strength locally based on this noise map. The performance of this adaptive NLM filter was evaluated in phantom studies in terms of in-plane and cross-plane high-contrast spatial resolution, noise power spectrum (NPS), subjective low-contrast spatial resolution using the American College of Radiology (ACR) accreditation phantom, and objective low-contrast spatial resolution using a channelized Hotelling model observer (CHO). Graphical processing units (GPU) implementation of this noise map calculation and the adaptive NLM filtering were developed to meet demands of clinical workflow. Adaptive NLM was piloted on lower dose scans in clinical practice. Results: The local noise level estimation matches the noise distribution determined from multiple repetitive scans of a phantom, demonstrated by small variations in the ratio map between the analytical noise map and the one calculated from repeated scans. The phantom studies demonstrated that the adaptive NLM filter can reduce noise substantially without degrading the high-contrast spatial resolution, as illustrated by modulation transfer function and slice sensitivity profile results. The NPS results show that adaptive NLM denoising preserves the
Nonlocal transform-domain denoising of volumetric data with groupwise adaptive variance estimation
NASA Astrophysics Data System (ADS)
Maggioni, Matteo; Foi, Alessandro
2012-03-01
We propose an extension of the BM4D volumetric filter to the denoising of data corrupted by spatially nonuniform noise. BM4D implements the grouping and collaborative filtering paradigm, where similar cubes of voxels are stacked into a four-dimensional "group". Each group undergoes a sparsifying four-dimensional transform, that exploits the local correlation among voxels in each cube and the nonlocal correlation between corresponding voxels of different cubes. Thus, signal and noise are effectively separated in transform domain. In this work we take advantage of the sparsity induced by the four-dimensional transform to provide a spatially adaptive estimation of the local noise variance by applying a robust median estimator of the absolute deviation to the spectrum of each filtered group. The adaptive variance estimates are then used during coefficients shrinkage. Finally, the inverse four-dimensional transform is applied to the filtered group, and each individual cube estimate is adaptively aggregated at its original location. Experiments on medical data corrupted by spatially varying Gaussian and Rician noise demonstrate the efficacy of the proposed approach in volumetric data denoising. In case of magnetic resonance signals, the adaptive variance estimate can be also used to compensate the estimation bias due to the non-zero-mean errors of the Rician-distributed data.
Liu, Qianshun; Bai, Jian; Yu, Feihong
2014-11-10
In an effort to improve compressive sensing and spare signal reconstruction by way of the backtracking-based adaptive orthogonal matching pursuit (BAOMP), a new sparse coding algorithm called improved adaptive backtracking-based OMP (ABOMP) is proposed in this study. Many aspects have been improved compared to the original BAOMP method, including replacing the fixed threshold with an adaptive one, adding residual feedback and support set verification, and others. Because of these ameliorations, the proposed algorithm can more precisely choose the atoms. By adding the adaptive step-size mechanism, it requires much less iteration and thus executes more efficiently. Additionally, a simple but effective contrast enhancement method is also adopted to further improve the denoising results and visual effect. By combining the IABOMP algorithm with the state-of-art dictionary learning algorithm K-SVD, the proposed algorithm achieves better denoising effects for astronomical images. Numerous experimental results show that the proposed algorithm performs successfully and effectively on Gaussian and Poisson noise removal.
Normalized iterative denoising ghost imaging based on the adaptive threshold
NASA Astrophysics Data System (ADS)
Li, Gaoliang; Yang, Zhaohua; Zhao, Yan; Yan, Ruitao; Liu, Xia; Liu, Baolei
2017-02-01
An approach for improving ghost imaging (GI) quality is proposed. In this paper, an iteration model based on normalized GI is built through theoretical analysis. An adaptive threshold value is selected in the iteration model. The initial value of the iteration model is estimated as a step to remove the correlated noise. The simulation and experimental results reveal that the proposed strategy reconstructs a better image than traditional and normalized GI, without adding complexity. The NIDGI-AT scheme does not require prior information regarding the object, and can also choose the threshold adaptively. More importantly, the signal-to-noise ratio (SNR) of the reconstructed image is greatly improved. Therefore, this methodology represents another step towards practical real-world applications.
Adaptive wavelet transform algorithm for image compression applications
NASA Astrophysics Data System (ADS)
Pogrebnyak, Oleksiy B.; Manrique Ramirez, Pablo
2003-11-01
A new algorithm of locally adaptive wavelet transform is presented. The algorithm implements the integer-to-integer lifting scheme. It performs an adaptation of the wavelet function at the prediction stage to the local image data activity. The proposed algorithm is based on the generalized framework for the lifting scheme that permits to obtain easily different wavelet coefficients in the case of the (N~,N) lifting. It is proposed to perform the hard switching between (2, 4) and (4, 4) lifting filter outputs according to an estimate of the local data activity. When the data activity is high, i.e., in the vicinity of edges, the (4, 4) lifting is performed. Otherwise, in the plain areas, the (2,4) decomposition coefficients are calculated. The calculations are rather simples that permit the implementation of the designed algorithm in fixed point DSP processors. The proposed adaptive transform possesses the perfect restoration of the processed data and possesses good energy compactation. The designed algorithm was tested on different images. The proposed adaptive transform algorithm can be used for image/signal lossless compression.
Multi-Scale SSA or Data-Adaptive Wavelets
NASA Astrophysics Data System (ADS)
Yiou, P.; Sornette, D.; Sornette, D.; Sornette, D.; Ghil, M.; Ghil, M.
2001-05-01
Using multi-scale ideas from wavelet analysis, the singular-spectrum analysis (SSA) is extended to the study of nonstationary time series, including the case where their variance diverges. The wavelet transform is similar to a local Fourier transform within a finite moving window whose width W, proportional to the major period of interest, is varied to explore a broad range of such periods. SSA, on the other hand, relies on the construction of the lag-correlation matrix C on M lagged copies of the time series over a fixed window width W proportional to M to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components. The proposed multi-scale SSA is a local SSA analysis within a moving window of width M<= W <= N, where N is the length of the time series. Multi-scale SSA varies W, while keeping a fixed W/M ratio, and uses the eigenvectors of the corresponding lag-correlation matrix C(M) as data-adaptive wavelets; successive eigenvectors of C(M) correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis. Multi-scale SSA thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time-frequency domain, by a suitable localization of the signal's correlation matrix. We present several examples of application to synthetic signals with fractal or power-law behavior which mimic selected features of certain climatic or geophysical time series. The method is applied to the monthly values of the Southern Oscillation index (SOI) which captures major features of the El Niño/Southern Oscillation in the Tropical Pacific. Our methodology highlights an abrupt periodicity shift in the SOI near 1960. This abrupt shift between 5 and 3 years supports the Devil's staircase scenario for the El Niño/Southern Oscillation phenomenon.
Wavelet domain image restoration with adaptive edge-preserving regularization.
Belge, M; Kilmer, M E; Miller, E L
2000-01-01
In this paper, we consider a wavelet based edge-preserving regularization scheme for use in linear image restoration problems. Our efforts build on a collection of mathematical results indicating that wavelets are especially useful for representing functions that contain discontinuities (i.e., edges in two dimensions or jumps in one dimension). We interpret the resulting theory in a statistical signal processing framework and obtain a highly flexible framework for adapting the degree of regularization to the local structure of the underlying image. In particular, we are able to adapt quite easily to scale-varying and orientation-varying features in the image while simultaneously retaining the edge preservation properties of the regularizer. We demonstrate a half-quadratic algorithm for obtaining the restorations from observed data.
Adaptive directional lifting-based wavelet transform for image coding.
Ding, Wenpeng; Wu, Feng; Wu, Xiaolin; Li, Shipeng; Li, Houqiang
2007-02-01
We present a novel 2-D wavelet transform scheme of adaptive directional lifting (ADL) in image coding. Instead of alternately applying horizontal and vertical lifting, as in present practice, ADL performs lifting-based prediction in local windows in the direction of high pixel correlation. Hence, it adapts far better to the image orientation features in local windows. The ADL transform is achieved by existing 1-D wavelets and is seamlessly integrated into the global wavelet transform. The predicting and updating signals of ADL can be derived even at the fractional pixel precision level to achieve high directional resolution, while still maintaining perfect reconstruction. To enhance the ADL performance, a rate-distortion optimized directional segmentation scheme is also proposed to form and code a hierarchical image partition adapting to local features. Experimental results show that the proposed ADL-based image coding technique outperforms JPEG 2000 in both PSNR and visual quality, with the improvement up to 2.0 dB on images with rich orientation features.
Color Image Denoising via Discriminatively Learned Iterative Shrinkage.
Sun, Jian; Sun, Jian; Xu, Zingben
2015-11-01
In this paper, we propose a novel model, a discriminatively learned iterative shrinkage (DLIS) model, for color image denoising. The DLIS is a generalization of wavelet shrinkage by iteratively performing shrinkage over patch groups and whole image aggregation. We discriminatively learn the shrinkage functions and basis from the training pairs of noisy/noise-free images, which can adaptively handle different noise characteristics in luminance/chrominance channels, and the unknown structured noise in real-captured color images. Furthermore, to remove the splotchy real color noises, we design a Laplacian pyramid-based denoising framework to progressively recover the clean image from the coarsest scale to the finest scale by the DLIS model learned from the real color noises. Experiments show that our proposed approach can achieve the state-of-the-art denoising results on both synthetic denoising benchmark and real-captured color images.
Denoising of single-trial matrix representations using 2D nonlinear diffusion filtering.
Mustaffa, I; Trenado, C; Schwerdtfeger, K; Strauss, D J
2010-01-15
In this paper we present a novel application of denoising by means of nonlinear diffusion filters (NDFs). NDFs have been successfully applied for image processing and computer vision areas, particularly in image denoising, smoothing, segmentation, and restoration. We apply two types of NDFs for the denoising of evoked responses in single-trials in a matrix form, the nonlinear isotropic and the anisotropic diffusion filters. We show that by means of NDFs we are able to denoise the evoked potentials resulting in a better extraction of physiologically relevant morphological features over the ongoing experiment. This technique offers the advantage of translation-invariance in comparison to other well-known methods, e.g., wavelet denoising based on maximally decimated filter banks, due to an adaptive diffusion feature. We compare the proposed technique with a wavelet denoising scheme that had been introduced before for evoked responses. It is concluded that NDFs represent a promising and useful approach in the denoising of event related potentials. Novel NDF applications of single-trials of auditory brain responses (ABRs) and the transcranial magnetic stimulation (TMS) evoked electroencephalographic responses denoising are presented in this paper.
Mathematics of adaptive wavelet transforms: relating continuous with discrete transforms
NASA Astrophysics Data System (ADS)
Szu, Harold H.; Telfer, Brian A.
1994-07-01
We prove several theorems and construct explicitly the bridge between the continuous and discrete adaptive wavelet transform (AWT). The computational efficiency of the AWT is a result of its compact support closely matching linearly the signal's time-frequency characteristics, and is also a result of a larger redundancy factor of the superposition-mother s(x) (super-mother), created adaptively by a linear superposition of other admissible mother wavelets. The super-mother always forms a complete basis, but is usually associated with a higher redundancy number than its constituent complete orthonormal bases. The robustness of super-mother suffers less noise contamination (since noise is everywhere, and a redundant sampling by bandpassings can suppress the noise and enhance the signal). Since the continuous super-mother has been created off-line by AWT (using least-mean- squares neural nets), we wish to accomplish fast AWT on line. Thus, we formulate AWT in discrete high-pass (H) and low-pass (L) filter bank coefficients via the quadrature mirror filter, (QMF), a digital subband lossless coding. A linear combination of two special cases of complete biorthogonal normalized (Cbi-ON) QMF [L(z), H(z), L+(z), H+(z)], called (alpha) -bank and (Beta) -bank, becomes a hybrid a(alpha) + b(Beta) -bank (for any real positive constants a and b) that is still admissible, meaning Cbi-ON and lossless. Finally, the power of AWT is the implementation by means of wavelet chips and neurochips, in which each node is a daughter wavelet similar to a radial basis function using dyadic affine scaling.
Application of adaptive wavelet transforms via lifting in image data compression
NASA Astrophysics Data System (ADS)
Ye, Shujiang; Zhang, Ye; Liu, Baisen
2008-10-01
The adaptive wavelet transforms via lifting is proposed. In the transform, update filter is selected by the signal's character. Perfect reconstruction is possible without any overhead cost. To make sure the system's stability, in the lifting scheme of adaptive wavelet, update step is placed before prediction step. The Adaptive wavelet transforms via lifting is benefit for the image compression, because of the high stability, the small coefficients of high frequency parts, and the perfect reconstruction. With the adaptive wavelet transforms via lifting and the SPIHT, the image compression is realized in this paper, and the result is pleasant.
Wavelet methods in multi-conjugate adaptive optics
NASA Astrophysics Data System (ADS)
Helin, T.; Yudytskiy, M.
2013-08-01
The next generation ground-based telescopes rely heavily on adaptive optics for overcoming the limitation of atmospheric turbulence. In the future adaptive optics modalities, like multi-conjugate adaptive optics (MCAO), atmospheric tomography is the major mathematical and computational challenge. In this severely ill-posed problem, a fast and stable reconstruction algorithm is needed that can take into account many real-life phenomena of telescope imaging. We introduce a novel reconstruction method for the atmospheric tomography problem and demonstrate its performance and flexibility in the context of MCAO. Our method is based on using locality properties of compactly supported wavelets, both in the spatial and frequency domains. The reconstruction in the atmospheric tomography problem is obtained by solving the Bayesian MAP estimator with a conjugate-gradient-based algorithm. An accelerated algorithm with preconditioning is also introduced. Numerical performance is demonstrated on the official end-to-end simulation tool OCTOPUS of European Southern Observatory.
NASA Astrophysics Data System (ADS)
Yang, Guang; Ye, Xujiong; Slabaugh, Greg; Keegan, Jennifer; Mohiaddin, Raad; Firmin, David
2016-03-01
In this paper, we propose a novel self-learning based single-image super-resolution (SR) method, which is coupled with dual-tree complex wavelet transform (DTCWT) based denoising to better recover high-resolution (HR) medical images. Unlike previous methods, this self-learning based SR approach enables us to reconstruct HR medical images from a single low-resolution (LR) image without extra training on HR image datasets in advance. The relationships between the given image and its scaled down versions are modeled using support vector regression with sparse coding and dictionary learning, without explicitly assuming reoccurrence or self-similarity across image scales. In addition, we perform DTCWT based denoising to initialize the HR images at each scale instead of simple bicubic interpolation. We evaluate our method on a variety of medical images. Both quantitative and qualitative results show that the proposed approach outperforms bicubic interpolation and state-of-the-art single-image SR methods while effectively removing noise.
Hongda Wang; Chiu-Sing Choy
2016-08-01
The ability of correlation integral for automatic seizure detection using scalp EEG data has been re-examined in this paper. To facilitate the detection performance and overcome the shortcoming of correlation integral, nonlinear adaptive denoising and Kalman filter have been adopted for pre-processing and post-processing. The three-stage algorithm has achieved 84.6% sensitivity and 0.087/h false detection rate, which are comparable to many machine learning based methods, but at much lower computational cost. Since this algorithm is tested with long-term scalp EEG, it has the potential to achieve higher performance with intracranial EEG. The clinical value of this algorithm includes providing a pre-judgement to assist the doctor's diagnosis procedure and acting as a reliable warning system in a wearable device for epilepsy patients.
Blind source separation of multichannel electroencephalogram based on wavelet transform and ICA
NASA Astrophysics Data System (ADS)
You, Rong-Yi; Chen, Zhong
2005-11-01
Combination of the wavelet transform and independent component analysis (ICA) was employed for blind source separation (BSS) of multichannel electroencephalogram (EEG). After denoising the original signals by discrete wavelet transform, high frequency components of some noises and artifacts were removed from the original signals. The denoised signals were reconstructed again for the purpose of ICA, such that the drawback that ICA cannot distinguish noises from source signals can be overcome effectively. The practical processing results showed that this method is an effective way to BSS of multichannel EEG. The method is actually a combination of wavelet transform with adaptive neural network, so it is also useful for BBS of other complex signals.
Efficient Combustion Simulation via the Adaptive Wavelet Collocation Method
NASA Astrophysics Data System (ADS)
Lung, Kevin; Brown-Dymkoski, Eric; Guerrero, Victor; Doran, Eric; Museth, Ken; Balme, Jo; Urberger, Bob; Kessler, Andre; Jones, Stephen; Moses, Billy; Crognale, Anthony
Rocket engine development continues to be driven by the intuition and experience of designers, progressing through extensive trial-and-error test campaigns. Extreme temperatures and pressures frustrate direct observation, while high-fidelity simulation can be impractically expensive owing to the inherent muti-scale, multi-physics nature of the problem. To address this cost, an adaptive multi-resolution PDE solver has been designed which targets the high performance, many-core architecture of GPUs. The adaptive wavelet collocation method is used to maintain a sparse-data representation of the high resolution simulation, greatly reducing the memory footprint while tightly controlling physical fidelity. The tensorial, stencil topology of wavelet-based grids lends itself to highly vectorized algorithms which are necessary to exploit the performance of GPUs. This approach permits efficient implementation of direct finite-rate kinetics, and improved resolution of steep thermodynamic gradients and the smaller mixing scales that drive combustion dynamics. Resolving these scales is crucial for accurate chemical kinetics, which are typically degraded or lost in statistical modeling approaches.
NASA Astrophysics Data System (ADS)
Xiang, Li; Xu, Zhang; Peng, Li; Xiaohui, Hu; Hongda, Chen
2016-05-01
A low power wavelet denoising chip for photoplethysmography (PPG) detection and portable heart rate monitoring is presented. To eliminate noise and improve detection accuracy, Harr wavelet (HWT) is chosen as the processing tool. An optimized finite impulse response structure is proposed to lower the computational complexity of proposed algorithm, which is benefit for reducing the power consumption of proposed chip. The modulus maxima pair location module is design to accurately locate the PPG peaks. A clock control unit is designed to further reduce the power consumption of the proposed chip. Fabricated with the 0.18 μm N-well CMOS 1P6M technology, the power consumption of proposed chip is only 8.12 μW in 1 V voltage supply. Validated with PPG signals in multiparameter intelligent monitoring in intensive care databases and signals acquired by the wrist photoelectric volume detection front end, the proposed chip can accurately detect PPG signals. The average sensitivity and positive prediction are 99.91% and 100%, respectively.
Su, Yi; Shoghi, Kooresh I
2008-11-07
Voxel-based estimation of PET images, generally referred to as parametric imaging, can provide invaluable information about the heterogeneity of an imaging agent in a given tissue. Due to high level of noise in dynamic images, however, the estimated parametric image is often noisy and unreliable. Several approaches have been developed to address this challenge, including spatial noise reduction techniques, cluster analysis and spatial constrained weighted nonlinear least-square (SCWNLS) methods. In this study, we develop and test several noise reduction techniques combined with SCWNLS using simulated dynamic PET images. Both spatial smoothing filters and wavelet-based noise reduction techniques are investigated. In addition, 12 different parametric imaging methods are compared using simulated data. With the combination of noise reduction techniques and SCWNLS methods, more accurate parameter estimation can be achieved than with either of the two techniques alone. A less than 10% relative root-mean-square error is achieved with the combined approach in the simulation study. The wavelet denoising based approach is less sensitive to noise and provides more accurate parameter estimation at higher noise levels. Further evaluation of the proposed methods is performed using actual small animal PET datasets. We expect that the proposed method would be useful for cardiac, neurological and oncologic applications.
Adaptive lifting scheme of wavelet transforms for image compression
NASA Astrophysics Data System (ADS)
Wu, Yu; Wang, Guoyin; Nie, Neng
2001-03-01
Aiming at the demand of adaptive wavelet transforms via lifting, a three-stage lifting scheme (predict-update-adapt) is proposed according to common two-stage lifting scheme (predict-update) in this paper. The second stage is updating stage. The third is adaptive predicting stage. Our scheme is an update-then-predict scheme that can detect jumps in image from the updated data and it needs not any more additional information. The first stage is the key in our scheme. It is the interim of updating. Its coefficient can be adjusted to adapt to data to achieve a better result. In the adaptive predicting stage, we use symmetric prediction filters in the smooth area of image, while asymmetric prediction filters at the edge of jumps to reduce predicting errors. We design these filters using spatial method directly. The inherent relationships between the coefficients of the first stage and the other stages are found and presented by equations. Thus, the design result is a class of filters with coefficient that are no longer invariant. Simulation result of image coding with our scheme is good.
An optimized locally adaptive non-local means denoising filter for cryo-electron microscopy data.
Wei, Dai-Yu; Yin, Chang-Cheng
2010-12-01
Cryo-electron microscopy (cryo-EM) now plays an important role in structural analysis of macromolecular complexes, organelles and cells. However, the cryo-EM images obtained close to focus and under low dose conditions have a very high level of noise and a very low contrast, which hinders high-resolution structural analysis. Here, an optimized locally adaptive non-local (LANL) means filter, which can preserve signal details and simultaneously significantly suppress noise for cryo-EM data, is presented. This filter takes advantage of a wide range of pixels to estimate the denoised pixel values instead of the traditional filter that only uses pixels in the local neighborhood. The filter performed well on simulated data and showed promising results on raw cryo-EM images and tomograms. The predominant advantage of this optimized LANL-means filter is the structural signal and the background are clearly distinguishable. This locally adaptive non-local means filter may become a useful tool in the analysis of cryo-EM data, such as automatic particle picking, extracting structural features and segmentation of tomograms.
Design Methodology of a New Wavelet Basis Function for Fetal Phonocardiographic Signals
Chourasia, Vijay S.; Tiwari, Anil Kumar
2013-01-01
Fetal phonocardiography (fPCG) based antenatal care system is economical and has a potential to use for long-term monitoring due to noninvasive nature of the system. The main limitation of this technique is that noise gets superimposed on the useful signal during its acquisition and transmission. Conventional filtering may result into loss of valuable diagnostic information from these signals. This calls for a robust, versatile, and adaptable denoising method applicable in different operative circumstances. In this work, a novel algorithm based on wavelet transform has been developed for denoising of fPCG signals. Successful implementation of wavelet theory in denoising is heavily dependent on selection of suitable wavelet basis function. This work introduces a new mother wavelet basis function for denoising of fPCG signals. The performance of newly developed wavelet is found to be better when compared with the existing wavelets. For this purpose, a two-channel filter bank, based on characteristics of fPCG signal, is designed. The resultant denoised fPCG signals retain the important diagnostic information contained in the original fPCG signal. PMID:23766693
Research of Gear Fault Detection in Morphological Wavelet Domain
NASA Astrophysics Data System (ADS)
Hong, Shi; Fang-jian, Shan; Bo, Cong; Wei, Qiu
2016-02-01
For extracting mutation information from gear fault signal and achieving a valid fault diagnosis, a gear fault diagnosis method based on morphological mean wavelet transform was designed. Morphological mean wavelet transform is a linear wavelet in the framework of morphological wavelet. Decomposing gear fault signal by this morphological mean wavelet transform could produce signal synthesis operators and detailed synthesis operators. For signal synthesis operators, it was just close to orginal signal, and for detailed synthesis operators, it contained fault impact signal or interference signal and could be catched. The simulation experiment result indicates that, compared with Fourier transform, the morphological mean wavelet transform method can do time-frequency analysis for original signal, effectively catch impact signal appears position; and compared with traditional linear wavelet transform, it has simple structure, easy realization, signal local extremum sensitivity and high denoising ability, so it is more adapted to gear fault real-time detection.
NASA Technical Reports Server (NTRS)
Momoh, James A.; Wang, Yanchun; Dolce, James L.
1997-01-01
This paper describes the application of neural network adaptive wavelets for fault diagnosis of space station power system. The method combines wavelet transform with neural network by incorporating daughter wavelets into weights. Therefore, the wavelet transform and neural network training procedure become one stage, which avoids the complex computation of wavelet parameters and makes the procedure more straightforward. The simulation results show that the proposed method is very efficient for the identification of fault locations.
NASA Astrophysics Data System (ADS)
Nazimov, A. I.; Pavlov, A. N.; Lychagov, V. V.; Semyachkina-Glushkovskaya, O. V.
2013-10-01
A method of adaptive wavelet analysis permitting one to set parameters of the wavelet transform based on principles of the optimization theory is proposed. Applying the method to optical coherent tomography data processing is considered. The efficiency of the proposed method for diagnosing functional disorders in the dynamics of cerebral vessels is illustrated.
Domain adaptation based on deep denoising auto-encoders for classification of remote sensing images
NASA Astrophysics Data System (ADS)
Riz, Emanuele; Demir, Begüm; Bruzzone, Lorenzo
2016-10-01
This paper investigates the effectiveness of deep learning (DL) for domain adaptation (DA) problems in the classification of remote sensing images to generate land-cover maps. To this end, we introduce two different DL architectures: 1) single-stage domain adaptation (SS-DA) architecture; and 2) hierarchal domain adaptation (H-DA) architecture. Both architectures require that a reliable training set is available only for one of the images (i.e., the source domain) from a previous analysis, whereas it is not for another image to be classified (i.e., the target domain). To classify the target domain image, the proposed architectures aim to learn a shared feature representation that is invariant across the source and target domains in a completely unsupervised fashion. To this end, both architectures are defined based on the stacked denoising auto-encoders (SDAEs) due to their high capability to define high-level feature representations. The SS-DA architecture leads to a common feature space by: 1) initially unifying the samples in source and target domains; and 2) then feeding them simultaneously into the SDAE. To further increase the robustness of the shared representations, the H-DA employs: 1) two SDAEs for learning independently the high level representations of source and target domains; and 2) a consensus SDAE to learn the domain invariant high-level features. After obtaining the domain invariant features through proposed architectures, the classifier is trained by the domain invariant labeled samples of the source domain, and then the domain invariant samples of the target domain are classified to generate the related classification map. Experimental results obtained for the classification of very high resolution images confirm the effectiveness of the proposed DL architectures.
Wavelet-Based Adaptive Solvers on Multi-core Architectures for the Simulation of Complex Systems
NASA Astrophysics Data System (ADS)
Rossinelli, Diego; Bergdorf, Michael; Hejazialhosseini, Babak; Koumoutsakos, Petros
We build wavelet-based adaptive numerical methods for the simulation of advection dominated flows that develop multiple spatial scales, with an emphasis on fluid mechanics problems. Wavelet based adaptivity is inherently sequential and in this work we demonstrate that these numerical methods can be implemented in software that is capable of harnessing the capabilities of multi-core architectures while maintaining their computational efficiency. Recent designs in frameworks for multi-core software development allow us to rethink parallelism as task-based, where parallel tasks are specified and automatically mapped into physical threads. This way of exposing parallelism enables the parallelization of algorithms that were considered inherently sequential, such as wavelet-based adaptive simulations. In this paper we present a framework that combines wavelet-based adaptivity with the task-based parallelism. We demonstrate good scaling performance obtained by simulating diverse physical systems on different multi-core and SMP architectures using up to 16 cores.
Mizukuchi, Takashi; Fujii, Masazumi; Hayashi, Yuichiro; Tsuzaka, Masatoshi
2014-01-01
In image-guided brain tumor surgery, intraoperative magnetic resonance imaging (iMRI) is a powerful tool for updating navigational information after brain shift, controlling the resection of brain tumors, and evaluating intraoperative complications. Low-field iMRI scans occasionally generate a lot of noise, the reason for which is yet to be determined. This noise adversely affects the neurosurgeons' interpretations. In this study, in order to improve the image quality of iMR images, we optimized and adapted an unbiased non-local means (UNLM) filter to iMR images. This noise appears to occur at a specific frequency-encoding band. In order to adapt the UNLM filter to the noise, we improved the UNLM, so that de-noising can be performed at different noise levels that occur at different frequency-encoding bands. As a result, clinical iMR images can be de-noised adequately while preserving crucial information, such as edges. The UNLM filter preserved the edges more clearly than did other classical filters attached to an anisotropic diffusion filter. In addition, UNLM de-noising can improve the signal-to-noise ratio of clinical iMR images by more than 2 times (p < 0.01). Although the computational time of the UNLM processing is very long, post-processing of UNLM filter images, for which the parameters were optimized, can be performed during other MRI scans. Therefore, The UNLM filter was more effective than increasing the number of signal averages. The iMR image quality was improved without extension of the MR scanning time. UNLM de-noising in post-processing is expected to improve the diagnosability of low-field iMR images.
Cannistraci, Carlo V; Montevecchi, Franco M; Alessio, Massimo
2009-11-01
Denoising is a fundamental early stage in 2-DE image analysis strongly influencing spot detection or pixel-based methods. A novel nonlinear adaptive spatial filter (median-modified Wiener filter, MMWF), is here compared with five well-established denoising techniques (Median, Wiener, Gaussian, and Polynomial-Savitzky-Golay filters; wavelet denoising) to suggest, by means of fuzzy sets evaluation, the best denoising approach to use in practice. Although median filter and wavelet achieved the best performance in spike and Gaussian denoising respectively, they are unsuitable for contemporary removal of different types of noise, because their best setting is noise-dependent. Vice versa, MMWF that arrived second in each single denoising category, was evaluated as the best filter for global denoising, being its best setting invariant of the type of noise. In addition, median filter eroded the edge of isolated spots and filled the space between close-set spots, whereas MMWF because of a novel filter effect (drop-off-effect) does not suffer from erosion problem, preserves the morphology of close-set spots, and avoids spot and spike fuzzyfication, an aberration encountered for Wiener filter. In our tests, MMWF was assessed as the best choice when the goal is to minimize spot edge aberrations while removing spike and Gaussian noise.
Reversible wavelet filter banks with side informationless spatially adaptive low-pass filters
NASA Astrophysics Data System (ADS)
Abhayaratne, Charith
2011-07-01
Wavelet transforms that have an adaptive low-pass filter are useful in applications that require the signal singularities, sharp transitions, and image edges to be left intact in the low-pass signal. In scalable image coding, the spatial resolution scalability is achieved by reconstructing the low-pass signal subband, which corresponds to the desired resolution level, and discarding other high-frequency wavelet subbands. In such applications, it is vital to have low-pass subbands that are not affected by smoothing artifacts associated with low-pass filtering. We present the mathematical framework for achieving 1-D wavelet transforms that have a spatially adaptive low-pass filter (SALP) using the prediction-first lifting scheme. The adaptivity decisions are computed using the wavelet coefficients, and no bookkeeping is required for the perfect reconstruction. Then, 2-D wavelet transforms that have a spatially adaptive low-pass filter are designed by extending the 1-D SALP framework. Because the 2-D polyphase decompositions are used in this case, the 2-D adaptivity decisions are made nonseparable as opposed to the separable 2-D realization using 1-D transforms. We present examples using the 2-D 5/3 wavelet transform and their lossless image coding and scalable decoding performances in terms of quality and resolution scalability. The proposed 2-D-SALP scheme results in better performance compared to the existing adaptive update lifting schemes.
Lossless image compression with projection-based and adaptive reversible integer wavelet transforms.
Deever, Aaron T; Hemami, Sheila S
2003-01-01
Reversible integer wavelet transforms are increasingly popular in lossless image compression, as evidenced by their use in the recently developed JPEG2000 image coding standard. In this paper, a projection-based technique is presented for decreasing the first-order entropy of transform coefficients and improving the lossless compression performance of reversible integer wavelet transforms. The projection technique is developed and used to predict a wavelet transform coefficient as a linear combination of other wavelet transform coefficients. It yields optimal fixed prediction steps for lifting-based wavelet transforms and unifies many wavelet-based lossless image compression results found in the literature. Additionally, the projection technique is used in an adaptive prediction scheme that varies the final prediction step of the lifting-based transform based on a modeling context. Compared to current fixed and adaptive lifting-based transforms, the projection technique produces improved reversible integer wavelet transforms with superior lossless compression performance. It also provides a generalized framework that explains and unifies many previous results in wavelet-based lossless image compression.
Adaptive-Anisotropic Wavelet Collocation Method on general curvilinear coordinate systems
NASA Astrophysics Data System (ADS)
Brown-Dymkoski, Eric; Vasilyev, Oleg V.
2017-03-01
A new general framework for an Adaptive-Anisotropic Wavelet Collocation Method (A-AWCM) for the solution of partial differential equations is developed. This proposed framework addresses two major shortcomings of existing wavelet-based adaptive numerical methodologies, namely the reliance on a rectangular domain and the "curse of anisotropy", i.e. drastic over-resolution of sheet- and filament-like features arising from the inability of the wavelet refinement mechanism to distinguish highly correlated directional information in the solution. The A-AWCM addresses both of these challenges by incorporating coordinate transforms into the Adaptive Wavelet Collocation Method for the solution of PDEs. The resulting integrated framework leverages the advantages of both the curvilinear anisotropic meshes and wavelet-based adaptive refinement in a complimentary fashion, resulting in greatly reduced cost of resolution for anisotropic features. The proposed Adaptive-Anisotropic Wavelet Collocation Method retains the a priori error control of the solution and fully automated mesh refinement, while offering new abilities through the flexible mesh geometry, including body-fitting. The new A-AWCM is demonstrated for a variety of cases, including parabolic diffusion, acoustic scattering, and unsteady external flow.
Subspace based adaptive denoising of surface EMG from neurological injury patients
NASA Astrophysics Data System (ADS)
Liu, Jie; Ying, Dongwen; Zev Rymer, William; Zhou, Ping
2014-10-01
Objective: After neurological injuries such as spinal cord injury, voluntary surface electromyogram (EMG) signals recorded from affected muscles are often corrupted by interferences, such as spurious involuntary spikes and background noises produced by physiological and extrinsic/accidental origins, imposing difficulties for signal processing. Conventional methods did not well address the problem caused by interferences. It is difficult to mitigate such interferences using conventional methods. The aim of this study was to develop a subspace-based denoising method to suppress involuntary background spikes contaminating voluntary surface EMG recordings. Approach: The Karhunen-Loeve transform was utilized to decompose a noisy signal into a signal subspace and a noise subspace. An optimal estimate of EMG signal is derived from the signal subspace and the noise power. Specifically, this estimator is capable of making a tradeoff between interference reduction and signal distortion. Since the estimator partially relies on the estimate of noise power, an adaptive method was presented to sequentially track the variation of interference power. The proposed method was evaluated using both semi-synthetic and real surface EMG signals. Main results: The experiments confirmed that the proposed method can effectively suppress interferences while keep the distortion of voluntary EMG signal in a low level. The proposed method can greatly facilitate further signal processing, such as onset detection of voluntary muscle activity. Significance: The proposed method can provide a powerful tool for suppressing background spikes and noise contaminating voluntary surface EMG signals of paretic muscles after neurological injuries, which is of great importance for their multi-purpose applications.
Computed Tomography Images De-noising using a Novel Two Stage Adaptive Algorithm.
Fadaee, Mojtaba; Shamsi, Mousa; Saberkari, Hamidreza; Sedaaghi, Mohammad Hossein
2015-01-01
In this paper, an optimal algorithm is presented for de-noising of medical images. The presented algorithm is based on improved version of local pixels grouping and principal component analysis. In local pixels grouping algorithm, blocks matching based on L (2) norm method is utilized, which leads to matching performance improvement. To evaluate the performance of our proposed algorithm, peak signal to noise ratio (PSNR) and structural similarity (SSIM) evaluation criteria have been used, which are respectively according to the signal to noise ratio in the image and structural similarity of two images. The proposed algorithm has two de-noising and cleanup stages. The cleanup stage is carried out comparatively; meaning that it is alternately repeated until the two conditions based on PSNR and SSIM are established. Implementation results show that the presented algorithm has a significant superiority in de-noising. Furthermore, the quantities of SSIM and PSNR values are higher in comparison to other methods.
Computed Tomography Images De-noising using a Novel Two Stage Adaptive Algorithm
Fadaee, Mojtaba; Shamsi, Mousa; Saberkari, Hamidreza; Sedaaghi, Mohammad Hossein
2015-01-01
In this paper, an optimal algorithm is presented for de-noising of medical images. The presented algorithm is based on improved version of local pixels grouping and principal component analysis. In local pixels grouping algorithm, blocks matching based on L2 norm method is utilized, which leads to matching performance improvement. To evaluate the performance of our proposed algorithm, peak signal to noise ratio (PSNR) and structural similarity (SSIM) evaluation criteria have been used, which are respectively according to the signal to noise ratio in the image and structural similarity of two images. The proposed algorithm has two de-noising and cleanup stages. The cleanup stage is carried out comparatively; meaning that it is alternately repeated until the two conditions based on PSNR and SSIM are established. Implementation results show that the presented algorithm has a significant superiority in de-noising. Furthermore, the quantities of SSIM and PSNR values are higher in comparison to other methods. PMID:26955565
NASA Astrophysics Data System (ADS)
DeVore, Ronald A.; Lucier, Bradley J.
The subject of `wavelets' is expanding at such a tremendous rate that it is impossible to give, within these few pages, a complete introduction to all aspects of its theory. We hope, however, to allow the reader to become sufficiently acquainted with the subject to understand, in part, the enthusiasm of its proponents toward its potential application to various numerical problems. Furthermore, we hope that our exposition can guide the reader who wishes to make more serious excursions into the subject. Our viewpoint is biased by our experience in approximation theory and data compression; we warn the reader that there are other viewpoints that are either not represented here or discussed only briefly. For example, orthogonal wavelets were developed primarily in the context of signal processing, an application upon which we touch only indirectly. However, there are several good expositions (e.g. Daubechies (1990) and Rioul and Vetterli (1991)) of this application. A discussion of wavelet decompositions in the context of Littlewood-Paley theory can be found in the monograph of Frazier et al. (1991). We shall also not attempt to give a complete discussion of the history of wavelets. Historical accounts can be found in the book of Meyer (1990) and the introduction of the article of Daubechies (1990). We shall try to give sufficient historical commentary in the course of our presentation to provide some feeling for the subject's development.
NASA Astrophysics Data System (ADS)
Zhang, Yan; Tang, Baoping; Liu, Ziran; Chen, Rengxiang
2016-02-01
Fault diagnosis of rolling element bearings is important for improving mechanical system reliability and performance. Vibration signals contain a wealth of complex information useful for state monitoring and fault diagnosis. However, any fault-related impulses in the original signal are often severely tainted by various noises and the interfering vibrations caused by other machine elements. Narrow-band amplitude demodulation has been an effective technique to detect bearing faults by identifying bearing fault characteristic frequencies. To achieve this, the key step is to remove the corrupting noise and interference, and to enhance the weak signatures of the bearing fault. In this paper, a new method based on adaptive wavelet filtering and spectral subtraction is proposed for fault diagnosis in bearings. First, to eliminate the frequency associated with interfering vibrations, the vibration signal is bandpass filtered with a Morlet wavelet filter whose parameters (i.e. center frequency and bandwidth) are selected in separate steps. An alternative and efficient method of determining the center frequency is proposed that utilizes the statistical information contained in the production functions (PFs). The bandwidth parameter is optimized using a local ‘greedy’ scheme along with Shannon wavelet entropy criterion. Then, to further reduce the residual in-band noise in the filtered signal, a spectral subtraction procedure is elaborated after wavelet filtering. Instead of resorting to a reference signal as in the majority of papers in the literature, the new method estimates the power spectral density of the in-band noise from the associated PF. The effectiveness of the proposed method is validated using simulated data, test rig data, and vibration data recorded from the transmission system of a helicopter. The experimental results and comparisons with other methods indicate that the proposed method is an effective approach to detecting the fault-related impulses
Study on torpedo fuze signal denoising method based on WPT
NASA Astrophysics Data System (ADS)
Zhao, Jun; Sun, Changcun; Zhang, Tao; Ren, Zhiliang
2013-07-01
Torpedo fuze signal denoising is an important action to ensure reliable operation of fuze. Based on the good characteristics of wavelet packet transform (WPT) in signal denoising, the paper used wavelet packet transform to denoise the fuze signal under a complex background interference, and a simulation of the denoising results with Matlab is performed. Simulation result shows that the WPT denoising method can effectively eliminate background noise exist in torpedo fuze target signal with higher precision and less distortion, leading to advance the reliability of torpedo fuze operation.
Shape-adaptive discrete wavelet transform for coding arbitrarily shaped texture
NASA Astrophysics Data System (ADS)
Li, Shipeng; Li, Weiping
1997-01-01
This paper presents a shape adaptive discrete wavelet transform (SA-DWT) scheme for coding arbitrarily shaped texture. The proposed SA-DWT can be used for object-oriented image coding. The number of coefficients after SA-DWT is identical to the number of pels contained in the arbitrarily shaped image objects. The locality property of wavelet transform and self-similarity among subbands are well preserved throughout this process.For a rectangular region, the SA-DWT is identical to a standard wavelet transform. With SA-DWT, conventional wavelet based coding schemes can be readily extended to the coding of arbitrarily shaped objects. The proposed shape adaptive wavelet transform is not unitary but the small energy increase is restricted at the boundary of objects in subbands. Two approaches of using the SA-DWT algorithm for object-oriented image and video coding are presented. One is to combine scalar SA-DWT with embedded zerotree wavelet (EZW) coding technique, the other is an extension of the normal vector wavelet coding (VWC) technique to arbitrarily shaped objects. Results of applying SA-VWC to real arbitrarily shaped texture coding are also given at the end of this paper.
NASA Technical Reports Server (NTRS)
Jawerth, Bjoern; Sweldens, Wim
1993-01-01
We present ideas on how to use wavelets in the solution of boundary value ordinary differential equations. Rather than using classical wavelets, we adapt their construction so that they become (bi)orthogonal with respect to the inner product defined by the operator. The stiffness matrix in a Galerkin method then becomes diagonal and can thus be trivially inverted. We show how one can construct an O(N) algorithm for various constant and variable coefficient operators.
Spatially adaptive bases in wavelet-based coding of semi-regular meshes
NASA Astrophysics Data System (ADS)
Denis, Leon; Florea, Ruxandra; Munteanu, Adrian; Schelkens, Peter
2010-05-01
In this paper we present a wavelet-based coding approach for semi-regular meshes, which spatially adapts the employed wavelet basis in the wavelet transformation of the mesh. The spatially-adaptive nature of the transform requires additional information to be stored in the bit-stream in order to allow the reconstruction of the transformed mesh at the decoder side. In order to limit this overhead, the mesh is first segmented into regions of approximately equal size. For each spatial region, a predictor is selected in a rate-distortion optimal manner by using a Lagrangian rate-distortion optimization technique. When compared against the classical wavelet transform employing the butterfly subdivision filter, experiments reveal that the proposed spatially-adaptive wavelet transform significantly decreases the energy of the wavelet coefficients for all subbands. Preliminary results show also that employing the proposed transform for the lowest-resolution subband systematically yields improved compression performance at low-to-medium bit-rates. For the Venus and Rabbit test models the compression improvements add up to 1.47 dB and 0.95 dB, respectively.
An adaptive wavelet neural network for spatio-temporal system identification.
Wei, H L; Billings, S A; Zhao, Y F; Guo, L Z
2010-12-01
Starting from the basic concept of coupled map lattices, a new family of adaptive wavelet neural networks (AWNN) is introduced for spatio-temporal system identification, by combining an efficient wavelet representation with a coupled map lattice model. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimization (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the orthogonal projection pursuit algorithm, significant wavelet neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated wavelet neurons are optimized using a particle swarm optimizer. The resultant network model, obtained in the first stage, may however be redundant. In the second stage, an orthogonal least squares algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet neurons from the network. The proposed two-stage hybrid training procedure can generally produce a parsimonious network model, where a ranked list of wavelet neurons, according to the capability of each neuron to represent the total variance in the system output signal is produced. Two spatio-temporal system identification examples are presented to demonstrate the performance of the proposed new modelling framework.
Yang, Zijing; Cai, Ligang; Gao, Lixin; Wang, Huaqing
2012-01-01
A least square method based on data fitting is proposed to construct a new lifting wavelet, together with the nonlinear idea and redundant algorithm, the adaptive redundant lifting transform based on fitting is firstly stated in this paper. By variable combination selections of basis function, sample number and dimension of basis function, a total of nine wavelets with different characteristics are constructed, which are respectively adopted to perform redundant lifting wavelet transforms on low-frequency approximate signals at each layer. Then the normalized lP norms of the new node-signal obtained through decomposition are calculated to adaptively determine the optimal wavelet for the decomposed approximate signal. Next, the original signal is taken for subsection power spectrum analysis to choose the node-signal for single branch reconstruction and demodulation. Experiment signals and engineering signals are respectively used to verify the above method and the results show that bearing faults can be diagnosed more effectively by the method presented here than by both spectrum analysis and demodulation analysis. Meanwhile, compared with the symmetrical wavelets constructed with Lagrange interpolation algorithm, the asymmetrical wavelets constructed based on data fitting are more suitable in feature extraction of fault signal of roller bearings. PMID:22666035
Coherent structure extraction in turbulent channel flow using boundary adapted wavelets
NASA Astrophysics Data System (ADS)
Sakurai, Teluo; Yoshimatsu, Katsunori; Schneider, Kai; Farge, Marie; Morishita, Koji; Ishihara, Takashi
2017-04-01
We present a construction of isotropic boundary adapted wavelets, which are orthogonal and yield a multi-resolution analysis. We analyze direct numerical simulation data of turbulent channel flow computed at a friction Reynolds number of 395, and investigate the role of coherent vorticity. Thresholding of the vorticity wavelet coefficients allows to split the flow into two parts, coherent and incoherent vorticity. The coherent vorticity is reconstructed from their few intense wavelet coefficients. The statistics of the coherent part, i.e., energy and enstrophy spectra, are close to the statistics of the total flow, and moreover, the nonlinear energy budgets are very well preserved. The remaining incoherent part, represented by the large majority of the weak wavelet coefficients, corresponds to a structureless, i.e., noise-like, background flow whose energy is equidistributed.
A New Adaptive Diffusive Function for Magnetic Resonance Imaging Denoising Based on Pixel Similarity
Heydari, Mostafa; Karami, Mohammad Reza
2015-01-01
Although there are many methods for image denoising, but partial differential equation (PDE) based denoising attracted much attention in the field of medical image processing such as magnetic resonance imaging (MRI). The main advantage of PDE-based denoising approach is laid in its ability to smooth image in a nonlinear way, which effectively removes the noise, as well as preserving edge through anisotropic diffusion controlled by the diffusive function. This function was first introduced by Perona and Malik (P-M) in their model. They proposed two functions that are most frequently used in PDE-based methods. Since these functions consider only the gradient information of a diffused pixel, they cannot remove noise in noisy images with low signal-to-noise (SNR). In this paper we propose a modified diffusive function with fractional power that is based on pixel similarity to improve P-M model for low SNR. We also will show that our proposed function will stabilize the P-M method. As experimental results show, our proposed function that is modified version of P-M function effectively improves the SNR and preserves edges more than P-M functions in low SNR. PMID:26955563
Serial identification of EEG patterns using adaptive wavelet-based analysis
NASA Astrophysics Data System (ADS)
Nazimov, A. I.; Pavlov, A. N.; Nazimova, A. A.; Grubov, V. V.; Koronovskii, A. A.; Sitnikova, E.; Hramov, A. E.
2013-10-01
A problem of recognition specific oscillatory patterns in the electroencephalograms with the continuous wavelet-transform is discussed. Aiming to improve abilities of the wavelet-based tools we propose a serial adaptive method for sequential identification of EEG patterns such as sleep spindles and spike-wave discharges. This method provides an optimal selection of parameters based on objective functions and enables to extract the most informative features of the recognized structures. Different ways of increasing the quality of patterns recognition within the proposed serial adaptive technique are considered.
Optical image compression based on adaptive directional prediction discrete wavelet transform
NASA Astrophysics Data System (ADS)
Zhang, Libao; Qiu, Bingchang
2013-11-01
The traditional lifting wavelet transform cannot effectively reconstruct the nonhorizontal and nonvertical high-frequency information of an image. In this paper, we present a new image compression method based on adaptive directional prediction discrete wavelet transform (ADP-DWT). We first design a directional prediction model to obtain the optimal transform direction of the lifting wavelet. Then, we execute the directional lifting transform along the optimal transform direction. The edge and texture energy can be reduced in the nonhorizontal and nonvertical directions of the high-frequency sub-bands. Finally, the wavelet coefficients are coded with the set partitioning in hierarchical trees (SPIHT) algorithm. The new method holds the advantages of both adaptive directional lifting (ADL) and direction-adaptive discrete wavelet transform (DA-DWT), and the computational complexity is far lower than that in these methods. For the images containing regular and fine textures or edges, the coding preformance of ADP-DWT is better than that of ADL and DA-DWT.
An adaptive non-local means filter for denoising live-cell images and improving particle detection.
Yang, Lei; Parton, Richard; Ball, Graeme; Qiu, Zhen; Greenaway, Alan H; Davis, Ilan; Lu, Weiping
2010-12-01
Fluorescence imaging of dynamical processes in live cells often results in a low signal-to-noise ratio. We present a novel feature-preserving non-local means approach to denoise such images to improve feature recovery and particle detection. The commonly used non-local means filter is not optimal for noisy biological images containing small features of interest because image noise prevents accurate determination of the correct coefficients for averaging, leading to over-smoothing and other artifacts. Our adaptive method addresses this problem by constructing a particle feature probability image, which is based on Haar-like feature extraction. The particle probability image is then used to improve the estimation of the correct coefficients for averaging. We show that this filter achieves higher peak signal-to-noise ratio in denoised images and has a greater capability in identifying weak particles when applied to synthetic data. We have applied this approach to live-cell images resulting in enhanced detection of end-binding-protein 1 foci on dynamically extending microtubules in photo-sensitive Drosophila tissues. We show that our feature-preserving non-local means filter can reduce the threshold of imaging conditions required to obtain meaningful data.
NASA Technical Reports Server (NTRS)
Sjoegreen, B.; Yee, H. C.
2001-01-01
The recently developed essentially fourth-order or higher low dissipative shock-capturing scheme of Yee, Sandham and Djomehri (1999) aimed at minimizing nu- merical dissipations for high speed compressible viscous flows containing shocks, shears and turbulence. To detect non smooth behavior and control the amount of numerical dissipation to be added, Yee et al. employed an artificial compression method (ACM) of Harten (1978) but utilize it in an entirely different context than Harten originally intended. The ACM sensor consists of two tuning parameters and is highly physical problem dependent. To minimize the tuning of parameters and physical problem dependence, new sensors with improved detection properties are proposed. The new sensors are derived from utilizing appropriate non-orthogonal wavelet basis functions and they can be used to completely switch to the extra numerical dissipation outside shock layers. The non-dissipative spatial base scheme of arbitrarily high order of accuracy can be maintained without compromising its stability at all parts of the domain where the solution is smooth. Two types of redundant non-orthogonal wavelet basis functions are considered. One is the B-spline wavelet (Mallat & Zhong 1992) used by Gerritsen and Olsson (1996) in an adaptive mesh refinement method, to determine regions where re nement should be done. The other is the modification of the multiresolution method of Harten (1995) by converting it to a new, redundant, non-orthogonal wavelet. The wavelet sensor is then obtained by computing the estimated Lipschitz exponent of a chosen physical quantity (or vector) to be sensed on a chosen wavelet basis function. Both wavelet sensors can be viewed as dual purpose adaptive methods leading to dynamic numerical dissipation control and improved grid adaptation indicators. Consequently, they are useful not only for shock-turbulence computations but also for computational aeroacoustics and numerical combustion. In addition, these
NASA Astrophysics Data System (ADS)
Messer, Sheila R.; Agzarian, John; Abbott, Derek
2001-05-01
Phonocardiograms (PCGs) have many advantages over traditional auscultation (listening to the heart) because they may be replayed, may be analyzed for spectral and frequency content, and frequencies inaudible to the human ear may be recorded. However, various sources of noise may pollute a PCG including lung sounds, environmental noise and noise generated from contact between the recording device and the skin. Because PCG signals are known to be nonlinear and it is often not possible to determine their noise content, traditional de-noising methods may not be effectively applied. However, other methods including wavelet de-noising, wavelet packet de-noising and averaging can be employed to de-noise the PCG. This study examines and compares these de-noising methods. This study answers such questions as to which de-noising method gives a better SNR, the magnitude of signal information that is lost as a result of the de-noising process, the appropriate uses of the different methods down to such specifics as to which wavelets and decomposition levels give best results in wavelet and wavelet packet de-noising. In general, the wavelet and wavelet packet de-noising performed roughly equally with optimal de-noising occurring at 3-5 levels of decomposition. Averaging also proved a highly useful de- noising technique; however, in some cases averaging is not appropriate. The Hilbert Transform is used to illustrate the results of the de-noising process and to extract instantaneous features including instantaneous amplitude, frequency, and phase.
1994-07-29
Douglas (MDA). This has been extended to the use of local SVD methods and the use of wavelet packets to provide a controlled sparsening. The goal is to be...possibilities for segmenting, compression and denoising signals and one of us (GVW) is using these wavelets to study edge sets with Prof. B. Jawerth. The
A comparison of Monte Carlo dose calculation denoising techniques
NASA Astrophysics Data System (ADS)
El Naqa, I.; Kawrakow, I.; Fippel, M.; Siebers, J. V.; Lindsay, P. E.; Wickerhauser, M. V.; Vicic, M.; Zakarian, K.; Kauffmann, N.; Deasy, J. O.
2005-03-01
Recent studies have demonstrated that Monte Carlo (MC) denoising techniques can reduce MC radiotherapy dose computation time significantly by preferentially eliminating statistical fluctuations ('noise') through smoothing. In this study, we compare new and previously published approaches to MC denoising, including 3D wavelet threshold denoising with sub-band adaptive thresholding, content adaptive mean-median-hybrid (CAMH) filtering, locally adaptive Savitzky-Golay curve-fitting (LASG), anisotropic diffusion (AD) and an iterative reduction of noise (IRON) method formulated as an optimization problem. Several challenging phantom and computed-tomography-based MC dose distributions with varying levels of noise formed the test set. Denoising effectiveness was measured in three ways: by improvements in the mean-square-error (MSE) with respect to a reference (low noise) dose distribution; by the maximum difference from the reference distribution and by the 'Van Dyk' pass/fail criteria of either adequate agreement with the reference image in low-gradient regions (within 2% in our case) or, in high-gradient regions, a distance-to-agreement-within-2% of less than 2 mm. Results varied significantly based on the dose test case: greater reductions in MSE were observed for the relatively smoother phantom-based dose distribution (up to a factor of 16 for the LASG algorithm); smaller reductions were seen for an intensity modulated radiation therapy (IMRT) head and neck case (typically, factors of 2-4). Although several algorithms reduced statistical noise for all test geometries, the LASG method had the best MSE reduction for three of the four test geometries, and performed the best for the Van Dyk criteria. However, the wavelet thresholding method performed better for the head and neck IMRT geometry and also decreased the maximum error more effectively than LASG. In almost all cases, the evaluated methods provided acceleration of MC results towards statistically more accurate
Non-parametric transient classification using adaptive wavelets
NASA Astrophysics Data System (ADS)
Varughese, Melvin M.; von Sachs, Rainer; Stephanou, Michael; Bassett, Bruce A.
2015-11-01
Classifying transients based on multiband light curves is a challenging but crucial problem in the era of GAIA and Large Synoptic Sky Telescope since the sheer volume of transients will make spectroscopic classification unfeasible. We present a non-parametric classifier that predicts the transient's class given training data. It implements two novel components: the use of the BAGIDIS wavelet methodology - a characterization of functional data using hierarchical wavelet coefficients - as well as the introduction of a ranked probability classifier on the wavelet coefficients that handles both the heteroscedasticity of the data in addition to the potential non-representativity of the training set. The classifier is simple to implement while a major advantage of the BAGIDIS wavelets is that they are translation invariant. Hence, BAGIDIS does not need the light curves to be aligned to extract features. Further, BAGIDIS is non-parametric so it can be used effectively in blind searches for new objects. We demonstrate the effectiveness of our classifier against the Supernova Photometric Classification Challenge to correctly classify supernova light curves as Type Ia or non-Ia. We train our classifier on the spectroscopically confirmed subsample (which is not representative) and show that it works well for supernova with observed light-curve time spans greater than 100 d (roughly 55 per cent of the data set). For such data, we obtain a Ia efficiency of 80.5 per cent and a purity of 82.4 per cent, yielding a highly competitive challenge score of 0.49. This indicates that our `model-blind' approach may be particularly suitable for the general classification of astronomical transients in the era of large synoptic sky surveys.
Foi, Alessandro; Katkovnik, Vladimir; Egiazarian, Karen
2007-05-01
The shape-adaptive discrete cosine transform ISA-DCT) transform can be computed on a support of arbitrary shape, but retains a computational complexity comparable to that of the usual separable block-DCT (B-DCT). Despite the near-optimal decorrelation and energy compaction properties, application of the SA-DCT has been rather limited, targeted nearly exclusively to video compression. In this paper, we present a novel approach to image filtering based on the SA-DCT. We use the SA-DCT in conjunction with the Anisotropic Local Polynomial Approximation-Intersection of Confidence Intervals technique, which defines the shape of the transform's support in a pointwise adaptive manner. The thresholded or attenuated SA-DCT coefficients are used to reconstruct a local estimate of the signal within the adaptive-shape support. Since supports corresponding to different points are in general overlapping, the local estimates are averaged together using adaptive weights that depend on the region's statistics. This approach can be used for various image-processing tasks. In this paper, we consider, in particular, image denoising and image deblocking and deringing from block-DCT compression. A special structural constraint in luminance-chrominance space is also proposed to enable an accurate filtering of color images. Simulation experiments show a state-of-the-art quality of the final estimate, both in terms of objective criteria and visual appearance. Thanks to the adaptive support, reconstructed edges are clean, and no unpleasant ringing artifacts are introduced by the fitted transform.
Weak transient fault feature extraction based on an optimized Morlet wavelet and kurtosis
NASA Astrophysics Data System (ADS)
Qin, Yi; Xing, Jianfeng; Mao, Yongfang
2016-08-01
Aimed at solving the key problem in weak transient detection, the present study proposes a new transient feature extraction approach using the optimized Morlet wavelet transform, kurtosis index and soft-thresholding. Firstly, a fast optimization algorithm based on the Shannon entropy is developed to obtain the optimized Morlet wavelet parameter. Compared to the existing Morlet wavelet parameter optimization algorithm, this algorithm has lower computation complexity. After performing the optimized Morlet wavelet transform on the analyzed signal, the kurtosis index is used to select the characteristic scales and obtain the corresponding wavelet coefficients. From the time-frequency distribution of the periodic impulsive signal, it is found that the transient signal can be reconstructed by the wavelet coefficients at several characteristic scales, rather than the wavelet coefficients at just one characteristic scale, so as to improve the accuracy of transient detection. Due to the noise influence on the characteristic wavelet coefficients, the adaptive soft-thresholding method is applied to denoise these coefficients. With the denoised wavelet coefficients, the transient signal can be reconstructed. The proposed method was applied to the analysis of two simulated signals, and the diagnosis of a rolling bearing fault and a gearbox fault. The superiority of the method over the fast kurtogram method was verified by the results of simulation analysis and real experiments. It is concluded that the proposed method is extremely suitable for extracting the periodic impulsive feature from strong background noise.
A wavelet phase filter for emission tomography
Olsen, E.T.; Lin, B.
1995-07-01
The presence of a high level of noise is a characteristic in some tomographic imaging techniques such as positron emission tomography (PET). Wavelet methods can smooth out noise while preserving significant features of images. Mallat et al. proposed a wavelet based denoising scheme exploiting wavelet modulus maxima, but the scheme is sensitive to noise. In this study, the authors explore the properties of wavelet phase, with a focus on reconstruction of emission tomography images. Specifically, they show that the wavelet phase of regular Poisson noise under a Haar-type wavelet transform converges in distribution to a random variable uniformly distributed on [0, 2{pi}). They then propose three wavelet-phase-based denoising schemes which exploit this property: edge tracking, local phase variance thresholding, and scale phase variation thresholding. Some numerical results are also presented. The numerical experiments indicate that wavelet phase techniques show promise for wavelet based denoising methods.
Denoising for 3-d photon-limited imaging data using nonseparable filterbanks.
Santamaria-Pang, Alberto; Bildea, Teodor Stefan; Tan, Shan; Kakadiaris, Ioannis A
2008-12-01
In this paper, we present a novel frame-based denoising algorithm for photon-limited 3-D images. We first construct a new 3-D nonseparable filterbank by adding elements to an existing frame in a structurally stable way. In contrast with the traditional 3-D separable wavelet system, the new filterbank is capable of using edge information in multiple directions. We then propose a data-adaptive hysteresis thresholding algorithm based on this new 3-D nonseparable filterbank. In addition, we develop a new validation strategy for denoising of photon-limited images containing sparse structures, such as neurons (the structure of interest is less than 5% of total volume). The validation method, based on tubular neighborhoods around the structure, is used to determine the optimal threshold of the proposed denoising algorithm. We compare our method with other state-of-the-art methods and report very encouraging results on applications utilizing both synthetic and real data.
Hyperspectral image compression: adapting SPIHT and EZW to anisotropic 3-D wavelet coding.
Christophe, Emmanuel; Mailhes, Corinne; Duhamel, Pierre
2008-12-01
Hyperspectral images present some specific characteristics that should be used by an efficient compression system. In compression, wavelets have shown a good adaptability to a wide range of data, while being of reasonable complexity. Some wavelet-based compression algorithms have been successfully used for some hyperspectral space missions. This paper focuses on the optimization of a full wavelet compression system for hyperspectral images. Each step of the compression algorithm is studied and optimized. First, an algorithm to find the optimal 3-D wavelet decomposition in a rate-distortion sense is defined. Then, it is shown that a specific fixed decomposition has almost the same performance, while being more useful in terms of complexity issues. It is shown that this decomposition significantly improves the classical isotropic decomposition. One of the most useful properties of this fixed decomposition is that it allows the use of zero tree algorithms. Various tree structures, creating a relationship between coefficients, are compared. Two efficient compression methods based on zerotree coding (EZW and SPIHT) are adapted on this near-optimal decomposition with the best tree structure found. Performances are compared with the adaptation of JPEG 2000 for hyperspectral images on six different areas presenting different statistical properties.
Isotropic boundary adapted wavelets for coherent vorticity extraction in turbulent channel flows
NASA Astrophysics Data System (ADS)
Farge, Marie; Sakurai, Teluo; Yoshimatsu, Katsunori; Schneider, Kai; Morishita, Koji; Ishihara, Takashi
2015-11-01
We present a construction of isotropic boundary adapted wavelets, which are orthogonal and yield a multi-resolution analysis. We analyze DNS data of turbulent channel flow computed at a friction-velocity based Reynolds number of 395 and investigate the role of coherent vorticity. Thresholding of the wavelet coefficients allows to split the flow into two parts, coherent and incoherent vorticity. The statistics of the former, i.e., energy and enstrophy spectra, are close to the ones of the total flow, and moreover the nonlinear energy budgets are well preserved. The remaining incoherent part, represented by the large majority of the weak wavelet coefficients, corresponds to a structureless, i.e., noise-like, background flow and exhibits an almost equi-distribution of energy.
Adaptive wavelet packet-based de-speckling of ultrasound images with bilateral filter.
Esakkirajan, Sankaralingam; Vimalraj, Chinna Thambi; Muhammed, Rashad; Subramanian, Ganapathi
2013-12-01
A new adaptive wavelet packet-based approach to minimize speckle noise in ultrasound images is proposed. This method combines wavelet packet thresholding with a bilateral filter. Here, the best bases after wavelet packet decomposition are selected by comparing the first singular value of all sub-bands, and the noisy coefficients are thresholded using a modified NeighShrink technique. The algorithm is tested with various ultrasound images, and the results, in terms of peak signal-to-noise ratio and mean structural similarity values, are compared with those for some well-known de-speckling techniques. The simulation results indicate that the proposed method has better potential to minimize speckle noise and retain fine details of the ultrasound image.
Remote sensing image denoising by using discrete multiwavelet transform techniques
NASA Astrophysics Data System (ADS)
Wang, Haihui; Wang, Jun; Zhang, Jian
2006-01-01
We present a new method by using GHM discrete multiwavelet transform in image denoising on this paper. The developments in wavelet theory have given rise to the wavelet thresholding method, for extracting a signal from noisy data. The method of signal denoising via wavelet thresholding was popularized. Multiwavelets have recently been introduced and they offer simultaneous orthogonality, symmetry and short support. This property makes multiwavelets more suitable for various image processing applications, especially denoising. It is based on thresholding of multiwavelet coefficients arising from the standard scalar orthogonal wavelet transform. It takes into account the covariance structure of the transform. Denoising of images via thresholding of the multiwavelet coefficients result from preprocessing and the discrete multiwavelet transform can be carried out by treating the output in this paper. The form of the threshold is carefully formulated and is the key to the excellent results obtained in the extensive numerical simulations of image denoising. We apply the multiwavelet-based to remote sensing image denoising. Multiwavelet transform technique is rather a new method, and it has a big advantage over the other techniques that it less distorts spectral characteristics of the image denoising. The experimental results show that multiwavelet based image denoising schemes outperform wavelet based method both subjectively and objectively.
A study of interceptor attitude control based on adaptive wavelet neural networks
NASA Astrophysics Data System (ADS)
Li, Da; Wang, Qing-chao
2005-12-01
This paper engages to study the 3-DOF attitude control problem of the kinetic interceptor. When the kinetic interceptor enters into terminal guidance it has to maneuver with large angles. The characteristic of interceptor attitude system is nonlinearity, strong-coupling and MIMO. A kind of inverse control approach based on adaptive wavelet neural networks was proposed in this paper. Instead of using one complex neural network as the controller, the nonlinear dynamics of the interceptor can be approximated by three independent subsystems applying exact feedback-linearization firstly, and then controllers for each subsystem are designed using adaptive wavelet neural networks respectively. This method avoids computing a large amount of the weights and bias in one massive neural network and the control parameters can be adaptive changed online. Simulation results betray that the proposed controller performs remarkably well.
Hill, Paul; Achim, Alin; Al-Mualla, Mohammed Ebrahim; Bull, David
2016-04-11
Accurate estimation of the contrast sensitivity of the human visual system is crucial for perceptually based image processing in applications such as compression, fusion and denoising. Conventional Contrast Sensitivity Functions (CSFs) have been obtained using fixed sized Gabor functions. However, the basis functions of multiresolution decompositions such as wavelets often resemble Gabor functions but are of variable size and shape. Therefore to use conventional contrast sensitivity functions in such cases is not appropriate. We have therefore conducted a set of psychophysical tests in order to obtain the contrast sensitivity function for a range of multiresolution transforms: the Discrete Wavelet Transform (DWT), the Steerable Pyramid, the Dual-Tree Complex Wavelet Transform (DT-CWT) and the Curvelet Transform. These measures were obtained using contrast variation of each transforms' basis functions in a 2AFC experiment combined with an adapted version of the QUEST psychometric function method. The results enable future image processing applications that exploit these transforms such as signal fusion, super-resolution processing, denoising and motion estimation, to be perceptually optimised in a principled fashion. The results are compared to an existing vision model (HDR-VDP2) and are used to show quantitative improvements within a denoising application compared to using conventional CSF values.
Multi-focus image fusion algorithm based on adaptive PCNN and wavelet transform
NASA Astrophysics Data System (ADS)
Wu, Zhi-guo; Wang, Ming-jia; Han, Guang-liang
2011-08-01
Being an efficient method of information fusion, image fusion has been used in many fields such as machine vision, medical diagnosis, military applications and remote sensing. In this paper, Pulse Coupled Neural Network (PCNN) is introduced in this research field for its interesting properties in image processing, including segmentation, target recognition et al. and a novel algorithm based on PCNN and Wavelet Transform for Multi-focus image fusion is proposed. First, the two original images are decomposed by wavelet transform. Then, based on the PCNN, a fusion rule in the Wavelet domain is given. This algorithm uses the wavelet coefficient in each frequency domain as the linking strength, so that its value can be chosen adaptively. Wavelet coefficients map to the range of image gray-scale. The output threshold function attenuates to minimum gray over time. Then all pixels of image get the ignition. So, the output of PCNN in each iteration time is ignition wavelet coefficients of threshold strength in different time. At this moment, the sequences of ignition of wavelet coefficients represent ignition timing of each neuron. The ignition timing of PCNN in each neuron is mapped to corresponding image gray-scale range, which is a picture of ignition timing mapping. Then it can judge the targets in the neuron are obvious features or not obvious. The fusion coefficients are decided by the compare-selection operator with the firing time gradient maps and the fusion image is reconstructed by wavelet inverse transform. Furthermore, by this algorithm, the threshold adjusting constant is estimated by appointed iteration number. Furthermore, In order to sufficient reflect order of the firing time, the threshold adjusting constant αΘ is estimated by appointed iteration number. So after the iteration achieved, each of the wavelet coefficient is activated. In order to verify the effectiveness of proposed rules, the experiments upon Multi-focus image are done. Moreover
Speckle Suppression in Ultrasonic Images Based on Undecimated Wavelets
NASA Astrophysics Data System (ADS)
Argenti, Fabrizio; Torricelli, Gionatan
2003-12-01
An original method to denoise ultrasonic images affected by speckle is presented. Speckle is modeled as a signal-dependent noise corrupting the image. Noise reduction is approached as a Wiener-like filtering performed in a shift-invariant wavelet domain by means of an adaptive rescaling of the coefficients of an undecimated octave decomposition. The scaling factor of each coefficient is calculated from local statistics of the degraded image, the parameters of the noise model, and the wavelet filters. Experimental results demonstrate that excellent background smoothing as well as preservation of edge sharpness and fine details can be obtained.
Sun, Jin; Xu, Xiaosu; Liu, Yiting; Zhang, Tao; Li, Yao
2016-07-12
In order to reduce the influence of fiber optic gyroscope (FOG) random drift error on inertial navigation systems, an improved auto regressive (AR) model is put forward in this paper. First, based on real-time observations at each restart of the gyroscope, the model of FOG random drift can be established online. In the improved AR model, the FOG measured signal is employed instead of the zero mean signals. Then, the modified Sage-Husa adaptive Kalman filter (SHAKF) is introduced, which can directly carry out real-time filtering on the FOG signals. Finally, static and dynamic experiments are done to verify the effectiveness. The filtering results are analyzed with Allan variance. The analysis results show that the improved AR model has high fitting accuracy and strong adaptability, and the minimum fitting accuracy of single noise is 93.2%. Based on the improved AR(3) model, the denoising method of SHAKF is more effective than traditional methods, and its effect is better than 30%. The random drift error of FOG is reduced effectively, and the precision of the FOG is improved.
Sun, Jin; Xu, Xiaosu; Liu, Yiting; Zhang, Tao; Li, Yao
2016-01-01
In order to reduce the influence of fiber optic gyroscope (FOG) random drift error on inertial navigation systems, an improved auto regressive (AR) model is put forward in this paper. First, based on real-time observations at each restart of the gyroscope, the model of FOG random drift can be established online. In the improved AR model, the FOG measured signal is employed instead of the zero mean signals. Then, the modified Sage-Husa adaptive Kalman filter (SHAKF) is introduced, which can directly carry out real-time filtering on the FOG signals. Finally, static and dynamic experiments are done to verify the effectiveness. The filtering results are analyzed with Allan variance. The analysis results show that the improved AR model has high fitting accuracy and strong adaptability, and the minimum fitting accuracy of single noise is 93.2%. Based on the improved AR(3) model, the denoising method of SHAKF is more effective than traditional methods, and its effect is better than 30%. The random drift error of FOG is reduced effectively, and the precision of the FOG is improved. PMID:27420062
Research on infrared-image denoising algorithm based on the noise analysis of the detector
NASA Astrophysics Data System (ADS)
Liu, Songtao; Zhou, Xiaodong; Shen, Tongsheng; Han, Yanli
2005-01-01
Since the conventional denoising algorithms have not considered the influence of certain concrete detector, they are not very effective to remove various noises contained in the low signal-to-noise ration infrared image. In this paper, a new thinking for infrared image denoising is proposed, which is based on the noise analyses of detector with an example of L model infrared multi-element detector. According to the noise analyses of this detector, the emphasis is placed on how to filter white noise and fractal noise in the preprocessing phase. Wavelet analysis is a good tool for analyzing 1/f process. 1/f process can be viewed as white noise approximately since its wavelet coefficients are stationary and uncorrelated. So if wavelet transform is adopted, the problem of removing white noise and fraction noise is simplified as the only one problem, i.e., removing white noise. To address this problem, a new wavelet domain adaptive wiener filtering algorithm is presented. From the viewpoint of quantitative and qualitative analyses, the filtering effect of our method is compared with those of traditional median filter, mean filter and wavelet thresholding algorithm in detail. The results show that our method can reduce various noises effectively and raise the ratio of signal-to-noise evidently.
Wavelet analysis deformation monitoring data of high-speed railway bridge
NASA Astrophysics Data System (ADS)
Tang, ShiHua; Huang, Qing; Zhou, Conglin; Xu, HongWei; Liu, YinTao; Li, FeiDa
2015-12-01
Deformation monitoring data of high-speed railway bridges will inevitably be affected because of noise pollution, A deformation monitoring point of high-speed railway bridge was measurd by using sokkia SDL30 electronic level for a long time,which got a large number of deformation monitoring data. Based on the characteristics of the deformation monitoring data of high-speed railway bridge, which contain lots of noise. Based on the MATLAB software platform, 120 groups of deformation monitoring data were applied to analysis of wavelet denoising.sym6,db6 wavelet basis function were selected to analyze and remove the noise.The original signal was broken into three layers wavelet,which contain high frequency coefficients and low frequency coefficients.However, high frequency coefficient have plenty of noise.Adaptive method of soft and hard threshold were used to handle in the high frequency coefficient.Then,high frequency coefficient that was removed much of noise combined with low frequency coefficient to reconstitute and obtain reconstruction wavelet signal.Root Mean Square Error (RMSE) and Signal-To-Noise Ratio (SNR) were regarded as evaluation index of denoising,The smaller the root mean square error and the greater signal-to-noise ratio indicate that them have a good effect in denoising. We can surely draw some conclusions in the experimental analysis:the db6 wavelet basis function has a good effect in wavelet denoising by using a adaptive soft threshold method,which root mean square error is minimum and signal-to-noise ratio is maximum.Moreover,the reconstructed image are more smooth than original signal denoising after wavelet denoising, which removed noise and useful signal are obtained in the original signal.Compared to the other three methods, this method has a good effect in denoising, which not only retain useful signal in the original signal, but aiso reach the goal of removing noise. So, it has a strong practical value in a actual deformation monitoring
NASA Astrophysics Data System (ADS)
Kakadiaris, Ioannis A.; Konstantinidis, Ioannis; Papadakis, Manos; Ding, Wei; Shen, Lixin
2005-08-01
Three dimensional (3D) surfaces can be sampled parametrically in the form of range image data. Smoothing/denoising of such raw data is usually accomplished by adapting techniques developed for intensity image processing, since both range and intensity images comprise parametrically sampled geometry and appearance measurements, respectively. We present a transform-based algorithm for surface denoising, motivated by our previous work on intensity image denoising, which utilizes a non-separable Parseval frame and an ensemble thresholding scheme. The frame is constructed from separable (tensor) products of a piecewise linear spline tight frame and incorporates the weighted average operator and the Sobel operators in directions that are integer multiples of 45°. We compare the performance of this algorithm with other transform-based methods from the recent literature. Our results indicate that such transform methods are suited to the task of smoothing range images.
Refinement trajectory and determination of eigenstates by a wavelet based adaptive method
Pipek, Janos; Nagy, Szilvia
2006-11-07
The detail structure of the wave function is analyzed at various refinement levels using the methods of wavelet analysis. The eigenvalue problem of a model system is solved in granular Hilbert spaces, and the trajectory of the eigenstates is traced in terms of the resolution. An adaptive method is developed for identifying the fine structure localization regions, where further refinement of the wave function is necessary.
Tian, Xiaoying; Li, Yongshuai; Zhou, Huan; Li, Xiang; Chen, Lisha; Zhang, Xuming
2016-01-01
Electrocardiogram (ECG) signals contain a great deal of essential information which can be utilized by physicians for the diagnosis of heart diseases. Unfortunately, ECG signals are inevitably corrupted by noise which will severely affect the accuracy of cardiovascular disease diagnosis. Existing ECG signal denoising methods based on wavelet shrinkage, empirical mode decomposition and nonlocal means (NLM) cannot provide sufficient noise reduction or well-detailed preservation, especially with high noise corruption. To address this problem, we have proposed a hybrid ECG signal denoising scheme by combining extreme-point symmetric mode decomposition (ESMD) with NLM. In the proposed method, the noisy ECG signals will first be decomposed into several intrinsic mode functions (IMFs) and adaptive global mean using ESMD. Then, the first several IMFs will be filtered by the NLM method according to the frequency of IMFs while the QRS complex detected from these IMFs as the dominant feature of the ECG signal and the remaining IMFs will be left unprocessed. The denoised IMFs and unprocessed IMFs are combined to produce the final denoised ECG signals. Experiments on both simulated ECG signals and real ECG signals from the MIT-BIH database demonstrate that the proposed method can suppress noise in ECG signals effectively while preserving the details very well, and it outperforms several state-of-the-art ECG signal denoising methods in terms of signal-to-noise ratio (SNR), root mean squared error (RMSE), percent root mean square difference (PRD) and mean opinion score (MOS) error index. PMID:27681729
NASA Astrophysics Data System (ADS)
Palaniswamy, Sumithra; Duraisamy, Prakash; Alam, Mohammad Showkat; Yuan, Xiaohui
2012-04-01
Automatic speech processing systems are widely used in everyday life such as mobile communication, speech and speaker recognition, and for assisting the hearing impaired. In speech communication systems, the quality and intelligibility of speech is of utmost importance for ease and accuracy of information exchange. To obtain an intelligible speech signal and one that is more pleasant to listen, noise reduction is essential. In this paper a new Time Adaptive Discrete Bionic Wavelet Thresholding (TADBWT) scheme is proposed. The proposed technique uses Daubechies mother wavelet to achieve better enhancement of speech from additive non- stationary noises which occur in real life such as street noise and factory noise. Due to the integration of human auditory system model into the wavelet transform, bionic wavelet transform (BWT) has great potential for speech enhancement which may lead to a new path in speech processing. In the proposed technique, at first, discrete BWT is applied to noisy speech to derive TADBWT coefficients. Then the adaptive nature of the BWT is captured by introducing a time varying linear factor which updates the coefficients at each scale over time. This approach has shown better performance than the existing algorithms at lower input SNR due to modified soft level dependent thresholding on time adaptive coefficients. The objective and subjective test results confirmed the competency of the TADBWT technique. The effectiveness of the proposed technique is also evaluated for speaker recognition task under noisy environment. The recognition results show that the TADWT technique yields better performance when compared to alternate methods specifically at lower input SNR.
Webster, Clayton G; Zhang, Guannan; Gunzburger, Max D
2012-10-01
Accurate predictive simulations of complex real world applications require numerical approximations to first, oppose the curse of dimensionality and second, converge quickly in the presence of steep gradients, sharp transitions, bifurcations or finite discontinuities in high-dimensional parameter spaces. In this paper we present a novel multi-dimensional multi-resolution adaptive (MdMrA) sparse grid stochastic collocation method, that utilizes hierarchical multiscale piecewise Riesz basis functions constructed from interpolating wavelets. The basis for our non-intrusive method forms a stable multiscale splitting and thus, optimal adaptation is achieved. Error estimates and numerical examples will used to compare the efficiency of the method with several other techniques.
Xiao, Qiyang; Li, Jian; Bai, Zhiliang; Sun, Jiedi; Zhou, Nan; Zeng, Zhoumo
2016-12-13
In this study, a small leak detection method based on variational mode decomposition (VMD) and ambiguity correlation classification (ACC) is proposed. The signals acquired from sensors were decomposed using the VMD, and numerous components were obtained. According to the probability density function (PDF), an adaptive de-noising algorithm based on VMD is proposed for noise component processing and de-noised components reconstruction. Furthermore, the ambiguity function image was employed for analysis of the reconstructed signals. Based on the correlation coefficient, ACC is proposed to detect the small leak of pipeline. The analysis of pipeline leakage signals, using 1 mm and 2 mm leaks, has shown that proposed detection method can detect a small leak accurately and effectively. Moreover, the experimental results have shown that the proposed method achieved better performances than support vector machine (SVM) and back propagation neural network (BP) methods.
Xiao, Qiyang; Li, Jian; Bai, Zhiliang; Sun, Jiedi; Zhou, Nan; Zeng, Zhoumo
2016-01-01
In this study, a small leak detection method based on variational mode decomposition (VMD) and ambiguity correlation classification (ACC) is proposed. The signals acquired from sensors were decomposed using the VMD, and numerous components were obtained. According to the probability density function (PDF), an adaptive de-noising algorithm based on VMD is proposed for noise component processing and de-noised components reconstruction. Furthermore, the ambiguity function image was employed for analysis of the reconstructed signals. Based on the correlation coefficient, ACC is proposed to detect the small leak of pipeline. The analysis of pipeline leakage signals, using 1 mm and 2 mm leaks, has shown that proposed detection method can detect a small leak accurately and effectively. Moreover, the experimental results have shown that the proposed method achieved better performances than support vector machine (SVM) and back propagation neural network (BP) methods. PMID:27983577
Applications of discrete multiwavelet techniques to image denoising
NASA Astrophysics Data System (ADS)
Wang, Haihui; Peng, Jiaxiong; Wu, Wei; Ye, Bin
2003-09-01
In this paper, we present a new method by using 2-D discrete multiwavelet transform in image denoising. The developments in wavelet theory have given rise to the wavelet thresholding method, for extracting a signal from noisy data. The method of signal denoising via wavelet thresholding was popularized. Multiwavelets have recently been introduced and they offer simultaneous orthogonality, symmetry and short support. This property makes multiwavelets more suitable for various image processing applications, especially denoising. It is based on thresholding of multiwavelet coefficients arising from the standard scalar orthogonal wavelet transform. It takes into account the covariance structure of the transform. Denoising is images via thresholding of the multiwavelet coefficients result from preprocessing and the discrete multiwavelet transform can be carried out by threating the output in this paper. The form of the threshold is carefully formulated and is the key to the excellent results obtained in the extensive numerical simulations of image denoising. The performances of multiwavelets are compared with those of scalar wavelets. Simulations reveal that multiwavelet based image denoising schemes outperform wavelet based method both subjectively and objectively.
Continuous digital ECG analysis over accurate R-peak detection using adaptive wavelet technique.
Gopalakrishnan Nair, T R; Geetha, A P; Asharani, M
2013-10-01
Worldwide, health care segment is under a severe challenge to achieve more accurate and intelligent biomedical systems in order to assist healthcare professionals with more accurate and consistent data as well as reliability. The role of ECG in healthcare is one of the paramount importances and it has got a multitude of abnormal relations and anomalies which characterizes intricate cardiovascular performance image. Until the recent past, ECG instruments and analysis played the role of providing the PQRST signal as raw observational output either on paper or on a console or in a file having many diagnostic clues embedded in the signal left to the expert cardiologist to look out for characteristic intervals and to detect the cardiovascular abnormality. Methods and practises are required more and more, to automate this process of cardiac expertise using knowledge engineering and an intelligent systems approach. This paper presents one of the challenging R-peak detections to classify diagnosis and estimate cardio disorders in a fully automated signal processing sequence. This study used an adaptive wavelet approach to generate an appropriate wavelet for R-signal identification under noise, baseband wandering and temporal variations of R-positions. This study designed an adaptive wavelet and successfully detected R- peak variations under various ECG signal conditions. The result and analysis of this method and the ways to use it for further purposes are presented here.
Effective wavelet-based compression method with adaptive quantization threshold and zerotree coding
NASA Astrophysics Data System (ADS)
Przelaskowski, Artur; Kazubek, Marian; Jamrogiewicz, Tomasz
1997-10-01
Efficient image compression technique especially for medical applications is presented. Dyadic wavelet decomposition by use of Antonini and Villasenor bank filters is followed by adaptive space-frequency quantization and zerotree-based entropy coding of wavelet coefficients. Threshold selection and uniform quantization is made on a base of spatial variance estimate built on the lowest frequency subband data set. Threshold value for each coefficient is evaluated as linear function of 9-order binary context. After quantization zerotree construction, pruning and arithmetic coding is applied for efficient lossless data coding. Presented compression method is less complex than the most effective EZW-based techniques but allows to achieve comparable compression efficiency. Specifically our method has similar to SPIHT efficiency in MR image compression, slightly better for CT image and significantly better in US image compression. Thus the compression efficiency of presented method is competitive with the best published algorithms in the literature across diverse classes of medical images.
Yoo, Sung Jin; Park, Jin Bae; Choi, Yoon Ho
2006-12-01
A new method for the robust control of flexible-joint (FJ) robots with model uncertainties in both robot dynamics and actuator dynamics is proposed. The proposed control system is a combination of the adaptive dynamic surface control (DSC) technique and the self-recurrent wavelet neural network (SRWNN). The adaptive DSC technique provides the ability to overcome the "explosion of complexity" problem in backstepping controllers. The SRWNNs are used to observe the arbitrary model uncertainties of FJ robots, and all their weights are trained online. From the Lyapunov stability analysis, their adaptation laws are induced, and the uniformly ultimately boundedness of all signals in a closed-loop adaptive system is proved. Finally, simulation results for a three-link FJ robot are utilized to validate the good position tracking performance and robustness against payload uncertainties and external disturbances of the proposed control system.
Adaptive three-dimensional motion-compensated wavelet transform for image sequence coding
NASA Astrophysics Data System (ADS)
Leduc, Jean-Pierre
1994-09-01
This paper describes a 3D spatio-temporal coding algorithm for the bit-rate compression of digital-image sequences. The coding scheme is based on different specificities namely, a motion representation with a four-parameter affine model, a motion-adapted temporal wavelet decomposition along the motion trajectories and a signal-adapted spatial wavelet transform. The motion estimation is performed on the basis of four-parameter affine transformation models also called similitude. This transformation takes into account translations, rotations and scalings. The temporal wavelet filter bank exploits bi-orthogonal linear-phase dyadic decompositions. The 2D spatial decomposition is based on dyadic signal-adaptive filter banks with either para-unitary or bi-orthogonal bases. The adaptive filtering is carried out according to a performance criterion to be optimized under constraints in order to eventually maximize the compression ratio at the expense of graceful degradations of the subjective image quality. The major principles of the present technique is, in the analysis process, to extract and to separate the motion contained in the sequences from the spatio-temporal redundancy and, in the compression process, to take into account of the rate-distortion function on the basis of the spatio-temporal psycho-visual properties to achieve the most graceful degradations. To complete this description of the coding scheme, the compression procedure is therefore composed of scalar quantizers which exploit the spatio-temporal 3D psycho-visual properties of the Human Visual System and of entropy coders which finalize the bit rate compression.
Wavelet despiking of fractographs
NASA Astrophysics Data System (ADS)
Aubry, Jean-Marie; Saito, Naoki
2000-12-01
Fractographs are elevation maps of the fracture zone of some broken material. The technique employed to create these maps often introduces noise composed of positive or negative 'spikes' that must be removed before further analysis. Since the roughness of these maps contains useful information, it must be preserved. Consequently, conventional denoising techniques cannot be employed. We use continuous and discrete wavelet transforms of these images, and the properties of wavelet coefficients related to pointwise Hoelder regularity, to detect and remove the spikes.
Multiscale image blind denoising.
Lebrun, Marc; Colom, Miguel; Morel, Jean-Michel
2015-10-01
Arguably several thousands papers are dedicated to image denoising. Most papers assume a fixed noise model, mainly white Gaussian or Poissonian. This assumption is only valid for raw images. Yet, in most images handled by the public and even by scientists, the noise model is imperfectly known or unknown. End users only dispose the result of a complex image processing chain effectuated by uncontrolled hardware and software (and sometimes by chemical means). For such images, recent progress in noise estimation permits to estimate from a single image a noise model, which is simultaneously signal and frequency dependent. We propose here a multiscale denoising algorithm adapted to this broad noise model. This leads to a blind denoising algorithm which we demonstrate on real JPEG images and on scans of old photographs for which the formation model is unknown. The consistency of this algorithm is also verified on simulated distorted images. This algorithm is finally compared with the unique state of the art previous blind denoising method.
Data-adaptive wavelets and multi-scale singular-spectrum analysis
NASA Astrophysics Data System (ADS)
Yiou, Pascal; Sornette, Didier; Ghil, Michael
2000-08-01
Using multi-scale ideas from wavelet analysis, we extend singular-spectrum analysis (SSA) to the study of nonstationary time series, including the case where intermittency gives rise to the divergence of their variance. The wavelet transform resembles a local Fourier transform within a finite moving window whose width W, proportional to the major period of interest, is varied to explore a broad range of such periods. SSA, on the other hand, relies on the construction of the lag-correlation matrix C on M lagged copies of the time series over a fixed window width W to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components; here W= MΔ t with Δ t as the time step. The proposed multi-scale SSA is a local SSA analysis within a moving window of width M≤ W≤ N, where N is the length of the time series. Multi-scale SSA varies W, while keeping a fixed W/ M ratio, and uses the eigenvectors of the corresponding lag-correlation matrix C(M) as data-adaptive wavelets; successive eigenvectors of C(M) correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis. Multi-scale SSA thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time-frequency domain by a suitable localization of the signal’s correlation matrix. We present several examples of application to synthetic signals with fractal or power-law behavior which mimic selected features of certain climatic or geophysical time series. The method is applied next to the monthly values of the Southern Oscillation Index (SOI) for 1933-1996; the SOI time series is widely believed to capture major features of the El Niño/Southern Oscillation (ENSO) in the Tropical Pacific. Our methodology highlights an abrupt periodicity shift in the SOI near 1960. This abrupt shift between 5 and 3 years supports the Devil’s staircase scenario for the ENSO phenomenon (preliminary results of this study
Lemeshewsky, G.P.; Rahman, Z.-U.; Schowengerdt, R.A.; Reichenbach, S.E.
2002-01-01
Enhanced false color images from mid-IR, near-IR (NIR), and visible bands of the Landsat thematic mapper (TM) are commonly used for visually interpreting land cover type. Described here is a technique for sharpening or fusion of NIR with higher resolution panchromatic (Pan) that uses a shift-invariant implementation of the discrete wavelet transform (SIDWT) and a reported pixel-based selection rule to combine coefficients. There can be contrast reversals (e.g., at soil-vegetation boundaries between NIR and visible band images) and consequently degraded sharpening and edge artifacts. To improve performance for these conditions, I used a local area-based correlation technique originally reported for comparing image-pyramid-derived edges for the adaptive processing of wavelet-derived edge data. Also, using the redundant data of the SIDWT improves edge data generation. There is additional improvement because sharpened subband imagery is used with the edge-correlation process. A reported technique for sharpening three-band spectral imagery used forward and inverse intensity, hue, and saturation transforms and wavelet-based sharpening of intensity. This technique had limitations with opposite contrast data, and in this study sharpening was applied to single-band multispectral-Pan image pairs. Sharpening used simulated 30-m NIR imagery produced by degrading the spatial resolution of a higher resolution reference. Performance, evaluated by comparison between sharpened and reference image, was improved when sharpened subband data were used with the edge correlation.
A wavelet-optimized, very high order adaptive grid and order numerical method
NASA Technical Reports Server (NTRS)
Jameson, Leland
1996-01-01
Differencing operators of arbitrarily high order can be constructed by interpolating a polynomial through a set of data followed by differentiation of this polynomial and finally evaluation of the polynomial at the point where a derivative approximation is desired. Furthermore, the interpolating polynomial can be constructed from algebraic, trigonometric, or, perhaps exponential polynomials. This paper begins with a comparison of such differencing operator construction. Next, the issue of proper grids for high order polynomials is addressed. Finally, an adaptive numerical method is introduced which adapts the numerical grid and the order of the differencing operator depending on the data. The numerical grid adaptation is performed on a Chebyshev grid. That is, at each level of refinement the grid is a Chebvshev grid and this grid is refined locally based on wavelet analysis.
Stabilized Conservative Level Set Method with Adaptive Wavelet-based Mesh Refinement
NASA Astrophysics Data System (ADS)
Shervani-Tabar, Navid; Vasilyev, Oleg V.
2016-11-01
This paper addresses one of the main challenges of the conservative level set method, namely the ill-conditioned behavior of the normal vector away from the interface. An alternative formulation for reconstruction of the interface is proposed. Unlike the commonly used methods which rely on the unit normal vector, Stabilized Conservative Level Set (SCLS) uses a modified renormalization vector with diminishing magnitude away from the interface. With the new formulation, in the vicinity of the interface the reinitialization procedure utilizes compressive flux and diffusive terms only in the normal direction to the interface, thus, preserving the conservative level set properties, while away from the interfaces the directional diffusion mechanism automatically switches to homogeneous diffusion. The proposed formulation is robust and general. It is especially well suited for use with adaptive mesh refinement (AMR) approaches due to need for a finer resolution in the vicinity of the interface in comparison with the rest of the domain. All of the results were obtained using the Adaptive Wavelet Collocation Method, a general AMR-type method, which utilizes wavelet decomposition to adapt on steep gradients in the solution while retaining a predetermined order of accuracy.
Adaptive Wavelet Galerkin Methods on Distorted Domains: Setup of the Algebraic System
2000-01-01
let T, and T• be the largest integers such that O E W7!,’°(!2) andj E wTf’,-(Q), respectively. Then, we set R:= min{Ro, Tý - II & II , Th - 11[111. We...the first time. Moreover, for computing the right-hand side, two Adaptive Wavelet Galerkin Methods 71 AI = Ij = jo, AI= jo, = jo + 1 AI= ii = Jo + 1 4J...during the preparation of this paper. The first author is extremely grateful to the Dipartimento di Matematica of the Politecnico di Torino for using its
Image denoising using local tangent space alignment
NASA Astrophysics Data System (ADS)
Feng, JianZhou; Song, Li; Huo, Xiaoming; Yang, XiaoKang; Zhang, Wenjun
2010-07-01
We propose a novel image denoising approach, which is based on exploring an underlying (nonlinear) lowdimensional manifold. Using local tangent space alignment (LTSA), we 'learn' such a manifold, which approximates the image content effectively. The denoising is performed by minimizing a newly defined objective function, which is a sum of two terms: (a) the difference between the noisy image and the denoised image, (b) the distance from the image patch to the manifold. We extend the LTSA method from manifold learning to denoising. We introduce the local dimension concept that leads to adaptivity to different kind of image patches, e.g. flat patches having lower dimension. We also plug in a basic denoising stage to estimate the local coordinate more accurately. It is found that the proposed method is competitive: its performance surpasses the K-SVD denoising method.
Dynamic Adaptive Binning: An Improved Quantification Technique for NMR Spectroscopic Data
2010-01-01
adaptive intelligent binning, which recursively identifies bin edges in existing bins (De Meyer et al. 2008). Another dynamic binning method is...43. Cancino-De-Greiff, H. F., Ramos-Garcia, R., & Lorenzo -Ginori, J. V. (2002). Signal de-noising in magnetic resonance spectroscopy using wavelet...for metabolomics data using the undecimated wavelet transform. Chemometrics and Intelligent Laboratory Systems, 85, 144–154. De Meyer , T., Sinnaeve, D
A robust adaptive denoising framework for real-time artifact removal in scalp EEG measurements
NASA Astrophysics Data System (ADS)
Kilicarslan, Atilla; Grossman, Robert G.; Contreras-Vidal, Jose Luis
2016-04-01
Objective. Non-invasive measurement of human neural activity based on the scalp electroencephalogram (EEG) allows for the development of biomedical devices that interface with the nervous system for scientific, diagnostic, therapeutic, or restorative purposes. However, EEG recordings are often considered as prone to physiological and non-physiological artifacts of different types and frequency characteristics. Among them, ocular artifacts and signal drifts represent major sources of EEG contamination, particularly in real-time closed-loop brain-machine interface (BMI) applications, which require effective handling of these artifacts across sessions and in natural settings. Approach. We extend the usage of a robust adaptive noise cancelling (ANC) scheme ({H}∞ filtering) for removal of eye blinks, eye motions, amplitude drifts and recording biases simultaneously. We also characterize the volume conduction, by estimating the signal propagation levels across all EEG scalp recording areas due to ocular artifact generators. We find that the amplitude and spatial distribution of ocular artifacts vary greatly depending on the electrode location. Therefore, fixed filtering parameters for all recording areas would naturally hinder the true overall performance of an ANC scheme for artifact removal. We treat each electrode as a separate sub-system to be filtered, and without the loss of generality, they are assumed to be uncorrelated and uncoupled. Main results. Our results show over 95-99.9% correlation between the raw and processed signals at non-ocular artifact regions, and depending on the contamination profile, 40-70% correlation when ocular artifacts are dominant. We also compare our results with the offline independent component analysis and artifact subspace reconstruction methods, and show that some local quantities are handled better by our sample-adaptive real-time framework. Decoding performance is also compared with multi-day experimental data from 2 subjects
NASA Astrophysics Data System (ADS)
Xie, Hua; Bosshard, John C.; Hill, Jason E.; Wright, Steven M.; Mitra, Sunanda
2016-03-01
Magnetic Resonance Imaging (MRI) offers noninvasive high resolution, high contrast cross-sectional anatomic images through the body. The data of the conventional MRI is collected in spatial frequency (Fourier) domain, also known as kspace. Because there is still a great need to improve temporal resolution of MRI, Compressed Sensing (CS) in MR imaging is proposed to exploit the sparsity of MR images showing great potential to reduce the scan time significantly, however, it poses its own unique problems. This paper revisits wavelet-encoded MR imaging which replaces phase encoding in conventional MRI data acquisition with wavelet encoding by applying wavelet-shaped spatially selective radiofrequency (RF) excitation, and keeps the readout direction as frequency encoding. The practicality of wavelet encoded MRI by itself is limited due to the SNR penalties and poor time resolution compared to conventional Fourier-based MRI. To compensate for those disadvantages, this paper first introduces an undersampling scheme named significance map for sparse wavelet-encoded k-space to speed up data acquisition as well as allowing for various adaptive imaging strategies. The proposed adaptive wavelet-encoded undersampling scheme does not require prior knowledge of the subject to be scanned. Multiband (MB) parallel imaging is also incorporated with wavelet-encoded MRI by exciting multiple regions simultaneously for further reduction in scan time desirable for medical applications. The simulation and experimental results are presented showing the feasibility of the proposed approach in further reduction of the redundancy of the wavelet k-space data while maintaining relatively high quality.
A Parallel Adaptive Wavelet Method for the Simulation of Compressible Reacting Flows
NASA Astrophysics Data System (ADS)
Zikoski, Zachary; Paolucci, Samuel
2011-11-01
The Wavelet Adaptive Multiresolution Representation (WAMR) method provides a robust method for controlling spatial grid adaption--fine grid spacing in regions of a solution requiring high resolution (i.e. near steep gradients, singularities, or near- singularities) and using much coarser grid spacing where the solution is slowly varying. The sparse grids produced using the WAMR method exhibit very high compression ratios compared to uniform grids of equivalent resolution. Subsequently, a wide range of spatial scales often occurring in continuum physics models can be captured efficiently. Furthermore, the wavelet transform provides a direct measure of local error at each grid point, effectively producing automatically verified solutions. The algorithm is parallelized using an MPI-based domain decomposition approach suitable for a wide range of distributed-memory parallel architectures. The method is applied to the solution of the compressible, reactive Navier-Stokes equations and includes multi-component diffusive transport and chemical kinetics models. Results for the method's parallel performance are reported, and its effectiveness on several challenging compressible reacting flow problems is highlighted.
Adaptive wavelet simulation of global ocean dynamics using a new Brinkman volume penalization
NASA Astrophysics Data System (ADS)
Kevlahan, N. K.-R.; Dubos, T.; Aechtner, M.
2015-12-01
In order to easily enforce solid-wall boundary conditions in the presence of complex coastlines, we propose a new mass and energy conserving Brinkman penalization for the rotating shallow water equations. This penalization does not lead to higher wave speeds in the solid region. The error estimates for the penalization are derived analytically and verified numerically for linearized one-dimensional equations. The penalization is implemented in a conservative dynamically adaptive wavelet method for the rotating shallow water equations on the sphere with bathymetry and coastline data from NOAA's ETOPO1 database. This code could form the dynamical core for a future global ocean model. The potential of the dynamically adaptive ocean model is illustrated by using it to simulate the 2004 Indonesian tsunami and wind-driven gyres.
Steerable pyramids and tight wavelet frames in L2(R(d)).
Unser, Michael; Chenouard, Nicolas; Van de Ville, Dimitri
2011-10-01
We present a functional framework for the design of tight steerable wavelet frames in any number of dimensions. The 2-D version of the method can be viewed as a generalization of Simoncelli's steerable pyramid that gives access to a larger palette of steerable wavelets via a suitable parametrization. The backbone of our construction is a primal isotropic wavelet frame that provides the multiresolution decomposition of the signal. The steerable wavelets are obtained by applying a one-to-many mapping (Nth-order generalized Riesz transform) to the primal ones. The shaping of the steerable wavelets is controlled by an M×M unitary matrix (where M is the number of wavelet channels) that can be selected arbitrarily; this allows for a much wider range of solutions than the traditional equiangular configuration (steerable pyramid). We give a complete functional description of these generalized wavelet transforms and derive their steering equations. We describe some concrete examples of transforms, including some built around a Mallat-type multiresolution analysis of L(2)(R(d)), and provide a fast Fourier transform-based decomposition algorithm. We also propose a principal-component-based method for signal-adapted wavelet design. Finally, we present some illustrative examples together with a comparison of the denoising performance of various brands of steerable transforms. The results are in favor of an optimized wavelet design (equalized principal component analysis), which consistently performs best.
Zhu, Xiaojun; Lei, Guangtsai; Pan, Guangwen
1997-04-01
In this paper, the continuous operator is discretized into matrix forms by Galerkin`s procedure, using periodic Battle-Lemarie wavelets as basis/testing functions. The polynomial decomposition of wavelets is applied to the evaluation of matrix elements, which makes the computational effort of the matrix elements no more expensive than that of method of moments (MoM) with conventional piecewise basis/testing functions. A new algorithm is developed employing the fast wavelet transform (FWT). Owing to localization, cancellation, and orthogonal properties of wavelets, very sparse matrices have been obtained, which are then solved by the LSQR iterative method. This algorithm is also adaptive in that one can add at will finer wavelet bases in the regions where fields vary rapidly, without any damage to the system orthogonality of the wavelet basis functions. To demonstrate the effectiveness of the new algorithm, we applied it to the evaluation of frequency-dependent resistance and inductance matrices of multiple lossy transmission lines. Numerical results agree with previously published data and laboratory measurements. The valid frequency range of the boundary integral equation results has been extended two to three decades in comparison with the traditional MoM approach. The new algorithm has been integrated into the computer aided design tool, MagiCAD, which is used for the design and simulation of high-speed digital systems and multichip modules Pan et al. 29 refs., 7 figs., 6 tabs.
Shi, Yan; Yang, Xiaoyuan; Guo, Yuhua
2014-01-01
This paper is devoted to the study of a directional lifting transform for wavelet frames. A nonsubsampled lifting structure is developed to maintain the translation invariance as it is an important property in image denoising. Then, the directionality of the lifting-based tight frame is explicitly discussed, followed by a specific translation invariant directional framelet transform (TIDFT). The TIDFT has two framelets ψ1, ψ2 with vanishing moments of order two and one respectively, which are able to detect singularities in a given direction set. It provides an efficient and sparse representation for images containing rich textures along with properties of fast implementation and perfect reconstruction. In addition, an adaptive block-wise orientation estimation method based on Gabor filters is presented instead of the conventional minimization of residuals. Furthermore, the TIDFT is utilized to exploit the capability of image denoising, incorporating the MAP estimator for multivariate exponential distribution. Consequently, the TIDFT is able to eliminate the noise effectively while preserving the textures simultaneously. Experimental results show that the TIDFT outperforms some other frame-based denoising methods, such as contourlet and shearlet, and is competitive to the state-of-the-art denoising approaches.
Goffin, Mark A.; Buchan, Andrew G.; Dargaville, Steven; Pain, Christopher C.; Smith, Paul N.; Smedley-Stevenson, Richard P.
2015-01-15
A method for applying goal-based adaptive methods to the angular resolution of the neutral particle transport equation is presented. The methods are applied to an octahedral wavelet discretisation of the spherical angular domain which allows for anisotropic resolution. The angular resolution is adapted across both the spatial and energy dimensions. The spatial domain is discretised using an inner-element sub-grid scale finite element method. The goal-based adaptive methods optimise the angular discretisation to minimise the error in a specific functional of the solution. The goal-based error estimators require the solution of an adjoint system to determine the importance to the specified functional. The error estimators and the novel methods to calculate them are described. Several examples are presented to demonstrate the effectiveness of the methods. It is shown that the methods can significantly reduce the number of unknowns and computational time required to obtain a given error. The novelty of the work is the use of goal-based adaptive methods to obtain anisotropic resolution in the angular domain for solving the transport equation. -- Highlights: •Wavelet angular discretisation used to solve transport equation. •Adaptive method developed for the wavelet discretisation. •Anisotropic angular resolution demonstrated through the adaptive method. •Adaptive method provides improvements in computational efficiency.
A nonlinear Bayesian filtering framework for ECG denoising.
Sameni, Reza; Shamsollahi, Mohammad B; Jutten, Christian; Clifford, Gari D
2007-12-01
In this paper, a nonlinear Bayesian filtering framework is proposed for the filtering of single channel noisy electrocardiogram (ECG) recordings. The necessary dynamic models of the ECG are based on a modified nonlinear dynamic model, previously suggested for the generation of a highly realistic synthetic ECG. A modified version of this model is used in several Bayesian filters, including the Extended Kalman Filter, Extended Kalman Smoother, and Unscented Kalman Filter. An automatic parameter selection method is also introduced, to facilitate the adaptation of the model parameters to a vast variety of ECGs. This approach is evaluated on several normal ECGs, by artificially adding white and colored Gaussian noises to visually inspected clean ECG recordings, and studying the SNR and morphology of the filter outputs. The results of the study demonstrate superior results compared with conventional ECG denoising approaches such as bandpass filtering, adaptive filtering, and wavelet denoising, over a wide range of ECG SNRs. The method is also successfully evaluated on real nonstationary muscle artifact. This method may therefore serve as an effective framework for the model-based filtering of noisy ECG recordings.
Spherical 3D isotropic wavelets
NASA Astrophysics Data System (ADS)
Lanusse, F.; Rassat, A.; Starck, J.-L.
2012-04-01
Context. Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. Aims: The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the SFB decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. Methods: We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. (2006). We also present a new fast discrete spherical Fourier-Bessel transform (DSFBT) based on both a discrete Bessel transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and find we can successfully remove noise without much loss to the large scale structure. Results: We have described a new spherical 3D isotropic wavelet transform, ideally suited to analyse and denoise future 3D spherical cosmological surveys, which uses a novel DSFBT. We illustrate its potential use for denoising using a toy model. All the algorithms presented in this paper are available for download as a public code called MRS3D at http://jstarck.free.fr/mrs3d.html
Image denoising using a combined criterion
NASA Astrophysics Data System (ADS)
Semenishchev, Evgeny; Marchuk, Vladimir; Shrafel, Igor; Dubovskov, Vadim; Onoyko, Tatyana; Maslennikov, Stansilav
2016-05-01
A new image denoising method is proposed in this paper. We are considering an optimization problem with a linear objective function based on two criteria, namely, L2 norm and the first order square difference. This method is a parametric, so by a choice of the parameters we can adapt a proposed criteria of the objective function. The denoising algorithm consists of the following steps: 1) multiple denoising estimates are found on local areas of the image; 2) image edges are determined; 3) parameters of the method are fixed and denoised estimates of the local area are found; 4) local window is moved to the next position (local windows are overlapping) in order to produce the final estimate. A proper choice of parameters of the introduced method is discussed. A comparative analysis of a new denoising method with existed ones is performed on a set of test images.
NASA Astrophysics Data System (ADS)
Rabbani, H.
2011-01-01
In this paper we introduce a new wavelet-based image denoising algorithm using maximum a posteriori (MAP) criterion. For this reason we propose Laplace distribution with local variance for clean image and two-sided Rayleigh model for noise in wavelet domain. The local Laplace probability density function (pdf) is able to simultaneously model the heavy-tailed nature of marginal distribution and intrascale dependency between spatial adjacent coefficients. Using local Laplace prior and two-sided Rayleigh noise, we derive a new shrinkage function for image denoising in the wavelet domain. We propose our new spatially adaptive wavelet-based image denoising algorithm for several low signal-to-noise ratio (SNR) magnetic resonance (MR) images and compare the results with other methods. The simulation results show that this algorithm is able to truly improve the visual quality of noisy MR images with very low computational cost. In case the input MR image is blurred, a blind deconvolution (BD) algorithm is necessary for visual quality improvement. Since BD techniques are usually sensitive to noise, in this paper we also apply a BD algorithm to an appropriate subband in the wavelet domain to eliminate the effect of noise in the BD procedure and to further improve visual quality.
Improved Denoising via Poisson Mixture Modeling of Image Sensor Noise.
Zhang, Jiachao; Hirakawa, Keigo
2017-04-01
This paper describes a study aimed at comparing the real image sensor noise distribution to the models of noise often assumed in image denoising designs. A quantile analysis in pixel, wavelet transform, and variance stabilization domains reveal that the tails of Poisson, signal-dependent Gaussian, and Poisson-Gaussian models are too short to capture real sensor noise behavior. A new Poisson mixture noise model is proposed to correct the mismatch of tail behavior. Based on the fact that noise model mismatch results in image denoising that undersmoothes real sensor data, we propose a mixture of Poisson denoising method to remove the denoising artifacts without affecting image details, such as edge and textures. Experiments with real sensor data verify that denoising for real image sensor data is indeed improved by this new technique.
Zhang, Chu; Ye, Hui; Liu, Fei; He, Yong; Kong, Wenwen; Sheng, Kuichuan
2016-01-01
Biomass energy represents a huge supplement for meeting current energy demands. A hyperspectral imaging system covering the spectral range of 874–1734 nm was used to determine the pH value of anaerobic digestion liquid produced by water hyacinth and rice straw mixtures used for methane production. Wavelet transform (WT) was used to reduce noises of the spectral data. Successive projections algorithm (SPA), random frog (RF) and variable importance in projection (VIP) were used to select 8, 15 and 20 optimal wavelengths for the pH value prediction, respectively. Partial least squares (PLS) and a back propagation neural network (BPNN) were used to build the calibration models on the full spectra and the optimal wavelengths. As a result, BPNN models performed better than the corresponding PLS models, and SPA-BPNN model gave the best performance with a correlation coefficient of prediction (rp) of 0.911 and root mean square error of prediction (RMSEP) of 0.0516. The results indicated the feasibility of using hyperspectral imaging to determine pH values during anaerobic digestion. Furthermore, a distribution map of the pH values was achieved by applying the SPA-BPNN model. The results in this study would help to develop an on-line monitoring system for biomass energy producing process by hyperspectral imaging. PMID:26901202
Zhang, Chu; Ye, Hui; Liu, Fei; He, Yong; Kong, Wenwen; Sheng, Kuichuan
2016-02-18
Biomass energy represents a huge supplement for meeting current energy demands. A hyperspectral imaging system covering the spectral range of 874-1734 nm was used to determine the pH value of anaerobic digestion liquid produced by water hyacinth and rice straw mixtures used for methane production. Wavelet transform (WT) was used to reduce noises of the spectral data. Successive projections algorithm (SPA), random frog (RF) and variable importance in projection (VIP) were used to select 8, 15 and 20 optimal wavelengths for the pH value prediction, respectively. Partial least squares (PLS) and a back propagation neural network (BPNN) were used to build the calibration models on the full spectra and the optimal wavelengths. As a result, BPNN models performed better than the corresponding PLS models, and SPA-BPNN model gave the best performance with a correlation coefficient of prediction (rp) of 0.911 and root mean square error of prediction (RMSEP) of 0.0516. The results indicated the feasibility of using hyperspectral imaging to determine pH values during anaerobic digestion. Furthermore, a distribution map of the pH values was achieved by applying the SPA-BPNN model. The results in this study would help to develop an on-line monitoring system for biomass energy producing process by hyperspectral imaging.
Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's
NASA Technical Reports Server (NTRS)
Cai, Wei; Wang, Jian-Zhong
1993-01-01
We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.
Simultaneous denoising and compression of multispectral images
NASA Astrophysics Data System (ADS)
Hagag, Ahmed; Amin, Mohamed; Abd El-Samie, Fathi E.
2013-01-01
A new technique for denoising and compression of multispectral satellite images to remove the effect of noise on the compression process is presented. One type of multispectral images has been considered: Landsat Enhanced Thematic Mapper Plus. The discrete wavelet transform (DWT), the dual-tree DWT, and a simple Huffman coder are used in the compression process. Simulation results show that the proposed technique is more effective than other traditional compression-only techniques.
Wavelet transform of neural spike trains
NASA Astrophysics Data System (ADS)
Kim, Youngtae; Jung, Min Whan; Kim, Yunbok
2000-02-01
Wavelet transform of neural spike trains recorded with a tetrode in the rat primary somatosensory cortex is described. Continuous wavelet transform (CWT) of the spike train clearly shows singularities hidden in the noisy or chaotic spike trains. A multiresolution analysis of the spike train is also carried out using discrete wavelet transform (DWT) for denoising and approximating at different time scales. Results suggest that this multiscale shape analysis can be a useful tool for classifying the spike trains.
Random seismic noise attenuation using the Wavelet Transform
NASA Astrophysics Data System (ADS)
Aliouane, L.; Ouadfeul, S.; Boudella, A.; Eladj, S.
2012-04-01
In this paper we propose a technique of random noises attenuation from seismic data using the discrete and continuous wavelet transforms. Firstly the discrete wavelet transform (DWT) is applied to denoise seismic data. This last is based on the threshold method applied at the modulus of the DWT. After we calculate the continuous wavelet transform of the denoised seismic seismogram, the final denoised seismic seismogram is the continuous wavelet transform coefficients at the low scale. Application at a synthetic seismic seismogram shows the robustness of the proposed tool for random noises attenuation. We have applied this idea at a real seismic data of a vertical seismic profile realized in Algeria. Keywords: Seismic data, denoising, DWT, CWT, random noise.
[A non-local means approach for PET image denoising].
Yin, Yong; Sun, Weifeng; Lu, Jie; Liu, Tonghai
2010-04-01
Denoising is an important issue for medical image processing. Based on the analysis of the Non-local means algorithm recently reported by Buades A, et al. in international journals we herein propose adapting it for PET image denoising. Experimental de-noising results for real clinical PET images show that Non-local means method is superior to median filtering and wiener filtering methods and it can suppress noise in PET images effectively and preserve important details of structure for diagnosis.
CW-THz image contrast enhancement using wavelet transform and Retinex
NASA Astrophysics Data System (ADS)
Chen, Lin; Zhang, Min; Hu, Qi-fan; Huang, Ying-Xue; Liang, Hua-Wei
2015-10-01
To enhance continuous wave terahertz (CW-THz) scanning images contrast and denoising, a method based on wavelet transform and Retinex theory was proposed. In this paper, the factors affecting the quality of CW-THz images were analysed. Second, an approach of combination of the discrete wavelet transform (DWT) and a designed nonlinear function in wavelet domain for the purpose of contrast enhancing was applied. Then, we combine the Retinex algorithm for further contrast enhancement. To evaluate the effectiveness of the proposed method in qualitative and quantitative, it was compared with the adaptive histogram equalization method, the homomorphic filtering method and the SSR(Single-Scale-Retinex) method. Experimental results demonstrated that the presented algorithm can effectively enhance the contrast of CW-THZ image and obtain better visual effect.
Classification of Underwater Signals Using Wavelet-Based Decompositions
1998-06-01
proposed by Learned and Willsky [21], uses the SVD information obtained from the power mapping, the second one selects the most within-a-class...34 SPIE, Vol. 2242, pp. 792-802, Wavelet Applications, 1994 [14] R. Coifman and D. Donoho, "Translation-Invariant Denoising ," Internal Report...J. Barsanti, Jr., Denoising of Ocean Acoustic Signals Using Wavelet-Based Techniques, MSEE Thesis, Naval Postgraduate School, Monterey, California
NASA Astrophysics Data System (ADS)
Hejazialhosseini, Babak; Rossinelli, Diego; Bergdorf, Michael; Koumoutsakos, Petros
2010-11-01
We present a space-time adaptive solver for single- and multi-phase compressible flows that couples average interpolating wavelets with high-order finite volume schemes. The solver introduces the concept of wavelet blocks, handles large jumps in resolution and employs local time-stepping for efficient time integration. We demonstrate that the inherently sequential wavelet-based adaptivity can be implemented efficiently in multicore computer architectures using task-based parallelism and introducing the concept of wavelet blocks. We validate our computational method on a number of benchmark problems and we present simulations of shock-bubble interaction at different Mach numbers, demonstrating the accuracy and computational performance of the method.
NASA Astrophysics Data System (ADS)
Regele, Jonathan D.
Multi-dimensional numerical modeling of detonation initiation is the primary goal of this thesis. The particular scenario under examination is initiating a detonation wave through acoustic timescale thermal power deposition. Physically this would correspond to igniting a reactive mixture with a laser pulse as opposed to a typical electric spark. Numerous spatial and temporal scales are involved, which makes these problems computationally challenging to solve. In order to model these problems, a shock capturing scheme is developed that utilizes the computational efficiency of the Adaptive Wavelet-Collocation Method (AWCM) to properly handle the multiple scales involved. With this technique, previous one-dimensional problems with unphysically small activation energies are revisited and simulated with the AWCM. The results demonstrate a qualitative agreement with previous work that used a uniform grid MacCormack scheme. Both sets of data show the basic sequence of events that are needed in order for a DDT process to occur. Instead of starting with a strong shock-coupled reaction zone as many other studies have done, the initial pulse is weak enough to allow the shock and the reaction zone to decouple. Reflected compression waves generated by the inertially confined reaction zone lead to localized reaction centers, which eventually explode and further accelerate the process. A shock-coupled reaction zone forms an initially overdriven detonation, which relaxes to a steady CJ wave. The one-dimensional problems are extended to two dimensions using a circular heat deposition in a channel. Two-dimensional results demonstrate the same sequence of events, which suggests that the concepts developed in the original one-dimensional work are applicable to multiple dimensions.
Study on De-noising Technology of Radar Life Signal
NASA Astrophysics Data System (ADS)
Yang, Xiu-Fang; Wang, Lian-Huan; Ma, Jiang-Fei; Wang, Pei-Pei
2016-05-01
Radar detection is a kind of novel life detection technology, which can be applied to medical monitoring, anti-terrorism and disaster relief street fighting, etc. As the radar life signal is very weak, it is often submerged in the noise. Because of non-stationary and randomness of these clutter signals, it is necessary to denoise efficiently before extracting and separating the useful signal. This paper improves the radar life signal's theoretical model of the continuous wave, does de-noising processing by introducing lifting wavelet transform and determine the best threshold function through comparing the de-noising effects of different threshold functions. The result indicates that both SNR and MSE of the signal are better than the traditional ones by introducing lifting wave transform and using a new improved soft threshold function de-noising method..
NASA Astrophysics Data System (ADS)
Rastigejev, Y.; Semakin, A. N.
2013-12-01
Accurate numerical simulations of global scale three-dimensional atmospheric chemical transport models (CTMs) are essential for studies of many important atmospheric chemistry problems such as adverse effect of air pollutants on human health, ecosystems and the Earth's climate. These simulations usually require large CPU time due to numerical difficulties associated with a wide range of spatial and temporal scales, nonlinearity and large number of reacting species. In our previous work we have shown that in order to achieve adequate convergence rate and accuracy, the mesh spacing in numerical simulation of global synoptic-scale pollution plume transport must be decreased to a few kilometers. This resolution is difficult to achieve for global CTMs on uniform or quasi-uniform grids. To address the described above difficulty we developed a three-dimensional Wavelet-based Adaptive Mesh Refinement (WAMR) algorithm. The method employs a highly non-uniform adaptive grid with fine resolution over the areas of interest without requiring small grid-spacing throughout the entire domain. The method uses multi-grid iterative solver that naturally takes advantage of a multilevel structure of the adaptive grid. In order to represent the multilevel adaptive grid efficiently, a dynamic data structure based on indirect memory addressing has been developed. The data structure allows rapid access to individual points, fast inter-grid operations and re-gridding. The WAMR method has been implemented on parallel computer architectures. The parallel algorithm is based on run-time partitioning and load-balancing scheme for the adaptive grid. The partitioning scheme maintains locality to reduce communications between computing nodes. The parallel scheme was found to be cost-effective. Specifically we obtained an order of magnitude increase in computational speed for numerical simulations performed on a twelve-core single processor workstation. We have applied the WAMR method for numerical
V S, Unni; Mishra, Deepak; Subrahmanyam, G R K S
2016-12-01
The need for image fusion in current image processing systems is increasing mainly due to the increased number and variety of image acquisition techniques. Image fusion is the process of combining substantial information from several sensors using mathematical techniques in order to create a single composite image that will be more comprehensive and thus more useful for a human operator or other computer vision tasks. This paper presents a new approach to multifocus image fusion based on sparse signal representation. Block-based compressive sensing integrated with a projection-driven compressive sensing (CS) recovery that encourages sparsity in the wavelet domain is used as a method to get the focused image from a set of out-of-focus images. Compression is achieved during the image acquisition process using a block compressive sensing method. An adaptive thresholding technique within the smoothed projected Landweber recovery process reconstructs high-resolution focused images from low-dimensional CS measurements of out-of-focus images. Discrete wavelet transform and dual-tree complex wavelet transform are used as the sparsifying basis for the proposed fusion. The main finding lies in the fact that sparsification enables a better selection of the fusion coefficients and hence better fusion. A Laplacian mixture model fit is done in the wavelet domain and estimation of the probability density function (pdf) parameters by expectation maximization leads us to the proper selection of the coefficients of the fused image. Using the proposed method compared with the fusion scheme without employing the projected Landweber (PL) scheme and the other existing CS-based fusion approaches, it is observed that with fewer samples itself, the proposed method outperforms other approaches.
A multiscale products technique for denoising of DNA capillary electrophoresis signals
NASA Astrophysics Data System (ADS)
Gao, Qingwei; Lu, Yixiang; Sun, Dong; Zhang, Dexiang
2013-06-01
Since noise degrades the accuracy and precision of DNA capillary electrophoresis (CE) analysis, signal denoising is thus important to facilitate the postprocessing of CE data. In this paper, a new denoising algorithm based on dyadic wavelet transform using multiscale products is applied for the removal of the noise in the DNA CE signal. The adjacent scale wavelet coefficients are first multiplied to amplify the significant features of the CE signal while diluting noise. Then, noise is suppressed by applying a multiscale threshold to the multiscale products instead of directly to the wavelet coefficients. Finally, the noise-free CE signal is recovered from the thresholded coefficients by using inverse dyadic wavelet transform. We compare the performance of the proposed algorithm with other denoising methods applied to the synthetic CE and real CE signals. Experimental results show that the new scheme achieves better removal of noise while preserving the shape of peaks corresponding to the analytes in the sample.
Portal imaging: Performance improvement in noise reduction by means of wavelet processing.
González-López, Antonio; Morales-Sánchez, Juan; Larrey-Ruiz, Jorge; Bastida-Jumilla, María-Consuelo; Verdú-Monedero, Rafael
2016-01-01
This paper discusses the suitability, in terms of noise reduction, of various methods which can be applied to an image type often used in radiation therapy: the portal image. Among these methods, the analysis focuses on those operating in the wavelet domain. Wavelet-based methods tested on natural images--such as the thresholding of the wavelet coefficients, the minimization of the Stein unbiased risk estimator on a linear expansion of thresholds (SURE-LET), and the Bayes least-squares method using as a prior a Gaussian scale mixture (BLS-GSM method)--are compared with other methods that operate on the image domain--an adaptive Wiener filter and a nonlocal mean filter (NLM). For the assessment of the performance, the peak signal-to-noise ratio (PSNR), the structural similarity index (SSIM), the Pearson correlation coefficient, and the Spearman rank correlation (ρ) coefficient are used. The performance of the wavelet filters and the NLM method are similar, but wavelet filters outperform the Wiener filter in terms of portal image denoising. It is shown how BLS-GSM and NLM filters produce the smoothest image, while keeping soft-tissue and bone contrast. As for the computational cost, filters using a decimated wavelet transform (decimated thresholding and SURE-LET) turn out to be the most efficient, with calculation times around 1 s.
Knaus, Claude; Zwicker, Matthias
2014-07-01
Image denoising continues to be an active research topic. Although state-of-the-art denoising methods are numerically impressive and approch theoretical limits, they suffer from visible artifacts.While they produce acceptable results for natural images, human eyes are less forgiving when viewing synthetic images. At the same time, current methods are becoming more complex, making analysis, and implementation difficult. We propose image denoising as a simple physical process, which progressively reduces noise by deterministic annealing. The results of our implementation are numerically and visually excellent. We further demonstrate that our method is particularly suited for synthetic images. Finally, we offer a new perspective on image denoising using robust estimators.
Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames.
Pad, Pedram; Uhlmann, Virginie; Unser, Michael
2016-03-22
A crucial component of steerable wavelets is the radial profile of the generating function in the frequency domain. In this work, we present an infinite-dimensional optimization scheme that helps us find the optimal profile for a given criterion over the space of tight frames. We consider two classes of criteria that measure the localization of the wavelet. The first class specifies the spatial localization of the wavelet profile, and the second that of the resulting wavelet coefficients. From these metrics and the proposed algorithm, we construct tight wavelet frames that are optimally localized and provide their analytical expression. In particular, one of the considered criterion helps us finding back the popular Simoncelli wavelet profile. Finally, the investigation of local orientation estimation, image reconstruction from detected contours in the wavelet domain, and denoising, indicate that optimizing wavelet localization improves the performance of steerable wavelets, since our new wavelets outperform the traditional ones.
Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames.
Pad, Pedram; Uhlmann, Virginie; Unser, Michael
2016-05-01
A crucial component of steerable wavelets is the radial profile of the generating function in the frequency domain. In this paper, we present an infinite-dimensional optimization scheme that helps us find the optimal profile for a given criterion over the space of tight frames. We consider two classes of criteria that measure the localization of the wavelet. The first class specifies the spatial localization of the wavelet profile, and the second that of the resulting wavelet coefficients. From these metrics and the proposed algorithm, we construct tight wavelet frames that are optimally localized and provide their analytical expression. In particular, one of the considered criterion helps us finding back the popular Simoncelli wavelet profile. Finally, the investigation of local orientation estimation, image reconstruction from detected contours in the wavelet domain, and denoising indicate that optimizing wavelet localization improves the performance of steerable wavelets, since our new wavelets outperform the traditional ones.
Anatomically-adapted graph wavelets for improved group-level fMRI activation mapping.
Behjat, Hamid; Leonardi, Nora; Sörnmo, Leif; Van De Ville, Dimitri
2015-12-01
A graph based framework for fMRI brain activation mapping is presented. The approach exploits the spectral graph wavelet transform (SGWT) for the purpose of defining an advanced multi-resolutional spatial transformation for fMRI data. The framework extends wavelet based SPM (WSPM), which is an alternative to the conventional approach of statistical parametric mapping (SPM), and is developed specifically for group-level analysis. We present a novel procedure for constructing brain graphs, with subgraphs that separately encode the structural connectivity of the cerebral and cerebellar gray matter (GM), and address the inter-subject GM variability by the use of template GM representations. Graph wavelets tailored to the convoluted boundaries of GM are then constructed as a means to implement a GM-based spatial transformation on fMRI data. The proposed approach is evaluated using real as well as semi-synthetic multi-subject data. Compared to SPM and WSPM using classical wavelets, the proposed approach shows superior type-I error control. The results on real data suggest a higher detection sensitivity as well as the capability to capture subtle, connected patterns of brain activity.
EEG Signal Decomposition and Improved Spectral Analysis Using Wavelet Transform
2001-10-25
research and medical applications. Wavelet transform (WT) is a new multi-resolution time-frequency analysis method. WT possesses localization feature both... wavelet transform , the EEG signals are successfully decomposed and denoised. In this paper we also use a ’quasi-detrending’ method for classification of EEG
Discrete multiscale wavelet shrinkage and integrodifferential equations
NASA Astrophysics Data System (ADS)
Didas, S.; Steidl, G.; Weickert, J.
2008-04-01
We investigate the relation between discrete wavelet shrinkage and integrodifferential equations in the context of simplification and denoising of one-dimensional signals. In the continuous setting, strong connections between these two approaches were discovered in 6 (see references). The key observation is that the wavelet transform can be understood as derivative operator after the convolution with a smoothing kernel. In this paper, we extend these ideas to the practically relevant discrete setting with both orthogonal and biorthogonal wavelets. In the discrete case, the behaviour of the smoothing kernels for different scales requires additional investigation. The results of discrete multiscale wavelet shrinkage and related discrete versions of integrodifferential equations are compared with respect to their denoising quality by numerical experiments.
Zahra, Noor e; Sevindir, Huliya A.; Aslan, Zafar; Siddiqi, A. H.
2012-07-17
The aim of this study is to provide emerging applications of wavelet methods to medical signals and images, such as electrocardiogram, electroencephalogram, functional magnetic resonance imaging, computer tomography, X-ray and mammography. Interpretation of these signals and images are quite important. Nowadays wavelet methods have a significant impact on the science of medical imaging and the diagnosis of disease and screening protocols. Based on our initial investigations, future directions include neurosurgical planning and improved assessment of risk for individual patients, improved assessment and strategies for the treatment of chronic pain, improved seizure localization, and improved understanding of the physiology of neurological disorders. We look ahead to these and other emerging applications as the benefits of this technology become incorporated into current and future patient care. In this chapter by applying Fourier transform and wavelet transform, analysis and denoising of one of the important biomedical signals like EEG is carried out. The presence of rhythm, template matching, and correlation is discussed by various method. Energy of EEG signal is used to detect seizure in an epileptic patient. We have also performed denoising of EEG signals by SWT.
NASA Astrophysics Data System (ADS)
Zahra, Noor e.; Sevindir, Hulya Kodal; Aslan, Zafer; Siddiqi, A. H.
2012-07-01
The aim of this study is to provide emerging applications of wavelet methods to medical signals and images, such as electrocardiogram, electroencephalogram, functional magnetic resonance imaging, computer tomography, X-ray and mammography. Interpretation of these signals and images are quite important. Nowadays wavelet methods have a significant impact on the science of medical imaging and the diagnosis of disease and screening protocols. Based on our initial investigations, future directions include neurosurgical planning and improved assessment of risk for individual patients, improved assessment and strategies for the treatment of chronic pain, improved seizure localization, and improved understanding of the physiology of neurological disorders. We look ahead to these and other emerging applications as the benefits of this technology become incorporated into current and future patient care. In this chapter by applying Fourier transform and wavelet transform, analysis and denoising of one of the important biomedical signals like EEG is carried out. The presence of rhythm, template matching, and correlation is discussed by various method. Energy of EEG signal is used to detect seizure in an epileptic patient. We have also performed denoising of EEG signals by SWT.
NASA Astrophysics Data System (ADS)
Rangel, T.; Caliste, D.; Genovese, L.; Torrent, M.
2016-11-01
We present a Projector Augmented-Wave (PAW) method based on a wavelet basis set. We implemented our wavelet-PAW method as a PAW library in the ABINIT package [http://www.abinit.org] and into BigDFT [http://www.bigdft.org]. We test our implementation in prototypical systems to illustrate the potential usage of our code. By using the wavelet-PAW method, we can simulate charged and special boundary condition systems with frozen-core all-electron precision. Furthermore, our work paves the way to large-scale and potentially order- N simulations within a PAW method.
Frames-Based Denoising in 3D Confocal Microscopy Imaging.
Konstantinidis, Ioannis; Santamaria-Pang, Alberto; Kakadiaris, Ioannis
2005-01-01
In this paper, we propose a novel denoising method for 3D confocal microscopy data based on robust edge detection. Our approach relies on the construction of a non-separable frame system in 3D that incorporates the Sobel operator in dual spatial directions. This multidirectional set of digital filters is capable of robustly detecting edge information by ensemble thresholding of the filtered data. We demonstrate the application of our method to both synthetic and real confocal microscopy data by comparing it to denoising methods based on separable 3D wavelets and 3D median filtering, and report very encouraging results.
NASA Astrophysics Data System (ADS)
Wang, Shibin; Zhu, Z. K.; He, Yingping; Huang, Weiguo
2010-12-01
Localized defects in rotating mechanical parts tend to result in impulse response in vibration signal, which contain important information about system dynamics being analyzed. Thus, parameter identification of impulse response provides a potential approach for localized fault diagnosis. A method combining the Morlet wavelet and correlation filtering, named Cyclic Morlet Wavelet Correlation Filtering (CMWCF), is proposed for identifying both parameters of impulse response and the cyclic period between adjacent impulses. Simulation study concerning cyclic impulse response signal with different SNR shows that CMWCF is effective in identifying the impulse response parameters and the cyclic period. Applications in parameter identification of gearbox vibration signal for localized fault diagnosis show that CMWCF is effective in identifying the parameters and thus provides a feature detection method for gearbox fault diagnosis.
A new performance evaluation scheme for jet engine vibration signal denoising
NASA Astrophysics Data System (ADS)
Sadooghi, Mohammad Saleh; Esmaeilzadeh Khadem, Siamak
2016-08-01
Denoising of a cargo-plane jet engine compressor vibration signal is investigated in this article. Discrete wavelet transform and two families of Donoho-Johnston and parameter method thresholding, are applied to vibration signal. Eighty four combinations of wavelet thresholding and mother wavelet are evaluated. A new performance evaluation scheme for optimal selection of mother wavelet and thresholding method combination is proposed in this paper, which is make a trade off between four performance criteria of signal to noise ratio, percentage root mean square difference, Cross-correlation, and mean square error. Dmeyer mother wavelet (dmey) combined with Rigorous SURE thresholding has the maximum trade off value and was selected as the most appropriate combination for denoising of the signal. It was shown that inappropriate combination leads to data losing. Also higher performance of proposed trade off with respect to other criteria was proven graphically.
Fast wavelet estimation of weak biosignals.
Causevic, Elvir; Morley, Robert E; Wickerhauser, M Victor; Jacquin, Arnaud E
2005-06-01
Wavelet-based signal processing has become commonplace in the signal processing community over the past decade and wavelet-based software tools and integrated circuits are now commercially available. One of the most important applications of wavelets is in removal of noise from signals, called denoising, accomplished by thresholding wavelet coefficients in order to separate signal from noise. Substantial work in this area was summarized by Donoho and colleagues at Stanford University, who developed a variety of algorithms for conventional denoising. However, conventional denoising fails for signals with low signal-to-noise ratio (SNR). Electrical signals acquired from the human body, called biosignals, commonly have below 0 dB SNR. Synchronous linear averaging of a large number of acquired data frames is universally used to increase the SNR of weak biosignals. A novel wavelet-based estimator is presented for fast estimation of such signals. The new estimation algorithm provides a faster rate of convergence to the underlying signal than linear averaging. The algorithm is implemented for processing of auditory brainstem response (ABR) and of auditory middle latency response (AMLR) signals. Experimental results with both simulated data and human subjects demonstrate that the novel wavelet estimator achieves superior performance to that of linear averaging.
Wavelet filtering of chaotic data
NASA Astrophysics Data System (ADS)
Grzesiak, M.
Satisfactory method of removing noise from experimental chaotic data is still an open problem. Normally it is necessary to assume certain properties of the noise and dynamics, which one wants to extract, from time series. The wavelet based method of denoising of time series originating from low-dimensional dynamical systems and polluted by the Gaussian white noise is considered. Its efficiency is investigated by comparing the correlation dimension of clean and noisy data generated for some well-known dynamical systems. The wavelet method is contrasted with the singular value decomposition (SVD) and finite impulse response (FIR) filter methods.
Combining interior and exterior characteristics for remote sensing image denoising
NASA Astrophysics Data System (ADS)
Peng, Ni; Sun, Shujin; Wang, Runsheng; Zhong, Ping
2016-04-01
Remote sensing image denoising faces many challenges since a remote sensing image usually covers a wide area and thus contains complex contents. Using the patch-based statistical characteristics is a flexible method to improve the denoising performance. There are usually two kinds of statistical characteristics available: interior and exterior characteristics. Different statistical characteristics have their own strengths to restore specific image contents. Combining different statistical characteristics to use their strengths together may have the potential to improve denoising results. This work proposes a method combining statistical characteristics to adaptively select statistical characteristics for different image contents. The proposed approach is implemented through a new characteristics selection criterion learned over training data. Moreover, with the proposed combination method, this work develops a denoising algorithm for remote sensing images. Experimental results show that our method can make full use of the advantages of interior and exterior characteristics for different image contents and thus improve the denoising performance.
Denoising of PET images by context modelling using local neighbourhood correlation
NASA Astrophysics Data System (ADS)
Huerga, Carlos; Castro, Pablo; Corredoira, Eva; Coronado, Monica; Delgado, Victor; Guibelalde, Eduardo
2017-01-01
Positron emission tomography (PET) images are characterised by low signal-to-noise ratio and blurred edges when compared with other image modalities. It is therefore advisable to use noise reduction methods for qualitative and quantitative analyses. Given the importance of the maximum and mean uptake values, it is necessary to avoid signal loss, which could modify the clinical significance. This paper proposes a method of non-linear image denoising for PET. It is based on spatially adaptive wavelet-shrinkage and uses context modelling, which explicitly considers the correlation between neighbouring pixels. This context modelling is able to maintain the uptake values and preserve the edges in significant regions. The algorithm is proposed as an alternative to the usual filtering that is performed after reconstruction.
A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov-Maxwell system
Besse, Nicolas Latu, Guillaume Ghizzo, Alain Sonnendruecker, Eric Bertrand, Pierre
2008-08-10
In this paper we present a new method for the numerical solution of the relativistic Vlasov-Maxwell system on a phase-space grid using an adaptive semi-Lagrangian method. The adaptivity is performed through a wavelet multiresolution analysis, which gives a powerful and natural refinement criterion based on the local measurement of the approximation error and regularity of the distribution function. Therefore, the multiscale expansion of the distribution function allows to get a sparse representation of the data and thus save memory space and CPU time. We apply this numerical scheme to reduced Vlasov-Maxwell systems arising in laser-plasma physics. Interaction of relativistically strong laser pulses with overdense plasma slabs is investigated. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by electromagnetic waves as electron trapping, particle acceleration, and electron plasma wavebreaking. However, the wavelet based adaptive method that we developed here, does not yield significant improvements compared to Vlasov solvers on a uniform mesh due to the substantial overhead that the method introduces. Nonetheless they might be a first step towards more efficient adaptive solvers based on different ideas for the grid refinement or on a more efficient implementation. Here the Vlasov simulations are performed in a two-dimensional phase-space where the development of thin filaments, strongly amplified by relativistic effects requires an important increase of the total number of points of the phase-space grid as they get finer as time goes on. The adaptive method could be more useful in cases where these thin filaments that need to be resolved are a very small fraction of the hyper-volume, which arises in higher dimensions because of the surface-to-volume scaling and the essentially one-dimensional structure of the filaments. Moreover, the main way to improve the efficiency of the adaptive method is to
Wavelet methods in data mining
NASA Astrophysics Data System (ADS)
Manchanda, P.
2012-07-01
Data mining (knowledge discovery in data base) is comparatively new interdisciplinary field developed by joint efforts of mathematicians, statisticians, computer scientists and engineers. There are twelve important ingredients of this field along with their applications in real world problems. In this chapter, we have reviewed application of wavelet methods to data mining, particularly denoising, dimension reduction, similarity search, feature extraction and prediction. Meteorological data of Saudi Arabia and Stock market data of India are considered for illustration.
Nonlinear denoising of transient signals with application to event-related potentials
NASA Astrophysics Data System (ADS)
Effern, A.; Lehnertz, K.; Schreiber, T.; Grunwald, T.; David, P.; Elger, C. E.
2000-06-01
We present a new wavelet-based method for the denoising of event-related potentials (ERPs), employing techniques recently developed for the paradigm of deterministic chaotic systems. The denoising scheme has been constructed to be appropriate for short and transient time sequences using circular state space embedding. Its effectiveness was successfully tested on simulated signals as well as on ERPs recorded from within a human brain. The method enables the study of individual ERPs against strong ongoing brain electrical activity.
Higher-density dyadic wavelet transform and its application
NASA Astrophysics Data System (ADS)
Qin, Yi; Tang, Baoping; Wang, Jiaxu
2010-04-01
This paper proposes a higher-density dyadic wavelet transform with two generators, whose corresponding wavelet filters are band-pass and high-pass. The wavelet coefficients at each scale in this case have the same length as the signal. This leads to a new redundant dyadic wavelet transform, which is strictly shift invariant and further increases the sampling in the time dimension. We describe the definition of higher-density dyadic wavelet transform, and discuss the condition of perfect reconstruction of the signal from its wavelet coefficients. The fast implementation algorithm for the proposed transform is given as well. Compared with the higher-density discrete wavelet transform, the proposed transform is shift invariant. Applications into signal denoising indicate that the proposed wavelet transform has better denoising performance than other commonly used wavelet transforms. In the end, various typical wavelet transforms are applied to analyze the vibration signals of two faulty roller bearings, the results show that the proposed wavelet transform can more effectively extract the fault characteristics of the roller bearings than the other wavelet transforms.
Optical Wavelet Signals Processing and Multiplexing
NASA Astrophysics Data System (ADS)
Cincotti, Gabriella; Moreolo, Michela Svaluto; Neri, Alessandro
2005-12-01
We present compact integrable architectures to perform the discrete wavelet transform (DWT) and the wavelet packet (WP) decomposition of an optical digital signal, and we show that the combined use of planar lightwave circuits (PLC) technology and multiresolution analysis (MRA) can add flexibility to current multiple access optical networks. We furnish the design guidelines to synthesize wavelet filters as two-port lattice-form planar devices, and we give some examples of optical signal denoising and compression/decompression techniques in the wavelet domain. Finally, we present a fully optical wavelet packet division multiplexing (WPDM) scheme where data signals are waveform-coded onto wavelet atom functions for transmission, and numerically evaluate its performances.
NASA Astrophysics Data System (ADS)
Scholkmann, Felix; Revol, Vincent; Kaufmann, Rolf; Baronowski, Heidrun; Kottler, Christian
2014-03-01
This paper introduces a new image denoising, fusion and enhancement framework for combining and optimal visualization of x-ray attenuation contrast (AC), differential phase contrast (DPC) and dark-field contrast (DFC) images retrieved from x-ray Talbot-Lau grating interferometry. The new image fusion framework comprises three steps: (i) denoising each input image (AC, DPC and DFC) through adaptive Wiener filtering, (ii) performing a two-step image fusion process based on the shift-invariant wavelet transform, i.e. first fusing the AC with the DPC image and then fusing the resulting image with the DFC image, and finally (iii) enhancing the fused image to obtain a final image using adaptive histogram equalization, adaptive sharpening and contrast optimization. Application examples are presented for two biological objects (a human tooth and a cherry) and the proposed method is compared to two recently published AC/DPC/DFC image processing techniques. In conclusion, the new framework for the processing of AC, DPC and DFC allows the most relevant features of all three images to be combined in one image while reducing the noise and enhancing adaptively the relevant image features. The newly developed framework may be used in technical and medical applications.
Scholkmann, Felix; Revol, Vincent; Kaufmann, Rolf; Baronowski, Heidrun; Kottler, Christian
2014-03-21
This paper introduces a new image denoising, fusion and enhancement framework for combining and optimal visualization of x-ray attenuation contrast (AC), differential phase contrast (DPC) and dark-field contrast (DFC) images retrieved from x-ray Talbot-Lau grating interferometry. The new image fusion framework comprises three steps: (i) denoising each input image (AC, DPC and DFC) through adaptive Wiener filtering, (ii) performing a two-step image fusion process based on the shift-invariant wavelet transform, i.e. first fusing the AC with the DPC image and then fusing the resulting image with the DFC image, and finally (iii) enhancing the fused image to obtain a final image using adaptive histogram equalization, adaptive sharpening and contrast optimization. Application examples are presented for two biological objects (a human tooth and a cherry) and the proposed method is compared to two recently published AC/DPC/DFC image processing techniques. In conclusion, the new framework for the processing of AC, DPC and DFC allows the most relevant features of all three images to be combined in one image while reducing the noise and enhancing adaptively the relevant image features. The newly developed framework may be used in technical and medical applications.
True 4D Image Denoising on the GPU.
Eklund, Anders; Andersson, Mats; Knutsson, Hans
2011-01-01
The use of image denoising techniques is an important part of many medical imaging applications. One common application is to improve the image quality of low-dose (noisy) computed tomography (CT) data. While 3D image denoising previously has been applied to several volumes independently, there has not been much work done on true 4D image denoising, where the algorithm considers several volumes at the same time. The problem with 4D image denoising, compared to 2D and 3D denoising, is that the computational complexity increases exponentially. In this paper we describe a novel algorithm for true 4D image denoising, based on local adaptive filtering, and how to implement it on the graphics processing unit (GPU). The algorithm was applied to a 4D CT heart dataset of the resolution 512 × 512 × 445 × 20. The result is that the GPU can complete the denoising in about 25 minutes if spatial filtering is used and in about 8 minutes if FFT-based filtering is used. The CPU implementation requires several days of processing time for spatial filtering and about 50 minutes for FFT-based filtering. The short processing time increases the clinical value of true 4D image denoising significantly.
Rezaee, Kh.; Haddadnia, J.
2013-01-01
Background: Breast cancer is currently one of the leading causes of death among women worldwide. The diagnosis and separation of cancerous tumors in mammographic images require accuracy, experience and time, and it has always posed itself as a major challenge to the radiologists and physicians. Objective: This paper proposes a new algorithm which draws on discrete wavelet transform and adaptive K-means techniques to transmute the medical images implement the tumor estimation and detect breast cancer tumors in mammograms in early stages. It also allows the rapid processing of the input data. Method: In the first step, after designing a filter, the discrete wavelet transform is applied to the input images and the approximate coefficients of scaling components are constructed. Then, the different parts of image are classified in continuous spectrum. In the next step, by using adaptive K-means algorithm for initializing and smart choice of clusters’ number, the appropriate threshold is selected. Finally, the suspicious cancerous mass is separated by implementing the image processing techniques. Results: We Received 120 mammographic images in LJPEG format, which had been scanned in Gray-Scale with 50 microns size, 3% noise and 20% INU from clinical data taken from two medical databases (mini-MIAS and DDSM). The proposed algorithm detected tumors at an acceptable level with an average accuracy of 92.32% and sensitivity of 90.24%. Also, the Kappa coefficient was approximately 0.85, which proved the suitable reliability of the system performance. Conclusion: The exact positioning of the cancerous tumors allows the radiologist to determine the stage of disease progression and suggest an appropriate treatment in accordance with the tumor growth. The low PPV and high NPV of the system is a warranty of the system and both clinical specialists and patients can trust its output. PMID:25505753
Avci, Derya; Leblebicioglu, Mehmet Kemal; Poyraz, Mustafa; Dogantekin, Esin
2014-02-01
So far, analysis and classification of urine cells number has become an important topic for medical diagnosis of some diseases. Therefore, in this study, we suggest a new technique based on Adaptive Discrete Wavelet Entropy Energy and Neural Network Classifier (ADWEENN) for Recognition of Urine Cells from Microscopic Images Independent of Rotation and Scaling. Some digital image processing methods such as noise reduction, contrast enhancement, segmentation, and morphological process are used for feature extraction stage of this ADWEENN in this study. Nowadays, the image processing and pattern recognition topics have come into prominence. The image processing concludes operation and design of systems that recognize patterns in data sets. In the past years, very difficulty in classification of microscopic images was the deficiency of enough methods to characterize. Lately, it is seen that, multi-resolution image analysis methods such as Gabor filters, discrete wavelet decompositions are superior to other classic methods for analysis of these microscopic images. In this study, the structure of the ADWEENN method composes of four stages. These are preprocessing stage, feature extraction stage, classification stage and testing stage. The Discrete Wavelet Transform (DWT) and adaptive wavelet entropy and energy is used for adaptive feature extraction in feature extraction stage to strengthen the premium features of the Artificial Neural Network (ANN) classifier in this study. Efficiency of the developed ADWEENN method was tested showing that an avarage of 97.58% recognition succes was obtained.
Adaptive fusion of multisensor precipitation using Gaussian-scale mixtures in the wavelet domain
NASA Astrophysics Data System (ADS)
Ebtehaj, Ardeshir Mohammad; Foufoula-Georgiou, Efi
2011-11-01
The past decades have witnessed a remarkable emergence of new sources of multiscale multisensor precipitation data, including global spaceborne active and passive sensors, regional ground-based weather surveillance radars, and local rain gauges. Optimal integration of these multisensor data promises a posteriori estimates of precipitation fluxes with increased accuracy and resolution to be used in hydrologic applications. In this context, a new framework is proposed for multiscale multisensor precipitation data fusion which capitalizes on two main observations: (1) non-Gaussian statistics of precipitation images, which are concisely parameterized in the wavelet domain via a class of Gaussian-scale mixtures, and (2) the conditionally Gaussian and weakly correlated local representation of remotely sensed precipitation data in the wavelet domain, which allows for exploiting the efficient linear estimation methodologies while capturing the non-Gaussian data structure of rainfall. The proposed methodology is demonstrated using a data set of coincidental observations of precipitation reflectivity images by the spaceborne precipitation radar aboard the Tropical Rainfall Measurement Mission satellite and by ground-based weather surveillance Doppler radars.
Anisotropic Nonlocal Means Denoising
2011-11-26
match the nuanced edges and textures of real-world images remains open, since we have considered only brutal binary images here. Finally, while NLM...com- puter vision. Denoising algorithms have evolved from the classical linear and median filters to more modern schemes like total variation denoising...underlying image gradients outperforms NLM by a signi cant margin. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Same
Optical Planar Discrete Fourier and Wavelet Transforms
NASA Astrophysics Data System (ADS)
Cincotti, Gabriella; Moreolo, Michela Svaluto; Neri, Alessandro
2007-10-01
We present all-optical architectures to perform discrete wavelet transform (DWT), wavelet packet (WP) decomposition and discrete Fourier transform (DFT) using planar lightwave circuits (PLC) technology. Any compact-support wavelet filter can be implemented as an optical planar two-port lattice-form device, and different subband filtering schemes are possible to denoise, or multiplex optical signals. We consider both parallel and serial input cases. We design a multiport decoder/decoder that is able to generate/process optical codes simultaneously and a flexible logarithmic wavelength multiplexer, with flat top profile and reduced crosstalk.
Automatic denoising of single-trial evoked potentials.
Ahmadi, Maryam; Quian Quiroga, Rodrigo
2013-02-01
We present an automatic denoising method based on the wavelet transform to obtain single trial evoked potentials. The method is based on the inter- and intra-scale variability of the wavelet coefficients and their deviations from baseline values. The performance of the method is tested with simulated event related potentials (ERPs) and with real visual and auditory ERPs. For the simulated data the presented method gives a significant improvement in the observation of single trial ERPs as well as in the estimation of their amplitudes and latencies, in comparison with a standard denoising technique (Donoho's thresholding) and in comparison with the noisy single trials. For the real data, the proposed method largely filters the spontaneous EEG activity, thus helping the identification of single trial visual and auditory ERPs. The proposed method provides a simple, automatic and fast tool that allows the study of single trial responses and their correlations with behavior.
NASA Astrophysics Data System (ADS)
Cui, Xiongwei; Yao, Xiongliang; Wang, Zhikai; Liu, Minghao
2017-03-01
A second generation wavelet-based adaptive finite-difference Lattice Boltzmann method (FD-LBM) is developed in this paper. In this approach, the adaptive wavelet collocation method (AWCM) is firstly, to the best of our knowledge, incorporated into the FD-LBM. According to the grid refinement criterion based on the wavelet amplitudes of density distribution functions, an adaptive sparse grid is generated by the omission and addition of collocation points. On the sparse grid, the finite differences are used to approximate the derivatives. To eliminate the special treatments in using the FD-based derivative approximation near boundaries, the immersed boundary method (IBM) is also introduced into FD-LBM. By using the adaptive technique, the adaptive code requires much less grid points as compared to the uniform-mesh code. As a consequence, the computational efficiency can be improved. To justify the proposed method, a series of test cases, including fixed boundary cases and moving boundary cases, are invested. A good agreement between the present results and the data in previous literatures is obtained, which demonstrates the accuracy and effectiveness of the present AWCM-IB-LBM.
Wavelet-based pavement image compression and noise reduction
NASA Astrophysics Data System (ADS)
Zhou, Jian; Huang, Peisen S.; Chiang, Fu-Pen
2005-08-01
For any automated distress inspection system, typically a huge number of pavement images are collected. Use of an appropriate image compression algorithm can save disk space, reduce the saving time, increase the inspection distance, and increase the processing speed. In this research, a modified EZW (Embedded Zero-tree Wavelet) coding method, which is an improved version of the widely used EZW coding method, is proposed. This method, unlike the two-pass approach used in the original EZW method, uses only one pass to encode both the coordinates and magnitudes of wavelet coefficients. An adaptive arithmetic encoding method is also implemented to encode four symbols assigned by the modified EZW into binary bits. By applying a thresholding technique to terminate the coding process, the modified EZW coding method can compress the image and reduce noise simultaneously. The new method is much simpler and faster. Experimental results also show that the compression ratio was increased one and one-half times compared to the EZW coding method. The compressed and de-noised data can be used to reconstruct wavelet coefficients for off-line pavement image processing such as distress classification and quantification.
Detecting the BAO using Discrete Wavelet Packets
NASA Astrophysics Data System (ADS)
Garcia, Noel Anthony; Wu, Yunyun; Kadowaki, Kevin; Pando, Jesus
2017-01-01
We use wavelet packets to investigate the clustering of matter on galactic scales in search of the Baryon Acoustic Oscillations. We do so in two ways. We develop a wavelet packet approach to measure the power spectrum and apply this method to the CMASS galaxy catalogue from the Sloan Digital Sky Survey (SDSS). We compare the resulting power spectrum to published BOSS results by measuring a parameter β that compares our wavelet detected oscillations to the results from the SDSS collaboration. We find that β=1 indicating that our wavelet packet methods are detecting the BAO at a similar level as traditional Fourier techniques. We then use wavelet packets to decompose, denoise, and then reconstruct the galaxy density field. Using this denoised field, we compute the standard two-point correlation function. We are able to successfully detect the BAO at r ≈ 105 h-1 Mpc in line with previous SDSS results. We conclude that wavelet packets do reproduce the results of the key clustering statistics computed by other means. The wavelet packets show distinct advantages in suppressing high frequency noise and in keeping information localized.
NASA Astrophysics Data System (ADS)
Li, Xueyang; Xiao, Aiguo
2014-06-01
The Gross-Pitaevskii equation is the model equation of the single-particle wave function in a Bose-Einstein condensation. A computation difficulty of the Gross-Pitaevskii equation comes from the semiclassical problem in supercritical case. In this paper, we apply a diffeomorphism to transform the original one-dimensional Gross-Pitaevskii equation into a modified equation. The adaptive grids are constructed through the interpolating wavelet method. Then, we use the time-splitting finite difference method with the wavelet-adaptive grids to solve the modified Gross-Pitaevskii equation, where the approximation to the second-order derivative is given by the Lagrange interpolation method. At last, the numerical results are given. It is shown that the obtained time-splitting finite difference method with the wavelet-adaptive grids is very efficient for solving the one-dimensional semiclassical Gross-Pitaevskii equation in supercritical case and it is suitable to deal with the local high oscillation of the solution.
Graham, Ryan B.; Wachowiak, Mark P.; Gurd, Brendon J.
2015-01-01
Peroxisome proliferator-activated receptor gamma coactivator 1 alpha (PGC-1α) is a transcription factor co-activator that helps coordinate mitochondrial biogenesis within skeletal muscle following exercise. While evidence gleaned from submaximal exercise suggests that intracellular pathways associated with the activation of PGC-1α, as well as the expression of PGC-1α itself are activated to a greater extent following higher intensities of exercise, we have recently shown that this effect does not extend to supramaximal exercise, despite corresponding increases in muscle activation amplitude measured with electromyography (EMG). Spectral analyses of EMG data may provide a more in-depth assessment of changes in muscle electrophysiology occurring across different exercise intensities, and therefore the goal of the present study was to apply continuous wavelet transforms (CWTs) to our previous data to comprehensively evaluate: 1) differences in muscle electrophysiological properties at different exercise intensities (i.e. 73%, 100%, and 133% of peak aerobic power), and 2) muscular effort and fatigue across a single interval of exercise at each intensity, in an attempt to shed mechanistic insight into our previous observations that the increase in PGC-1α is dissociated from exercise intensity following supramaximal exercise. In general, the CWTs revealed that localized muscle fatigue was only greater than the 73% condition in the 133% exercise intensity condition, which directly matched the work rate results. Specifically, there were greater drop-offs in frequency, larger changes in burst power, as well as greater changes in burst area under this intensity, which were already observable during the first interval. As a whole, the results from the present study suggest that supramaximal exercise causes extreme localized muscular fatigue, and it is possible that the blunted PGC-1α effects observed in our previous study are the result of fatigue-associated increases in
MRI denoising using non-local means.
Manjón, José V; Carbonell-Caballero, José; Lull, Juan J; García-Martí, Gracián; Martí-Bonmatí, Luís; Robles, Montserrat
2008-08-01
Magnetic Resonance (MR) images are affected by random noise which limits the accuracy of any quantitative measurements from the data. In the present work, a recently proposed filter for random noise removal is analyzed and adapted to reduce this noise in MR magnitude images. This parametric filter, named Non-Local Means (NLM), is highly dependent on the setting of its parameters. The aim of this paper is to find the optimal parameter selection for MR magnitude image denoising. For this purpose, experiments have been conducted to find the optimum parameters for different noise levels. Besides, the filter has been adapted to fit with specific characteristics of the noise in MR image magnitude images (i.e. Rician noise). From the results over synthetic and real images we can conclude that this filter can be successfully used for automatic MR denoising.
NASA Astrophysics Data System (ADS)
Chamundeeswari, V. V.; Singh, D.; Singh, K.
2007-12-01
In single band and single polarized synthetic aperture radar (SAR) images, the information is limited to intensity and texture only and it is very difficult to interpret such SAR images without any a priori information. For unsupervised classification of SAR images, M-band wavelet decomposition is performed on the SAR image and sub-band selection on the basis of energy levels is applied to improve the classification results since sparse representation of sub-bands degrades the performance of classification. Then, textural features are obtained from selected sub-bands and integrated with intensity features. An adaptive neuro-fuzzy algorithm is used to improve computational efficiency by extracting significant features. K-means classification is performed on the extracted features and land features are labeled. This classification algorithm involves user defined parameters. To remove the user dependency and to obtain maximum achievable classification accuracy, an algorithm is developed in this paper for classification accuracy in terms of the parameters involved in the segmentation process. This is very helpful to develop the automated land-cover monitoring system with SAR, where optimized parameters are to be identified only once and these parameters can be applied to SAR imagery of the same scene obtained year after year. A single band, single polarized SAR image is classified into water, urban and vegetation areas using this method and overall classification accuracy is obtained in the range of 85.92%-93.70% by comparing with ground truth data.
A Comparison of PDE-based Non-Linear Anisotropic Diffusion Techniques for Image Denoising
Weeratunga, S K; Kamath, C
2003-01-06
PDE-based, non-linear diffusion techniques are an effective way to denoise images. In a previous study, we investigated the effects of different parameters in the implementation of isotropic, non-linear diffusion. Using synthetic and real images, we showed that for images corrupted with additive Gaussian noise, such methods are quite effective, leading to lower mean-squared-error values in comparison with spatial filters and wavelet-based approaches. In this paper, we extend this work to include anisotropic diffusion, where the diffusivity is a tensor valued function which can be adapted to local edge orientation. This allows smoothing along the edges, but not perpendicular to it. We consider several anisotropic diffusivity functions as well as approaches for discretizing the diffusion operator that minimize the mesh orientation effects. We investigate how these tensor-valued diffusivity functions compare in image quality, ease of use, and computational costs relative to simple spatial filters, the more complex bilateral filters, wavelet-based methods, and isotropic non-linear diffusion based techniques.
Comparison of PDE-based non-linear anistropic diffusion techniques for image denoising
NASA Astrophysics Data System (ADS)
Weeratunga, Sisira K.; Kamath, Chandrika
2003-05-01
PDE-based, non-linear diffusion techniques are an effective way to denoise images.In a previous study, we investigated the effects of different parameters in the implementation of isotropic, non-linear diffusion. Using synthetic and real images, we showed that for images corrupted with additive Gaussian noise, such methods are quite effective, leading to lower mean-squared-error values in comparison with spatial filters and wavelet-based approaches. In this paper, we extend this work to include anisotropic diffusion, where the diffusivity is a tensor valued function which can be adapted to local edge orientation. This allows smoothing along the edges, but not perpendicular to it. We consider several anisotropic diffusivity functions as well as approaches for discretizing the diffusion operator that minimize the mesh orientation effects. We investigate how these tensor-valued diffusivity functions compare in image quality, ease of use, and computational costs relative to simple spatial filters, the more complex bilateral filters, wavelet-based methods, and isotropic non-linear diffusion based techniques.
Nonlinear Image Denoising Methodologies
2002-05-01
53 5.3 A Multiscale Approach to Scale-Space Analysis . . . . . . . . . . . . . . . . 53 5.4...etc. In this thesis, Our approach to denoising is first based on a controlled nonlinear stochastic random walk to achieve a scale space analysis ( as in... stochastic treatment or interpretation of the diffusion. In addition, unless a specific stopping time is known to be adequate, the resulting evolution
NASA Astrophysics Data System (ADS)
Thangaswamy, Sree Sharmila; Kadarkarai, Ramar; Thangaswamy, Sree Renga Raja
2013-01-01
Satellite images are corrupted by noise during image acquisition and transmission. The removal of noise from the image by attenuating the high-frequency image components removes important details as well. In order to retain the useful information, improve the visual appearance, and accurately classify an image, an effective denoising technique is required. We discuss three important steps such as image denoising, resolution enhancement, and classification for improving accuracy in a noisy image. An effective denoising technique, hybrid directional lifting, is proposed to retain the important details of the images and improve visual appearance. The discrete wavelet transform based interpolation is developed for enhancing the resolution of the denoised image. The image is then classified using a support vector machine, which is superior to other neural network classifiers. The quantitative performance measures such as peak signal to noise ratio and classification accuracy show the significance of the proposed techniques.
Wavelet-based target detection using multiscale directional analysis
NASA Astrophysics Data System (ADS)
Chambers, Bradley J.; Reynolds, William D., Jr.; Campbell, Derrick S.; Fennell, Darius K.; Ansari, Rashid
2007-04-01
Efficient processing of imagery derived from remote sensing systems has become ever more important due to increasing data sizes, rates, and bit depths. This paper proposes a target detection method that uses a special class of wavelets based on highly frequency-selective directional filter banks. The approach helps isolate object features in different directional filter output components. These components lend themselves well to the application of powerful denoising and edge detection procedures in the wavelet domain. Edge information is derived from directional wavelet decompositions to detect targets of known dimension in electro optical imagery. Results of successful detection of objects using the proposed method are presented in the paper. The approach highlights many of the benefits of working with directional wavelet analysis for image denoising and detection.
Coherent noise removal in seismic data with dual-tree M-band wavelets
NASA Astrophysics Data System (ADS)
Duval, Laurent; Chaux, Caroline; Ker, Stéphan
2007-09-01
Seismic data and their complexity still challenge signal processing algorithms in several applications. The advent of wavelet transforms has allowed improvements in tackling denoising problems. We propose here coherent noise filtering in seismic data with the dual-tree M-band wavelet transform. They offer the possibility to decompose data locally with improved multiscale directions and frequency bands. Denoising is performed in a deterministic fashion in the directional subbands, depending of the coherent noise properties. Preliminary results show that they consistently better preserve seismic signal of interest embedded in highly energetic directional noises than discrete critically sampled and redundant separable wavelet transforms.
Noise reduction in LOS wind velocity of Doppler lidar using discrete wavelet analysis
NASA Astrophysics Data System (ADS)
Wu, Songhua; Liu, Zhishen; Sun, Dapeng
2003-12-01
The line of sight (LOS) wind velocity can be determined from the incoherent Doppler lidar backscattering signals. Noise and interference in the measurement greatly degrade the inversion accuracy. In this paper, we apply the discrete wavelet denoising method by using biorthogonal wavelets and adopt a distancedependent thresholds algorithm to improve the accuracy of wind velocity measurement by incoherent Doppler lidar. The noisy simulation data are processed and compared with the true LOS wind velocity. The results are compared by the evaluation of both the standard deviation and correlation coefficient.The results suggest that wavelet denoising with distance-dependent thresholds can considerably reduce the noise and interfering turbulence for wind lidar measurement.
Fast Translation Invariant Multiscale Image Denoising.
Li, Meng; Ghosal, Subhashis
2015-12-01
Translation invariant (TI) cycle spinning is an effective method for removing artifacts from images. However, for a method using O(n) time, the exact TI cycle spinning by averaging all possible circulant shifts requires O(n(2)) time where n is the number of pixels, and therefore is not feasible in practice. Existing literature has investigated efficient algorithms to calculate TI version of some denoising approaches such as Haar wavelet. Multiscale methods, especially those based on likelihood decomposition, such as penalized likelihood estimator and Bayesian methods, have become popular in image processing because of their effectiveness in denoising images. As far as we know, there is no systematic investigation of the TI calculation corresponding to general multiscale approaches. In this paper, we propose a fast TI (FTI) algorithm and a more general k-TI (k-TI) algorithm allowing TI for the last k scales of the image, which are applicable to general d-dimensional images (d = 2, 3, …) with either Gaussian or Poisson noise. The proposed FTI leads to the exact TI estimation but only requires O(n log2 n) time. The proposed k-TI can achieve almost the same performance as the exact TI estimation, but requires even less time. We achieve this by exploiting the regularity present in the multiscale structure, which is justified theoretically. The proposed FTI and k-TI are generic in that they are applicable on any smoothing techniques based on the multiscale structure. We demonstrate the FTI and k-TI algorithms on some recently proposed state-of-the-art methods for both Poisson and Gaussian noised images. Both simulations and real data application confirm the appealing performance of the proposed algorithms. MATLAB toolboxes are online accessible to reproduce the results and be implemented for general multiscale denoising approaches provided by the users.
[Wavelet NeighShrink method for grid texture removal in image of solar radio bursts].
Zhao, Rui-zhen; Hu, Zhan-yi
2007-01-01
The data received from solar bursts contain a lot of noise, which makes further processing more difficult. To remove the noise and enhance the image, we studied the properties of the NeighShrink threshold function and analyzed the influence of neighborhood window size on the denoising result, on the basis of which a new wavelet NeighShrink square root method for image denoising is presented. Firstly, each channel of the solar burst image is normalized, which can, to some extent, remove the horizontal grid texture in the image. Secondly, the preprocessed image is decomposed by wavelet transform, and the obtained wavelet coefficients are thresholded by NeighShrink square root method. Finally, the denoised image is reconstructed by inverse wavelet transform. The experimental results show that the presented method is effective in noise removal and image enhancement.
NASA Astrophysics Data System (ADS)
Pan, Jun; Chen, Jinglong; Zi, Yanyang; Li, Yueming; He, Zhengjia
2016-05-01
Due to the multi-modulation feature in most of the vibration signals, the extraction of embedded fault information from condition monitoring data for mechanical fault diagnosis still is not a relaxed task. Despite the reported achievements, Wavelet transform follows the dyadic partition scheme and would not allow a data-driven frequency partition. And then Empirical Wavelet Transform (EWT) is used to extract inherent modulation information by decomposing signal into mono-components under an orthogonal basis and non-dyadic partition scheme. However, the pre-defined segment way of Fourier spectrum without dependence on analyzed signals may result in inaccurate mono-component identification. In this paper, the modified EWT (MEWT) method via data-driven adaptive Fourier spectrum segment is proposed for mechanical fault identification. First, inner product is calculated between the Fourier spectrum of analyzed signal and Gaussian function for scale representation. Then, adaptive spectrum segment is achieved by detecting local minima of the scale representation. Finally, empirical modes can be obtained by adaptively merging mono-components based on their envelope spectrum similarity. The adaptively extracted empirical modes are analyzed for mechanical fault identification. A simulation experiment and two application cases are used to verify the effectiveness of the proposed method and the results show its outstanding performance.
CT reconstruction via denoising approximate message passing
NASA Astrophysics Data System (ADS)
Perelli, Alessandro; Lexa, Michael A.; Can, Ali; Davies, Mike E.
2016-05-01
In this paper, we adapt and apply a compressed sensing based reconstruction algorithm to the problem of computed tomography reconstruction for luggage inspection. Specifically, we propose a variant of the denoising generalized approximate message passing (D-GAMP) algorithm and compare its performance to the performance of traditional filtered back projection and to a penalized weighted least squares (PWLS) based reconstruction method. D-GAMP is an iterative algorithm that at each iteration estimates the conditional probability of the image given the measurements and employs a non-linear "denoising" function which implicitly imposes an image prior. Results on real baggage show that D-GAMP is well-suited to limited-view acquisitions.
NASA Astrophysics Data System (ADS)
Wang, Zhengzi; Ren, Zhong; Liu, Guodong
2016-10-01
In this paper, the wavelet threshold denoising method was used into the filtered back-projection algorithm of imaging reconstruction. To overcome the drawbacks of the traditional soft- and hard-threshold functions, a modified wavelet threshold function was proposed. The modified wavelet threshold function has two threshold values and two variants. To verify the feasibility of the modified wavelet threshold function, the standard test experiments were performed by using the software platform of MATLAB. Experimental results show that the filtered back-projection reconstruction algorithm based on the modified wavelet threshold function has better reconstruction effect because of more flexible advantage.
Quantum Boolean image denoising
NASA Astrophysics Data System (ADS)
Mastriani, Mario
2015-05-01
A quantum Boolean image processing methodology is presented in this work, with special emphasis in image denoising. A new approach for internal image representation is outlined together with two new interfaces: classical to quantum and quantum to classical. The new quantum Boolean image denoising called quantum Boolean mean filter works with computational basis states (CBS), exclusively. To achieve this, we first decompose the image into its three color components, i.e., red, green and blue. Then, we get the bitplanes for each color, e.g., 8 bits per pixel, i.e., 8 bitplanes per color. From now on, we will work with the bitplane corresponding to the most significant bit (MSB) of each color, exclusive manner. After a classical-to-quantum interface (which includes a classical inverter), we have a quantum Boolean version of the image within the quantum machine. This methodology allows us to avoid the problem of quantum measurement, which alters the results of the measured except in the case of CBS. Said so far is extended to quantum algorithms outside image processing too. After filtering of the inverted version of MSB (inside quantum machine), the result passes through a quantum-classical interface (which involves another classical inverter) and then proceeds to reassemble each color component and finally the ending filtered image. Finally, we discuss the more appropriate metrics for image denoising in a set of experimental results.
3D Wavelet-Based Filter and Method
Moss, William C.; Haase, Sebastian; Sedat, John W.
2008-08-12
A 3D wavelet-based filter for visualizing and locating structural features of a user-specified linear size in 2D or 3D image data. The only input parameter is a characteristic linear size of the feature of interest, and the filter output contains only those regions that are correlated with the characteristic size, thus denoising the image.
The use of ensemble empirical mode decomposition as a novel denoising technique
NASA Astrophysics Data System (ADS)
Gaci, Said; Hachay, Olga; Zaourar, Naima
2016-04-01
Denoising is of a high importance in geophysical data processing. This paper suggests a new denoising technique based on the Ensemble Empirical mode decomposition (EEMD). This technique has been compared with the discrete wavelet transform (DWT) thresholding. Firstly, both methods have been implemented on synthetic signals with diverse waveforms ('blocks', 'heavy sine', 'Doppler', and 'mishmash'). The EEMD denoising method is proved to be the most efficient for 'blocks', 'heavy sine' and 'mishmash' signals for all the considered signal-to-noise ratio (SNR) values. However, the results obtained using the DWT thresholding are the most reliable for 'Doppler' signal, and the difference between the calculated mean square error (MSE) values using the studied methods is slight and decreases as the SNR value gets smaller values. Secondly, the denoising methods have been applied on real seismic traces recorded in the Algerian Sahara. It is shown that the proposed technique outperforms the DWT thresholding. In conclusion, the EEMD technique can provide a powerful tool for denoising seismic signals. Keywords: Ensemble Empirical mode decomposition (EEMD), Discrete wavelet transform (DWT), seismic signal.
NASA Astrophysics Data System (ADS)
Duan, Yabo; Song, Chengtian
2016-12-01
Empirical mode decomposition (EMD) is a recently proposed nonlinear and nonstationary laser signal denoising method. A noisy signal is broken down using EMD into oscillatory components that are called intrinsic mode functions (IMFs). Thresholding-based denoising and correlation-based partial reconstruction of IMFs are the two main research directions for EMD-based denoising. Similar to other decomposition-based denoising approaches, EMD-based denoising methods require a reliable threshold to determine which IMFs are noise components and which IMFs are noise-free components. In this work, we propose a new approach in which each IMF is first denoised using EMD interval thresholding (EMD-IT), and then a robust thresholding process based on Spearman correlation coefficient is used for relevant modes selection. The proposed method tackles the problem using a thresholding-based denoising approach coupled with partial reconstruction of the relevant IMFs. Other traditional denoising methods, including correlation-based EMD partial reconstruction (EMD-Correlation), discrete Fourier transform and wavelet-based methods, are investigated to provide a comparison with the proposed technique. Simulation and test results demonstrate the superior performance of the proposed method when compared with the other methods.
The use of wavelet filters for reducing noise in posterior fossa Computed Tomography images
Pita-Machado, Reinado; Perez-Diaz, Marlen Lorenzo-Ginori, Juan V. Bravo-Pino, Rolando
2014-11-07
Wavelet transform based de-noising like wavelet shrinkage, gives the good results in CT. This procedure affects very little the spatial resolution. Some applications are reconstruction methods, while others are a posteriori de-noising methods. De-noising after reconstruction is very difficult because the noise is non-stationary and has unknown distribution. Therefore, methods which work on the sinogram-space don’t have this problem, because they always work over a known noise distribution at this point. On the other hand, the posterior fossa in a head CT is a very complex region for physicians, because it is commonly affected by artifacts and noise which are not eliminated during the reconstruction procedure. This can leads to some false positive evaluations. The purpose of our present work is to compare different wavelet shrinkage de-noising filters to reduce noise, particularly in images of the posterior fossa within CT scans in the sinogram-space. This work describes an experimental search for the best wavelets, to reduce Poisson noise in Computed Tomography (CT) scans. Results showed that de-noising with wavelet filters improved the quality of posterior fossa region in terms of an increased CNR, without noticeable structural distortions.
Study on the FOG's signal based on wavelet
NASA Astrophysics Data System (ADS)
Tang, Ji-qiang; Fang, Jian-cheng; Zhang, Yan-shun
2006-11-01
In order to study on the fiber optical gyro (abbreviated as FOG) signal based on wavelet, this paper researches the FOG signal drift model and the properties of wavelet analyzed noise, introduces the wavelet filtering method, wavelet base selection, soft and hard threshold value de-noising algorithm and compulsive filtering based on The Haar wavelet. These threshold value filtering results of both of the soft and of the hard threshold value for the same wavelet base of db4 with the same Donoho threshold values and these results of compulsive filtering based on The Haar wavelet and db4 wavelet are presented also in this paper and then these main conclusions based on foregoing analysis are reached: Larger the resolving scale is, the filtering effect is more perfect. The soft threshold value filtering effect is better than that of the hard threshold value filtering at the cost of calculation when the threshold value is same. The zero shift of the compulsive filtering is least when both the wavelet and the resolving scale are same for these filtering methods. For the compulsive filtering with same wavelets, the filtering effect of Harr is better than that of db4 and the calculation of the former is fewer. Finally the author point out that applying the compulsive filtering with the Harr wavelet base and suitable resolving scale to the signal processing of FOG be helpful for the FOG's design and manufacturing.
New trends in despeckling: undecimated-wavelet shrinkage and fuzzy matching-pursuits estimation
NASA Astrophysics Data System (ADS)
Aiazzi, Bruno; Alparone, Luciano; Argenti, Fabrizio; Baronti, Stefano
2002-02-01
This paper presents two novel approaches to speckle reduction in SAR images. The former relies on the multiplicative speckle model as an MMSE filtering performed in the wavelet domain by means of an adaptive shrinkage of the detail coefficients of an undecimated decomposition. Each coefficient is shrunk by the variance ratio of the noise-free coefficient to the noisy one. All the above quantities are analytically calculated from the speckled image, the noise variance, and the wavelet filters only, without resorting to any model to describe the underlying backscatter. Estimation of the local statistics driving the filter is expedited and layered processing allows to extend adaptivity also across the spatial scale. The latter is not model-based and provides a blind estimation of the backscatter underlying the speckled image stated as a problem of matching pursuits. The local adaptive MMSE estimator is obtained as an expansion in series of a finite number of prototype estimators, fitting the spatial features of the different statistical classes encountered, e.g., edges and textures. Such estimators are calculated in a fuzzy fashion through an automatic training procedure. The space-varying coefficients of the expansion are stated as degrees of fuzzy membership of a pixel to each of the estimators. A thorough performance comparison is carried out with the Gamma-MAP filter and with the Rational Laplacian Pyramid (RLP) filter, recently introduced by three of the authors. On simulated speckled images both the proposed filters gain almost 3 dB SNR with respect to conventional local-statistics (Lee/Kuan) filtering. Experiments carried out on widespread test SAR images and on a speckled mosaic image, comprising synthetic shapes, textures, and details from true SAR images, demonstrate that the visual quality of the results is excellent in terms of both background smoothing and preservation of edge sharpness, textures, and point targets. The absence of decimation in the
A comparison of wavelet analysis techniques in digital holograms
NASA Astrophysics Data System (ADS)
Molony, Karen M.; Maycock, Jonathan; McDonald, John B.; Hennelly, Bryan M.; Naughton, Thomas J.
2008-04-01
This study explores the effectiveness of wavelet analysis techniques on digital holograms of real-world 3D objects. Stationary and discrete wavelet transform techniques have been applied for noise reduction and compared. Noise is a common problem in image analysis and successful reduction of noise without degradation of content is difficult to achieve. These wavelet transform denoising techniques are contrasted with traditional noise reduction techniques; mean filtering, median filtering, Fourier filtering. The different approaches are compared in terms of speckle reduction, edge preservation and resolution preservation.
A fast non-local image denoising algorithm
NASA Astrophysics Data System (ADS)
Dauwe, A.; Goossens, B.; Luong, H. Q.; Philips, W.
2008-02-01
In this paper we propose several improvements to the original non-local means algorithm introduced by Buades et al. which obtains state-of-the-art denoising results. The strength of this algorithm is to exploit the repetitive character of the image in order to denoise the image unlike conventional denoising algorithms, which typically operate in a local neighbourhood. Due to the enormous amount of weight computations, the original algorithm has a high computational cost. An improvement of image quality towards the original algorithm is to ignore the contributions from dissimilar windows. Even though their weights are very small at first sight, the new estimated pixel value can be severely biased due to the many small contributions. This bad influence of dissimilar windows can be eliminated by setting their corresponding weights to zero. Using the preclassification based on the first three statistical moments, only contributions from similar neighborhoods are computed. To decide whether a window is similar or dissimilar, we will derive thresholds for images corrupted with additive white Gaussian noise. Our accelerated approach is further optimized by taking advantage of the symmetry in the weights, which roughly halves the computation time, and by using a lookup table to speed up the weight computations. Compared to the original algorithm, our proposed method produces images with increased PSNR and better visual performance in less computation time. Our proposed method even outperforms state-of-the-art wavelet denoising techniques in both visual quality and PSNR values for images containing a lot of repetitive structures such as textures: the denoised images are much sharper and contain less artifacts. The proposed optimizations can also be applied in other image processing tasks which employ the concept of repetitive structures such as intra-frame super-resolution or detection of digital image forgery.
Optimal FPGA implementation of CL multiwavelets architecture for signal denoising application
NASA Astrophysics Data System (ADS)
Mohan Kumar, B.; Vidhya Lavanya, R.; Sumesh, E. P.
2013-03-01
Wavelet transform is considered one of the efficient transforms of this decade for real time signal processing. Due to implementation constraints scalar wavelets do not possess the properties such as compact support, regularity, orthogonality and symmetry, which are desirable qualities to provide a good signal to noise ratio (SNR) in case of signal denoising. This leads to the evolution of the new dimension of wavelet called 'multiwavelets', which possess more than one scaling and wavelet filters. The architecture implementation of multiwavelets is an emerging area of research. In real time, the signals are in scalar form, which demands the processing architecture to be scalar. But the conventional Donovan Geronimo Hardin Massopust (DGHM) and Chui-Lian (CL) multiwavelets are vectored and are also unbalanced. In this article, the vectored multiwavelet transforms are converted into a scalar form and its architecture is implemented in FPGA (Field Programmable Gate Array) for signal denoising application. The architecture is compared with DGHM multiwavelets architecture in terms of several objective and performance measures. The CL multiwavelets architecture is further optimised for best performance by using DSP48Es. The results show that CL multiwavelet architecture is suited better for the signal denoising application.
Schlossnagle, G.; Restrepo, J.M.; Leaf, G.K.
1993-12-01
The properties of periodized Daubechies wavelets on [0,1] are detailed and contrasted against their counterparts which form a basis for L{sup 2}(R). Numerical examples illustrate the analytical estimates for convergence and demonstrate by comparison with Fourier spectral methods the superiority of wavelet projection methods for approximations. The analytical solution to inner products of periodized wavelets and their derivatives, which are known as connection coefficients, is presented, and several tabulated values are included.
NASA Astrophysics Data System (ADS)
Hortos, William S.
2008-04-01
Proposed distributed wavelet-based algorithms are a means to compress sensor data received at the nodes forming a wireless sensor network (WSN) by exchanging information between neighboring sensor nodes. Local collaboration among nodes compacts the measurements, yielding a reduced fused set with equivalent information at far fewer nodes. Nodes may be equipped with multiple sensor types, each capable of sensing distinct phenomena: thermal, humidity, chemical, voltage, or image signals with low or no frequency content as well as audio, seismic or video signals within defined frequency ranges. Compression of the multi-source data through wavelet-based methods, distributed at active nodes, reduces downstream processing and storage requirements along the paths to sink nodes; it also enables noise suppression and more energy-efficient query routing within the WSN. Targets are first detected by the multiple sensors; then wavelet compression and data fusion are applied to the target returns, followed by feature extraction from the reduced data; feature data are input to target recognition/classification routines; targets are tracked during their sojourns through the area monitored by the WSN. Algorithms to perform these tasks are implemented in a distributed manner, based on a partition of the WSN into clusters of nodes. In this work, a scheme of collaborative processing is applied for hierarchical data aggregation and decorrelation, based on the sensor data itself and any redundant information, enabled by a distributed, in-cluster wavelet transform with lifting that allows multiple levels of resolution. The wavelet-based compression algorithm significantly decreases RF bandwidth and other resource use in target processing tasks. Following wavelet compression, features are extracted. The objective of feature extraction is to maximize the probabilities of correct target classification based on multi-source sensor measurements, while minimizing the resource expenditures at
Wavelets based on Hermite cubic splines
NASA Astrophysics Data System (ADS)
Cvejnová, Daniela; Černá, Dana; Finěk, Václav
2016-06-01
In 2000, W. Dahmen et al. designed biorthogonal multi-wavelets adapted to the interval [0,1] on the basis of Hermite cubic splines. In recent years, several more simple constructions of wavelet bases based on Hermite cubic splines were proposed. We focus here on wavelet bases with respect to which both the mass and stiffness matrices are sparse in the sense that the number of nonzero elements in any column is bounded by a constant. Then, a matrix-vector multiplication in adaptive wavelet methods can be performed exactly with linear complexity for any second order differential equation with constant coefficients. In this contribution, we shortly review these constructions and propose a new wavelet which leads to improved Riesz constants. Wavelets have four vanishing wavelet moments.
Talebi, Hossein; Milanfar, Peyman
2014-02-01
Most existing state-of-the-art image denoising algorithms are based on exploiting similarity between a relatively modest number of patches. These patch-based methods are strictly dependent on patch matching, and their performance is hamstrung by the ability to reliably find sufficiently similar patches. As the number of patches grows, a point of diminishing returns is reached where the performance improvement due to more patches is offset by the lower likelihood of finding sufficiently close matches. The net effect is that while patch-based methods, such as BM3D, are excellent overall, they are ultimately limited in how well they can do on (larger) images with increasing complexity. In this paper, we address these shortcomings by developing a paradigm for truly global filtering where each pixel is estimated from all pixels in the image. Our objectives in this paper are two-fold. First, we give a statistical analysis of our proposed global filter, based on a spectral decomposition of its corresponding operator, and we study the effect of truncation of this spectral decomposition. Second, we derive an approximation to the spectral (principal) components using the Nyström extension. Using these, we demonstrate that this global filter can be implemented efficiently by sampling a fairly small percentage of the pixels in the image. Experiments illustrate that our strategy can effectively globalize any existing denoising filters to estimate each pixel using all pixels in the image, hence improving upon the best patch-based methods.
NASA Astrophysics Data System (ADS)
Ren, Zhong; Liu, Guodong; Huang, Zhen
2016-10-01
In this study, the filtered back-projection algorithm was used to reconstruct the photoacoustic imaging. To improve the quality of the reconstructed image, the wavelet threshold denoising method was combined into the filtered back-projection reconstruction algorithm. To obtain the reconstructed effect of the photoacoustic imaging, a modified wavelet threshold function was proposed. To verify the feasibility of the modified wavelet threshold function, the simulation experiments of the standard test phantom were performed by using three different wavelet threshold functions. Compared with the soft- and hard-threshold functions, the modified wavelet threshold function has better denoised and reconstructed effect. Moreover, the peak signal-to-noises ratio (PSNR) value of the modified function is largest, and its mean root square error (MRSE) value is lest than that of two others. Therefore, the filtered back-projection reconstruction algorithm combined with the modified wavelet threshold function has potential value in the reconstruction of the photoacoustic imaging.
NASA Astrophysics Data System (ADS)
Richard, Nelly; Laursen, Bettina; Grupe, Morten; Drewes, Asbjørn M.; Graversen, Carina; Sørensen, Helge B. D.; Bastlund, Jesper F.
2017-04-01
Objective. Active auditory oddball paradigms are simple tone discrimination tasks used to study the P300 deflection of event-related potentials (ERPs). These ERPs may be quantified by time-frequency analysis. As auditory stimuli cause early high frequency and late low frequency ERP oscillations, the continuous wavelet transform (CWT) is often chosen for decomposition due to its multi-resolution properties. However, as the conventional CWT traditionally applies only one mother wavelet to represent the entire spectrum, the time-frequency resolution is not optimal across all scales. To account for this, we developed and validated a novel method specifically refined to analyse P300-like ERPs in rats. Approach. An adapted CWT (aCWT) was implemented to preserve high time-frequency resolution across all scales by commissioning of multiple wavelets operating at different scales. First, decomposition of simulated ERPs was illustrated using the classical CWT and the aCWT. Next, the two methods were applied to EEG recordings obtained from prefrontal cortex in rats performing a two-tone auditory discrimination task. Main results. While only early ERP frequency changes between responses to target and non-target tones were detected by the CWT, both early and late changes were successfully described with strong accuracy by the aCWT in rat ERPs. Increased frontal gamma power and phase synchrony was observed particularly within theta and gamma frequency bands during deviant tones. Significance. The study suggests superior performance of the aCWT over the CWT in terms of detailed quantification of time-frequency properties of ERPs. Our methodological investigation indicates that accurate and complete assessment of time-frequency components of short-time neural signals is feasible with the novel analysis approach which may be advantageous for characterisation of several types of evoked potentials in particularly rodents.
Comparison of de-noising techniques for FIRST images
Fodor, I K; Kamath, C
2001-01-22
Data obtained through scientific observations are often contaminated by noise and artifacts from various sources. As a result, a first step in mining these data is to isolate the signal of interest by minimizing the effects of the contaminations. Once the data has been cleaned or de-noised, data mining can proceed as usual. In this paper, we describe our work in denoising astronomical images from the Faint Images of the Radio Sky at Twenty-Centimeters (FIRST) survey. We are mining this survey to detect radio-emitting galaxies with a bent-double morphology. This task is made difficult by the noise in the images caused by the processing of the sensor data. We compare three different approaches to de-noising: thresholding of wavelet coefficients advocated in the statistical community, traditional Altering methods used in the image processing community, and a simple thresholding scheme proposed by FIRST astronomers. While each approach has its merits and pitfalls, we found that for our purpose, the simple thresholding scheme worked relatively well for the FIRST dataset.
A hybrid spatial-spectral denoising method for infrared hyperspectral images using 2DPCA
NASA Astrophysics Data System (ADS)
Huang, Jun; Ma, Yong; Mei, Xiaoguang; Fan, Fan
2016-11-01
The traditional noise reduction methods for 3-D infrared hyperspectral images typically operate independently in either the spatial or spectral domain, and such methods overlook the relationship between the two domains. To address this issue, we propose a hybrid spatial-spectral method in this paper to link both domains. First, principal component analysis and bivariate wavelet shrinkage are performed in the 2-D spatial domain. Second, 2-D principal component analysis transformation is conducted in the 1-D spectral domain to separate the basic components from detail ones. The energy distribution of noise is unaffected by orthogonal transformation; therefore, the signal-to-noise ratio of each component is used as a criterion to determine whether a component should be protected from over-denoising or denoised with certain 1-D denoising methods. This study implements the 1-D wavelet shrinking threshold method based on Stein's unbiased risk estimator, and the quantitative results on publicly available datasets demonstrate that our method can improve denoising performance more effectively than other state-of-the-art methods can.
Shao, Yu; Chang, Chip-Hong
2007-08-01
We present a new speech enhancement scheme for a single-microphone system to meet the demand for quality noise reduction algorithms capable of operating at a very low signal-to-noise ratio. A psychoacoustic model is incorporated into the generalized perceptual wavelet denoising method to reduce the residual noise and improve the intelligibility of speech. The proposed method is a generalized time-frequency subtraction algorithm, which advantageously exploits the wavelet multirate signal representation to preserve the critical transient information. Simultaneous masking and temporal masking of the human auditory system are modeled by the perceptual wavelet packet transform via the frequency and temporal localization of speech components. The wavelet coefficients are used to calculate the Bark spreading energy and temporal spreading energy, from which a time-frequency masking threshold is deduced to adaptively adjust the subtraction parameters of the proposed method. An unvoiced speech enhancement algorithm is also integrated into the system to improve the intelligibility of speech. Through rigorous objective and subjective evaluations, it is shown that the proposed speech enhancement system is capable of reducing noise with little speech degradation in adverse noise environments and the overall performance is superior to several competitive methods.
Discrete directional wavelet bases for image compression
NASA Astrophysics Data System (ADS)
Dragotti, Pier L.; Velisavljevic, Vladan; Vetterli, Martin; Beferull-Lozano, Baltasar
2003-06-01
The application of the wavelet transform in image processing is most frequently based on a separable construction. Lines and columns in an image are treated independently and the basis functions are simply products of the corresponding one dimensional functions. Such method keeps simplicity in design and computation, but is not capable of capturing properly all the properties of an image. In this paper, a new truly separable discrete multi-directional transform is proposed with a subsampling method based on lattice theory. Alternatively, the subsampling can be omitted and this leads to a multi-directional frame. This transform can be applied in many areas like denoising, non-linear approximation and compression. The results on non-linear approximation and denoising show very interesting gains compared to the standard two-dimensional analysis.
NASA Astrophysics Data System (ADS)
Kang, Shanlin; Wang, Bingjun; Kang, Yuzhe
2006-11-01
By combining wavelet transform (WT ) with fractal theory, a novel approach is put forward to detect early short-circuit fault. The application of signal denoising based on the statistic rule is brought forward to determine the threshold of each order of wavelet space, and an effective method is proposed to determine the decomposition adaptively, increasing the signal-noise-ratio (SNR). In a view of the inter relationship of wavelet transform and fractal theory, the whole and local fractal exponents obtained from WT coefficients as features are presented for extracting fault signals. The effectiveness of the new algorithm used to extract the characteristic signal is described, which can be realized by the value of the fractal dimensions of those types of short-circuit fault. In accordance with the threshold value of each type of short-circuit fault in each frequency band, the correlation between the type of short-circuit and the fractal dimensions can be figured to perform extraction. This model incorporates the advantages of morphological filter and multi-scale WT to extract the feature of faults meanwhile restraining various noises. Besides, it can be implemented in real time using the available hardware. The effectiveness of this model was verified with the simulation results.
Wavelet applied to computer vision in astrophysics
NASA Astrophysics Data System (ADS)
Bijaoui, Albert; Slezak, Eric; Traina, Myriam
2004-02-01
Multiscale analyses can be provided by application wavelet transforms. For image processing purposes, we applied algorithms which imply a quasi isotropic vision. For a uniform noisy image, a wavelet coefficient W has a probability density function (PDF) p(W) which depends on the noise statistic. The PDF was determined for many statistical noises: Gauss, Poission, Rayleigh, exponential. For CCD observations, the Anscombe transform was generalized to a mixed Gasus+Poisson noise. From the discrete wavelet transform a set of significant wavelet coefficients (SSWC)is obtained. Many applications have been derived like denoising and deconvolution. Our main application is the decomposition of the image into objects, i.e the vision. At each scale an image labelling is performed in the SSWC. An interscale graph linking the fields of significant pixels is then obtained. The objects are identified using this graph. The wavelet coefficients of the tree related to a given object allow one to reconstruct its image by a classical inverse method. This vision model has been applied to astronomical images, improving the analysis of complex structures.
Fletcher, Joel G.; Hara, Amy K.; Fidler, Jeff L.; Silva, Alvin C.; Barlow, John M.; Carter, Rickey E.; Bartley, Adam; Shiung, Maria; Holmes, David R.; Weber, Nicolas K.; Bruining, David H.; Yu, Lifeng; McCollough, Cynthia H.
2015-01-01
Purpose The purpose of this study was to compare observer performance for detection of intestinal inflammation for low-dose CT enterography (LD-CTE) using scanner-based iterative reconstruction (IR) vs. vendor-independent, adaptive image-based noise reduction (ANLM) or filtered back projection (FBP). Methods Sixty-two LD-CTE exams were performed. LD-CTE images were reconstructed using IR, ANLM, and FBP. Three readers, blinded to image type, marked intestinal inflammation directly on patient images using a specialized workstation over three sessions, interpreting one image type/patient/session. Reference standard was created by a gastroenterologist and radiologist, who reviewed all available data including dismissal Gastroenterology records, and who marked all inflamed bowel segments on the same workstation. Reader and reference localizations were then compared. Non-inferiority was tested using Jackknife free-response ROC (JAFROC) figures of merit (FOM) for ANLM and FBP compared to IR. Patient-level analyses for the presence or absence of inflammation were also conducted. Results There were 46 inflamed bowel segments in 24/62 patients (CTDIvol interquartile range 6.9–10.1 mGy). JAFROC FOM for ANLM and FBP were 0.84 (95% CI 0.75–0.92) and 0.84 (95% CI 0.75–0.92), and were statistically non-inferior to IR (FOM 0.84; 95% CI 0.76–0.93). Patient-level pooled confidence intervals for sensitivity widely overlapped, as did specificities. Image quality was rated as better with IR and AMLM compared to FBP (p < 0.0001), with no difference in reading times (p = 0.89). Conclusions Vendor-independent adaptive image-based noise reduction and FBP provided observer performance that was non-inferior to scanner-based IR methods. Adaptive image-based noise reduction maintained or improved upon image quality ratings compared to FBP when performing CTE at lower dose levels. PMID:25725794
A Wavelet Perspective on the Allan Variance.
Percival, Donald B
2016-04-01
The origins of the Allan variance trace back 50 years ago to two seminal papers, one by Allan (1966) and the other by Barnes (1966). Since then, the Allan variance has played a leading role in the characterization of high-performance time and frequency standards. Wavelets first arose in the early 1980s in the geophysical literature, and the discrete wavelet transform (DWT) became prominent in the late 1980s in the signal processing literature. Flandrin (1992) briefly documented a connection between the Allan variance and a wavelet transform based upon the Haar wavelet. Percival and Guttorp (1994) noted that one popular estimator of the Allan variance-the maximal overlap estimator-can be interpreted in terms of a version of the DWT now widely referred to as the maximal overlap DWT (MODWT). In particular, when the MODWT is based on the Haar wavelet, the variance of the resulting wavelet coefficients-the wavelet variance-is identical to the Allan variance when the latter is multiplied by one-half. The theory behind the wavelet variance can thus deepen our understanding of the Allan variance. In this paper, we review basic wavelet variance theory with an emphasis on the Haar-based wavelet variance and its connection to the Allan variance. We then note that estimation theory for the wavelet variance offers a means of constructing asymptotically correct confidence intervals (CIs) for the Allan variance without reverting to the common practice of specifying a power-law noise type a priori. We also review recent work on specialized estimators of the wavelet variance that are of interest when some observations are missing (gappy data) or in the presence of contamination (rogue observations or outliers). It is a simple matter to adapt these estimators to become estimators of the Allan variance. Finally we note that wavelet variances based upon wavelets other than the Haar offer interesting generalizations of the Allan variance.
Wavelet Local Extrema Applied to Image Processing
1992-12-01
The research project had two components. In the first part, we developed a numerical method, based on the wavelet transform , for the solution of...on the orthogonal wavelet transform , that adapts the computational resolution in space and time to the regularity of the solution. This scheme saves
Sonar target enhancement by shrinkage of incoherent wavelet coefficients.
Hunter, Alan J; van Vossen, Robbert
2014-01-01
Background reverberation can obscure useful features of the target echo response in broadband low-frequency sonar images, adversely affecting detection and classification performance. This paper describes a resolution and phase-preserving means of separating the target response from the background reverberation noise using a coherence-based wavelet shrinkage method proposed recently for de-noising magnetic resonance images. The algorithm weights the image wavelet coefficients in proportion to their coherence between different looks under the assumption that the target response is more coherent than the background. The algorithm is demonstrated successfully on experimental synthetic aperture sonar data from a broadband low-frequency sonar developed for buried object detection.
A de-noising algorithm to improve SNR of segmented gamma scanner for spectrum analysis
NASA Astrophysics Data System (ADS)
Li, Huailiang; Tuo, Xianguo; Shi, Rui; Zhang, Jinzhao; Henderson, Mark Julian; Courtois, Jérémie; Yan, Minhao
2016-05-01
An improved threshold shift-invariant wavelet transform de-noising algorithm for high-resolution gamma-ray spectroscopy is proposed to optimize the threshold function of wavelet transforms and reduce signal resulting from pseudo-Gibbs artificial fluctuations. This algorithm was applied to a segmented gamma scanning system with large samples in which high continuum levels caused by Compton scattering are routinely encountered. De-noising data from the gamma ray spectrum measured by segmented gamma scanning system with improved, shift-invariant and traditional wavelet transform algorithms were all evaluated. The improved wavelet transform method generated significantly enhanced performance of the figure of merit, the root mean square error, the peak area, and the sample attenuation correction in the segmented gamma scanning system assays. We also found that the gamma energy spectrum can be viewed as a low frequency signal as well as high frequency noise superposition by the spectrum analysis. Moreover, a smoothed spectrum can be appropriate for straightforward automated quantitative analysis.
Simultaneous Fusion and Denoising of Panchromatic and Multispectral Satellite Images
NASA Astrophysics Data System (ADS)
Ragheb, Amr M.; Osman, Heba; Abbas, Alaa M.; Elkaffas, Saleh M.; El-Tobely, Tarek A.; Khamis, S.; Elhalawany, Mohamed E.; Nasr, Mohamed E.; Dessouky, Moawad I.; Al-Nuaimy, Waleed; Abd El-Samie, Fathi E.
2012-12-01
To identify objects in satellite images, multispectral (MS) images with high spectral resolution and low spatial resolution, and panchromatic (Pan) images with high spatial resolution and low spectral resolution need to be fused. Several fusion methods such as the intensity-hue-saturation (IHS), the discrete wavelet transform, the discrete wavelet frame transform (DWFT), and the principal component analysis have been proposed in recent years to obtain images with both high spectral and spatial resolutions. In this paper, a hybrid fusion method for satellite images comprising both the IHS transform and the DWFT is proposed. This method tries to achieve the highest possible spectral and spatial resolutions with as small distortion in the fused image as possible. A comparison study between the proposed hybrid method and the traditional methods is presented in this paper. Different MS and Pan images from Landsat-5, Spot, Landsat-7, and IKONOS satellites are used in this comparison. The effect of noise on the proposed hybrid fusion method as well as the traditional fusion methods is studied. Experimental results show the superiority of the proposed hybrid method to the traditional methods. The results show also that a wavelet denoising step is required when fusion is performed at low signal-to-noise ratios.
Phase-preserving speckle reduction based on soft thresholding in quaternion wavelet domain
NASA Astrophysics Data System (ADS)
Liu, Yipeng; Jin, Jing; Wang, Qiang; Shen, Yi
2012-10-01
Speckle reduction is a difficult task for ultrasound image processing because of low resolution and contrast. As a novel tool of image analysis, quaternion wavelet (QW) has some superior properties compared to discrete wavelets, such as nearly shift-invariant wavelet coefficients and phase-based texture presentation. We aim to exploit the excellent performance of speckle reduction in quaternion wavelet domain based on the soft thresholding method. First, we exploit the characteristics of magnitude and phases in quaternion wavelet transform (QWT) to the denoising application, and find that the QWT phases of the images are little influenced by the noises. Then we model the QWT magnitude using the Rayleigh distribution, and derive the thresholding criterion. Furthermore, we conduct several experiments on synthetic speckle images and real ultrasound images. The performance of the proposed speckle reduction algorithm, using QWT with soft thresholding, demonstrates superiority to those using discrete wavelet transform and classical algorithms.
Applications of continuous and orthogonal wavelet transforms to MHD and plasma turbulence
NASA Astrophysics Data System (ADS)
Farge, Marie; Schneider, Kai
2016-10-01
Wavelet analysis and compression tools are presented and different applications to study MHD and plasma turbulence are illustrated. We use the continuous and the orthogonal wavelet transform to develop several statistical diagnostics based on the wavelet coefficients. We show how to extract coherent structures out of fully developed turbulent flows using wavelet-based denoising and describe multiscale numerical simulation schemes using wavelets. Several examples for analyzing, compressing and computing one, two and three dimensional turbulent MHD or plasma flows are presented. Details can be found in M. Farge and K. Schneider. Wavelet transforms and their applications to MHD and plasma turbulence: A review. Support by the French Research Federation for Fusion Studies within the framework of the European Fusion Development Agreement (EFDA) is thankfully acknowledged.
Wavelet-based density estimation for noise reduction in plasma simulations using particles
NASA Astrophysics Data System (ADS)
van yen, Romain Nguyen; del-Castillo-Negrete, Diego; Schneider, Kai; Farge, Marie; Chen, Guangye
2010-04-01
For given computational resources, the accuracy of plasma simulations using particles is mainly limited by the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on wavelet analysis is proposed and tested to reduce this noise. The method, known as wavelet-based density estimation (WBDE), was previously introduced in the statistical literature to estimate probability densities given a finite number of independent measurements. Its novel application to plasma simulations can be viewed as a natural extension of the finite size particles (FSP) approach, with the advantage of estimating more accurately distribution functions that have localized sharp features. The proposed method preserves the moments of the particle distribution function to a good level of accuracy, has no constraints on the dimensionality of the system, does not require an a priori selection of a global smoothing scale, and its able to adapt locally to the smoothness of the density based on the given discrete particle data. Moreover, the computational cost of the denoising stage is of the same order as one time step of a FSP simulation. The method is compared with a recently proposed proper orthogonal decomposition based method, and it is tested with three particle data sets involving different levels of collisionality and interaction with external and self-consistent fields.
Wavelet-based density estimation for noise reduction in plasma simulations using particles
Nguyen van yen, Romain; Del-Castillo-Negrete, Diego B; Schneider, Kai; Farge, Marie; Chen, Guangye
2010-01-01
For given computational resources, one of the main limitations in the accuracy of plasma simulations using particles comes from the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on wavelet multiresolution analysis is proposed and tested to reduce this noise. The method, known as wavelet based density estimation (WBDE), was previously introduced in the statistical literature to estimate probability densities given a nite number of independent measurements. Its novel application to plasma simulations can be viewed as a natural extension of the nite size particles (FSP) approach, with the advantage of estimating more accurately distribution functions that have localized sharp features. The proposed method preserves the moments of the particle distribution function to a good level of accuracy, has no constraints on the dimensionality of the system, does not require an a priori selection of a global smoothing scale, and its able to adapt locally to the smoothness of the density based on the given discrete particle data. Most importantly, the computational cost of the denoising stage is of the same order as one timestep of a FSP simulation. The method is compared with a recently proposed proper orthogonal decomposition based method, and it is tested with particle data corresponding to strongly collisional, weakly collisional, and collisionless plasmas simulations.
NASA Astrophysics Data System (ADS)
Chen, Xinyuan; Song, Li; Yang, Xiaokang
2016-09-01
Video denoising can be described as the problem of mapping from a specific length of noisy frames to clean one. We propose a deep architecture based on Recurrent Neural Network (RNN) for video denoising. The model learns a patch-based end-to-end mapping between the clean and noisy video sequences. It takes the corrupted video sequences as the input and outputs the clean one. Our deep network, which we refer to as deep Recurrent Neural Networks (deep RNNs or DRNNs), stacks RNN layers where each layer receives the hidden state of the previous layer as input. Experiment shows (i) the recurrent architecture through temporal domain extracts motion information and does favor to video denoising, and (ii) deep architecture have large enough capacity for expressing mapping relation between corrupted videos as input and clean videos as output, furthermore, (iii) the model has generality to learned different mappings from videos corrupted by different types of noise (e.g., Poisson-Gaussian noise). By training on large video databases, we are able to compete with some existing video denoising methods.
Chiron, Lionel; van Agthoven, Maria A.; Kieffer, Bruno; Rolando, Christian; Delsuc, Marc-André
2014-01-01
Modern scientific research produces datasets of increasing size and complexity that require dedicated numerical methods to be processed. In many cases, the analysis of spectroscopic data involves the denoising of raw data before any further processing. Current efficient denoising algorithms require the singular value decomposition of a matrix with a size that scales up as the square of the data length, preventing their use on very large datasets. Taking advantage of recent progress on random projection and probabilistic algorithms, we developed a simple and efficient method for the denoising of very large datasets. Based on the QR decomposition of a matrix randomly sampled from the data, this approach allows a gain of nearly three orders of magnitude in processing time compared with classical singular value decomposition denoising. This procedure, called urQRd (uncoiled random QR denoising), strongly reduces the computer memory footprint and allows the denoising algorithm to be applied to virtually unlimited data size. The efficiency of these numerical tools is demonstrated on experimental data from high-resolution broadband Fourier transform ion cyclotron resonance mass spectrometry, which has applications in proteomics and metabolomics. We show that robust denoising is achieved in 2D spectra whose interpretation is severely impaired by scintillation noise. These denoising procedures can be adapted to many other data analysis domains where the size and/or the processing time are crucial. PMID:24390542
Analyzing Planck-Like Data with Wavelets
NASA Astrophysics Data System (ADS)
Sanz, J. L.; Barreiro, R. B.; Cayón, L.; Martinez-González, E.; Ruiz, G. A.; Diaz, F. J.; Argüeso, F.; Toffolatti, L.
Basics on the continuous and discrete wavelet transform with two scales are outlined. We study maps representing anisotropies in the cosmic microwave background radiation (CMB) and the relation to the standard approach, based on the Cl's, is establised through the introduction of a wavelet spectrum. We apply this technique to small angular scale CMB map simulations of size 12.8 x 12.8 degrees and filtered with a 4'.5 Gaussian beam. This resolution resembles the experimental one expected for future high resolution experiments (e.g. the Planck mission). We consider temperature fluctuations derived from standard, open and flat-Lambda CDM models. We also introduce Gaussian noise (uniform and non-uniform) at different S/N levels and results are given regarding denoising.
A novel de-noising method for B ultrasound images
NASA Astrophysics Data System (ADS)
Tian, Da-Yong; Mo, Jia-qing; Yu, Yin-Feng; Lv, Xiao-Yi; Yu, Xiao; Jia, Zhen-Hong
2015-12-01
B ultrasound as a kind of ultrasonic imaging, which has become the indispensable diagnosis method in clinical medicine. However, the presence of speckle noise in ultrasound image greatly reduces the image quality and interferes with the accuracy of the diagnosis. Therefore, how to construct a method which can eliminate the speckle noise effectively, and at the same time keep the image details effectively is the research target of the current ultrasonic image de-noising. This paper is intended to remove the inherent speckle noise of B ultrasound image. The novel algorithm proposed is based on both wavelet transformation of B ultrasound images and data fusion of B ultrasound images, with a smaller mean squared error (MSE) and greater signal to noise ratio (SNR) compared with other algorithms. The results of this study can effectively remove speckle noise from B ultrasound images, and can well preserved the details and edge information which will produce better visual effects.
Merlin, Thibaut; Visvikis, Dimitris; Fernandez, Philippe; Lamare, Frederic
2015-02-15
Purpose: Partial volume effect (PVE) plays an important role in both qualitative and quantitative PET image accuracy, especially for small structures. A previously proposed voxelwise PVE correction method applied on PET reconstructed images involves the use of Lucy–Richardson deconvolution incorporating wavelet-based denoising to limit the associated propagation of noise. The aim of this study is to incorporate the deconvolution, coupled with the denoising step, directly inside the iterative reconstruction process to further improve PVE correction. Methods: The list-mode ordered subset expectation maximization (OSEM) algorithm has been modified accordingly with the application of the Lucy–Richardson deconvolution algorithm to the current estimation of the image, at each reconstruction iteration. Acquisitions of the NEMA NU2-2001 IQ phantom were performed on a GE DRX PET/CT system to study the impact of incorporating the deconvolution inside the reconstruction [with and without the point spread function (PSF) model] in comparison to its application postreconstruction and to standard iterative reconstruction incorporating the PSF model. The impact of the denoising step was also evaluated. Images were semiquantitatively assessed by studying the trade-off between the intensity recovery and the noise level in the background estimated as relative standard deviation. Qualitative assessments of the developed methods were additionally performed on clinical cases. Results: Incorporating the deconvolution without denoising within the reconstruction achieved superior intensity recovery in comparison to both standard OSEM reconstruction integrating a PSF model and application of the deconvolution algorithm in a postreconstruction process. The addition of the denoising step permitted to limit the SNR degradation while preserving the intensity recovery. Conclusions: This study demonstrates the feasibility of incorporating the Lucy–Richardson deconvolution associated with a
MRS3D: 3D Spherical Wavelet Transform on the Sphere
NASA Astrophysics Data System (ADS)
Lanusse, F.; Rassat, A.; Starck, J.-L.
2011-12-01
Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. We present a new fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel Transform and the HEALPIX angular pixelisation scheme. We tested the 3D wavelet transform and as a toy-application, applied a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and found we can successfully remove noise without much loss to the large scale structure. The new spherical 3D isotropic wavelet transform, called MRS3D, is ideally suited to analysing and denoising future 3D spherical cosmological surveys; it uses a novel discrete spherical Fourier-Bessel Transform. MRS3D is based on two packages, IDL and Healpix and can be used only if these two packages have been installed.
Wavelet and wavelet packet compression of electrocardiograms.
Hilton, M L
1997-05-01
Wavelets and wavelet packets have recently emerged as powerful tools for signal compression. Wavelet and wavelet packet-based compression algorithms based on embedded zerotree wavelet (EZW) coding are developed for electrocardiogram (ECG) signals, and eight different wavelets are evaluated for their ability to compress Holter ECG data. Pilot data from a blind evaluation of compressed ECG's by cardiologists suggest that the clinically useful information present in original ECG signals is preserved by 8:1 compression, and in most cases 16:1 compressed ECG's are clinically useful.
Perceptually Lossless Wavelet Compression
NASA Technical Reports Server (NTRS)
Watson, Andrew B.; Yang, Gloria Y.; Solomon, Joshua A.; Villasenor, John
1996-01-01
The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp -1), where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We propose a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a 'perceptually lossless' quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.
Extensions to total variation denoising
NASA Astrophysics Data System (ADS)
Blomgren, Peter; Chan, Tony F.; Mulet, Pep
1997-10-01
The total variation denoising method, proposed by Rudin, Osher and Fatermi, 92, is a PDE-based algorithm for edge-preserving noise removal. The images resulting from its application are usually piecewise constant, possibly with a staircase effect at smooth transitions and may contain significantly less fine details than the original non-degraded image. In this paper we present some extensions to this technique that aim to improve the above drawbacks, through redefining the total variation functional or the noise constraints.
Denoising two-photon calcium imaging data.
Malik, Wasim Q; Schummers, James; Sur, Mriganka; Brown, Emery N
2011-01-01
Two-photon calcium imaging is now an important tool for in vivo imaging of biological systems. By enabling neuronal population imaging with subcellular resolution, this modality offers an approach for gaining a fundamental understanding of brain anatomy and physiology. Proper analysis of calcium imaging data requires denoising, that is separating the signal from complex physiological noise. To analyze two-photon brain imaging data, we present a signal plus colored noise model in which the signal is represented as harmonic regression and the correlated noise is represented as an order autoregressive process. We provide an efficient cyclic descent algorithm to compute approximate maximum likelihood parameter estimates by combing a weighted least-squares procedure with the Burg algorithm. We use Akaike information criterion to guide selection of the harmonic regression and the autoregressive model orders. Our flexible yet parsimonious modeling approach reliably separates stimulus-evoked fluorescence response from background activity and noise, assesses goodness of fit, and estimates confidence intervals and signal-to-noise ratio. This refined separation leads to appreciably enhanced image contrast for individual cells including clear delineation of subcellular details and network activity. The application of our approach to in vivo imaging data recorded in the ferret primary visual cortex demonstrates that our method yields substantially denoised signal estimates. We also provide a general Volterra series framework for deriving this and other signal plus correlated noise models for imaging. This approach to analyzing two-photon calcium imaging data may be readily adapted to other computational biology problems which apply correlated noise models.
Denoising and Multivariate Analysis of Time-Of-Flight SIMS Images
Wickes, Bronwyn; Kim, Y.; Castner, David G.
2003-08-30
Time-of-flight SIMS (ToF-SIMS) imaging offers a modality for simultaneously visualizing the spatial distribution of different surface species. However, the utility of ToF-SIMS datasets may be limited by their large size, degraded mass resolution and low ion counts per pixel. Through denoising and multivariate image analysis, regions of similar chemistries may be differentiated more readily in ToF-SIMS image data. Three established denoising algorithms down-binning, boxcar and wavelet filtering were applied to ToF-SIMS images of different surface geometries and chemistries. The effect of these filters on the performance of principal component analysis (PCA) was evaluated in terms of the capture of important chemical image features in the principal component score images, the quality of the principal component
Denoising infrared maritime imagery using tailored dictionaries via modified K-SVD algorithm.
Smith, L N; Olson, C C; Judd, K P; Nichols, J M
2012-06-10
Recent work has shown that tailored overcomplete dictionaries can provide a better image model than standard basis functions for a variety of image processing tasks. Here we propose a modified K-SVD dictionary learning algorithm designed to maintain the advantages of the original approach but with a focus on improved convergence. We then use the learned model to denoise infrared maritime imagery and compare the performance to the original K-SVD algorithm, several overcomplete "fixed" dictionaries, and a standard wavelet denoising algorithm. Results indicate the superiority of overcomplete representations and show that our tailored approach provides similar peak signal-to-noise ratios as the traditional K-SVD at roughly half the computational cost.
Fst-Filter: A flexible spatio-temporal filter for biomedical multichannel data denoising.
Nuanprasert, Somchai; Adachi, Yoshiaki; Suzuki, Takashi
2015-08-01
In this paper, we present the noise reduction method for a multichannel measurement system where the true underlying signal is spatially low-rank and contaminated by spatially correlated noise. Our proposed formulation applies generalized singular value decomposition (GSVD) with signal recovery approach to extend the conventional subspace-based methods for performing the spatio-temporal filtering. Without necessarily requiring the noise covariance data in advance, the implemented optimization scheme allows users to choose the denoising function, F(·) flexibly satisfying for different temporal noise characteristics from a variety of existing efficient temporal filters. An effectiveness of proposed method is demonstrated by yielding the better accuracy for the brain source estimation on simulated magnetoencephalography (MEG) experiments than some traditional methods, e.g., principal component analysis (PCA), robust principal component analysis (RPCA) and multivariate wavelet denoising (MWD).
Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising.
Zhang, Kai; Zuo, Wangmeng; Chen, Yunjin; Meng, Deyu; Zhang, Lei
2017-02-01
Discriminative model learning for image denoising has been recently attracting considerable attentions due to its favorable denoising performance. In this paper, we take one step forward by investigating the construction of feed-forward denoising convolutional neural networks (DnCNNs) to embrace the progress in very deep architecture, learning algorithm, and regularization method into image denoising. Specifically, residual learning and batch normalization are utilized to speed up the training process as well as boost the denoising performance. Different from the existing discriminative denoising models which usually train a specific model for additive white Gaussian noise (AWGN) at a certain noise level, our DnCNN model is able to handle Gaussian denoising with unknown noise level (i.e., blind Gaussian denoising). With the residual learning strategy, DnCNN implicitly removes the latent clean image in the hidden layers. This property motivates us to train a single DnCNN model to tackle with several general image denoising tasks such as Gaussian denoising, single image super-resolution and JPEG image deblocking. Our extensive experiments demonstrate that our DnCNN model can not only exhibit high effectiveness in several general image denoising tasks, but also be efficiently implemented by benefiting from GPU computing.
NASA Astrophysics Data System (ADS)
Yang, Huijuan; Guan, Cuntai; Sui Geok Chua, Karen; San Chok, See; Wang, Chuan Chu; Kok Soon, Phua; Tang, Christina Ka Yin; Keng Ang, Kai
2014-06-01
Objective. Detection of motor imagery of hand/arm has been extensively studied for stroke rehabilitation. This paper firstly investigates the detection of motor imagery of swallow (MI-SW) and motor imagery of tongue protrusion (MI-Ton) in an attempt to find a novel solution for post-stroke dysphagia rehabilitation. Detection of MI-SW from a simple yet relevant modality such as MI-Ton is then investigated, motivated by the similarity in activation patterns between tongue movements and swallowing and there being fewer movement artifacts in performing tongue movements compared to swallowing. Approach. Novel features were extracted based on the coefficients of the dual-tree complex wavelet transform to build multiple training models for detecting MI-SW. The session-to-session classification accuracy was boosted by adaptively selecting the training model to maximize the ratio of between-classes distances versus within-class distances, using features of training and evaluation data. Main results. Our proposed method yielded averaged cross-validation (CV) classification accuracies of 70.89% and 73.79% for MI-SW and MI-Ton for ten healthy subjects, which are significantly better than the results from existing methods. In addition, averaged CV accuracies of 66.40% and 70.24% for MI-SW and MI-Ton were obtained for one stroke patient, demonstrating the detectability of MI-SW and MI-Ton from the idle state. Furthermore, averaged session-to-session classification accuracies of 72.08% and 70% were achieved for ten healthy subjects and one stroke patient using the MI-Ton model. Significance. These results and the subjectwise strong correlations in classification accuracies between MI-SW and MI-Ton demonstrated the feasibility of detecting MI-SW from MI-Ton models.
ECG Signal Analysis and Arrhythmia Detection using Wavelet Transform
NASA Astrophysics Data System (ADS)
Kaur, Inderbir; Rajni, Rajni; Marwaha, Anupma
2016-12-01
Electrocardiogram (ECG) is used to record the electrical activity of the heart. The ECG signal being non-stationary in nature, makes the analysis and interpretation of the signal very difficult. Hence accurate analysis of ECG signal with a powerful tool like discrete wavelet transform (DWT) becomes imperative. In this paper, ECG signal is denoised to remove the artifacts and analyzed using Wavelet Transform to detect the QRS complex and arrhythmia. This work is implemented in MATLAB software for MIT/BIH Arrhythmia database and yields the sensitivity of 99.85 %, positive predictivity of 99.92 % and detection error rate of 0.221 % with wavelet transform. It is also inferred that DWT outperforms principle component analysis technique in detection of ECG signal.
Green channel guiding denoising on bayer image.
Tan, Xin; Lai, Shiming; Liu, Yu; Zhang, Maojun
2014-01-01
Denoising is an indispensable function for digital cameras. In respect that noise is diffused during the demosaicking, the denoising ought to work directly on bayer data. The difficulty of denoising on bayer image is the interlaced mosaic pattern of red, green, and blue. Guided filter is a novel time efficient explicit filter kernel which can incorporate additional information from the guidance image, but it is still not applied for bayer image. In this work, we observe that the green channel of bayer mode is higher in both sampling rate and Signal-to-Noise Ratio (SNR) than the red and blue ones. Therefore the green channel can be used to guide denoising. This kind of guidance integrates the different color channels together. Experiments on both actual and simulated bayer images indicate that green channel acts well as the guidance signal, and the proposed method is competitive with other popular filter kernel denoising methods.
Exact reconstruction with directional wavelets on the sphere
NASA Astrophysics Data System (ADS)
Wiaux, Y.; McEwen, J. D.; Vandergheynst, P.; Blanc, O.
2008-08-01
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of a previously developed wavelet formalism developed by Antoine & Vandergheynst and Wiaux et al. The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation are first identified. A scale-discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of interest notably for the denoising or the deconvolution of signals on the sphere with a sparse expansion in wavelets. In astrophysics, it finds a particular application for the identification of localized directional features in the cosmic microwave background data, such as the imprint of topological defects, in particular, cosmic strings, and for their reconstruction after separation from the other signal components.
3D steerable wavelets in practice.
Chenouard, Nicolas; Unser, Michael
2012-11-01
We introduce a systematic and practical design for steerable wavelet frames in 3D. Our steerable wavelets are obtained by applying a 3D version of the generalized Riesz transform to a primary isotropic wavelet frame. The novel transform is self-reversible (tight frame) and its elementary constituents (Riesz wavelets) can be efficiently rotated in any 3D direction by forming appropriate linear combinations. Moreover, the basis functions at a given location can be linearly combined to design custom (and adaptive) steerable wavelets. The features of the proposed method are illustrated with the processing and analysis of 3D biomedical data. In particular, we show how those wavelets can be used to characterize directional patterns and to detect edges by means of a 3D monogenic analysis. We also propose a new inverse-problem formalism along with an optimization algorithm for reconstructing 3D images from a sparse set of wavelet-domain edges. The scheme results in high-quality image reconstructions which demonstrate the feature-reduction ability of the steerable wavelets as well as their potential for solving inverse problems.
Denoised and texture enhanced MVCT to improve soft tissue conspicuity
Sheng, Ke Qi, Sharon X.; Gou, Shuiping; Wu, Jiaolong
2014-10-15
Purpose: MVCT images have been used in TomoTherapy treatment to align patients based on bony anatomies but its usefulness for soft tissue registration, delineation, and adaptive radiation therapy is limited due to insignificant photoelectric interaction components and the presence of noise resulting from low detector quantum efficiency of megavoltage x-rays. Algebraic reconstruction with sparsity regularizers as well as local denoising methods has not significantly improved the soft tissue conspicuity. The authors aim to utilize a nonlocal means denoising method and texture enhancement to recover the soft tissue information in MVCT (DeTECT). Methods: A block matching 3D (BM3D) algorithm was adapted to reduce the noise while keeping the texture information of the MVCT images. Following imaging denoising, a saliency map was created to further enhance visual conspicuity of low contrast structures. In this study, BM3D and saliency maps were applied to MVCT images of a CT imaging quality phantom, a head and neck, and four prostate patients. Following these steps, the contrast-to-noise ratios (CNRs) were quantified. Results: By applying BM3D denoising and saliency map, postprocessed MVCT images show remarkable improvements in imaging contrast without compromising resolution. For the head and neck patient, the difficult-to-see lymph nodes and vein in the carotid space in the original MVCT image became conspicuous in DeTECT. For the prostate patients, the ambiguous boundary between the bladder and the prostate in the original MVCT was clarified. The CNRs of phantom low contrast inserts were improved from 1.48 and 3.8 to 13.67 and 16.17, respectively. The CNRs of two regions-of-interest were improved from 1.5 and 3.17 to 3.14 and 15.76, respectively, for the head and neck patient. DeTECT also increased the CNR of prostate from 0.13 to 1.46 for the four prostate patients. The results are substantially better than a local denoising method using anisotropic diffusion
Li, Fang; Wang, Ji-hua; Lu, An-xiang; Han, Ping
2015-04-01
The concentration of Cr, Cu, Zn, As and Pb in soil was tested by portable X-ray fluorescence spectrometer. Each sample was tested for 3 times, then after using wavelet threshold noise filtering method for denoising and smoothing the spectra, a standard curve for each heavy metal was established according to the standard values of heavy metals in soil and the corresponding counts which was the average of the 3 processed spectra. The signal to noise ratio (SNR), mean square error (MSE) and information entropy (H) were taken to assess the effects of denoising when using wavelet threshold noise filtering method for determining the best wavelet basis and wavelet decomposition level. Some samples with different concentrations and H3 B03 (blank) were chosen to retest this instrument to verify its stability. The results show that: the best denoising result was obtained with the coif3 wavelet basis at the decomposition level of 3 when using the wavelet transform method. The determination coefficient (R2) range of the instrument is 0.990-0.996, indicating that a high degree of linearity was found between the contents of heavy metals in soil and each X-ray fluorescence spectral characteristic peak intensity with the instrument measurement within the range (0-1,500 mg · kg(-1)). After retesting and calculating, the results indicate that all the detection limits of the instrument are below the soil standards at national level. The accuracy of the model has been effectively improved, and the instrument also shows good precision with the practical application of wavelet transform to the establishment and improvement of X-ray fluorescence spectrometer detection model. Thus the instrument can be applied in on-site rapid screening of heavy metal in contaminated soil.
Brechet, Laurent; Lucas, Marie-Françoise; Doncarli, Christian; Farina, Dario
2007-12-01
We propose a novel scheme for signal compression based on the discrete wavelet packet transform (DWPT) decompositon. The mother wavelet and the basis of wavelet packets were optimized and the wavelet coefficients were encoded with a modified version of the embedded zerotree algorithm. This signal dependant compression scheme was designed by a two-step process. The first (internal optimization) was the best basis selection that was performed for a given mother wavelet. For this purpose, three additive cost functions were applied and compared. The second (external optimization) was the selection of the mother wavelet based on the minimal distortion of the decoded signal given a fixed compression ratio. The mother wavelet was parameterized in the multiresolution analysis framework by the scaling filter, which is sufficient to define the entire decomposition in the orthogonal case. The method was tested on two sets of ten electromyographic (EMG) and ten electrocardiographic (ECG) signals that were compressed with compression ratios in the range of 50%-90%. For 90% compression ratio of EMG (ECG) signals, the percent residual difference after compression decreased from (mean +/- SD) 48.6 +/- 9.9% (21.5 +/- 8.4%) with discrete wavelet transform (DWT) using the wavelet leading to poorest performance to 28.4 +/- 3.0% (6.7 +/- 1.9%) with DWPT, with optimal basis selection and wavelet optimization. In conclusion, best basis selection and optimization of the mother wavelet through parameterization led to substantial improvement of performance in signal compression with respect to DWT and randon selection of the mother wavelet. The method provides an adaptive approach for optimal signal representation for compression and can thus be applied to any type of biomedical signal.
Zhao, Qinglin; Hu, Bin; Shi, Yujun; Li, Yang; Moore, Philip; Sun, Minghou; Peng, Hong
2014-06-01
Electroencephalogram (EEG) signals have a long history of use as a noninvasive approach to measure brain function. An essential component in EEG-based applications is the removal of Ocular Artifacts (OA) from the EEG signals. In this paper we propose a hybrid de-noising method combining Discrete Wavelet Transformation (DWT) and an Adaptive Predictor Filter (APF). A particularly novel feature of the proposed method is the use of the APF based on an adaptive autoregressive model for prediction of the waveform of signals in the ocular artifact zones. In our test, based on simulated data, the accuracy of noise removal in the proposed model was significantly increased when compared to existing methods including: Wavelet Packet Transform (WPT) and Independent Component Analysis (ICA), Discrete Wavelet Transform (DWT) and Adaptive Noise Cancellation (ANC). The results demonstrate that the proposed method achieved a lower mean square error and higher correlation between the original and corrected EEG. The proposed method has also been evaluated using data from calibration trials for the Online Predictive Tools for Intervention in Mental Illness (OPTIMI) project. The results of this evaluation indicate an improvement in performance in terms of the recovery of true EEG signals with EEG tracking and computational speed in the analysis. The proposed method is well suited to applications in portable environments where the constraints with respect to acceptable wearable sensor attachments usually dictate single channel devices.
Analysis of phonocardiogram signals using wavelet transform.
Meziani, F; Debbal, S M; Atbi, A
2012-08-01
Phonocardiograms (PCG) are recordings of the acoustic waves produced by the mechanical action of the heart. They generally consist of two kinds of acoustic vibrations: heart sounds and heart murmurs. Heart murmurs are often the first signs of pathological changes of the heart valves, and are usually found during auscultation in primary health care. Heart auscultation has been recognized for a long time as an important tool for the diagnosis of heart disease, although its accuracy is still insufficient to diagnose some heart diseases. It does not enable the analyst to obtain both qualitative and quantitative characteristics of the PCG signals. The efficiency of diagnosis can be improved considerably by using modern digital signal processing techniques. Therefore, these last can provide useful and valuable information on these signals. The aim of this study is to analyse PCG signals using wavelet transform. This analysis is based on an algorithm for the detection of heart sounds (the first and second sounds, S1 and S2) and heart murmurs using the PCG signal as the only source. The segmentation algorithm, which separates the components of the heart signal, is based on denoising by wavelet transform (DWT). This algorithm makes it possible to isolate individual sounds (S1 or S2) and murmurs. Thus, the analysis of various PCGs signals using wavelet transform can provide a wide range of statistical parameters related to the phonocardiogram signal.
Image denoising using nonsubsampled shearlet transform and twin support vector machines.
Yang, Hong-Ying; Wang, Xiang-Yang; Niu, Pan-Pan; Liu, Yang-Cheng
2014-09-01
Denoising of images is one of the most basic tasks of image processing. It is a challenging work to design a edge/texture-preserving image denoising scheme. Nonsubsampled shearlet transform (NSST) is an effective multi-scale and multi-direction analysis method, it not only can exactly compute the shearlet coefficients based on a multiresolution analysis, but also can provide nearly optimal approximation for a piecewise smooth function. Based on NSST, a new edge/texture-preserving image denoising using twin support vector machines (TSVMs) is proposed in this paper. Firstly, the noisy image is decomposed into different subbands of frequency and orientation responses using the NSST. Secondly, the feature vector for a pixel in a noisy image is formed by the spatial geometric regularity in NSST domain, and the TSVMs model is obtained by training. Then the NSST detail coefficients are divided into information-related coefficients and noise-related ones by TSVMs training model. Finally, the detail subbands of NSST coefficients are denoised by using the adaptive threshold. Extensive experimental results demonstrate that our method can obtain better performances in terms of both subjective and objective evaluations than those state-of-the-art denoising techniques. Especially, the proposed method can preserve edges and textures very well while removing noise.
Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain.
Pang, Jiahao; Cheung, Gene
2017-04-01
Inverse imaging problems are inherently underdetermined, and hence, it is important to employ appropriate image priors for regularization. One recent popular prior-the graph Laplacian regularizer-assumes that the target pixel patch is smooth with respect to an appropriately chosen graph. However, the mechanisms and implications of imposing the graph Laplacian regularizer on the original inverse problem are not well understood. To address this problem, in this paper, we interpret neighborhood graphs of pixel patches as discrete counterparts of Riemannian manifolds and perform analysis in the continuous domain, providing insights into several fundamental aspects of graph Laplacian regularization for image denoising. Specifically, we first show the convergence of the graph Laplacian regularizer to a continuous-domain functional, integrating a norm measured in a locally adaptive metric space. Focusing on image denoising, we derive an optimal metric space assuming non-local self-similarity of pixel patches, leading to an optimal graph Laplacian regularizer for denoising in the discrete domain. We then interpret graph Laplacian regularization as an anisotropic diffusion scheme to explain its behavior during iterations, e.g., its tendency to promote piecewise smooth signals under certain settings. To verify our analysis, an iterative image denoising algorithm is developed. Experimental results show that our algorithm performs competitively with state-of-the-art denoising methods, such as BM3D for natural images, and outperforms them significantly for piecewise smooth images.
Denoising Medical Images using Calculus of Variations.
Kohan, Mahdi Nakhaie; Behnam, Hamid
2011-07-01
We propose a method for medical image denoising using calculus of variations and local variance estimation by shaped windows. This method reduces any additive noise and preserves small patterns and edges of images. A pyramid structure-texture decomposition of images is used to separate noise and texture components based on local variance measures. The experimental results show that the proposed method has visual improvement as well as a better SNR, RMSE and PSNR than common medical image denoising methods. Experimental results in denoising a sample Magnetic Resonance image show that SNR, PSNR and RMSE have been improved by 19, 9 and 21 percents respectively.
Discrete directional wavelet bases and frames: analysis and applications
NASA Astrophysics Data System (ADS)
Dragotti, Pier Luigi; Velisavljevic, Vladan; Vetterli, Martin; Beferull-Lozano, Baltasar
2003-11-01
The application of the wavelet transform in image processing is most frequently based on a separable construction. Lines and columns in an image are treated independently and the basis functions are simply products of the corresponding one dimensional functions. Such method keeps simplicity in design and computation, but is not capable of capturing properly all the properties of an image. In this paper, a new truly separable discrete multi-directional transform is proposed with a subsampling method based on lattice theory. Alternatively, the subsampling can be omitted and this leads to a multi-directional frame. This transform can be applied in many areas like denoising, non-linear approximation and compression. The results on non-linear approximation and denoising show interesting gains compared to the standard two-dimensional analysis.
Nitzken, Matthew; Bajaj, Nihit; Aslan, Sevda; Gimel’farb, Georgy; Ovechkin, Alexander
2013-01-01
Surface Electromyography (EMG) is a standard method used in clinical practice and research to assess motor function in order to help with the diagnosis of neuromuscular pathology in human and animal models. EMG recorded from trunk muscles involved in the activity of breathing can be used as a direct measure of respiratory motor function in patients with spinal cord injury (SCI) or other disorders associated with motor control deficits. However, EMG potentials recorded from these muscles are often contaminated with heart-induced electrocardiographic (ECG) signals. Elimination of these artifacts plays a critical role in the precise measure of the respiratory muscle electrical activity. This study was undertaken to find an optimal approach to eliminate the ECG artifacts from EMG recordings. Conventional global filtering can be used to decrease the ECG-induced artifact. However, this method can alter the EMG signal and changes physiologically relevant information. We hypothesize that, unlike global filtering, localized removal of ECG artifacts will not change the original EMG signals. We develop an approach to remove the ECG artifacts without altering the amplitude and frequency components of the EMG signal by using an externally recorded ECG signal as a mask to locate areas of the ECG spikes within EMG data. These segments containing ECG spikes were decomposed into 128 sub-wavelets by a custom-scaled Morlet Wavelet Transform. The ECG-related sub-wavelets at the ECG spike location were removed and a de-noised EMG signal was reconstructed. Validity of the proposed method was proven using mathematical simulated synthetic signals and EMG obtained from SCI patients. We compare the Root-mean Square Error and the Relative Change in Variance between this method, global, notch and adaptive filters. The results show that the localized wavelet-based filtering has the benefit of not introducing error in the native EMG signal and accurately removing ECG artifacts from EMG signals
Wavelet transform processing applied to partial discharge evaluation
NASA Astrophysics Data System (ADS)
Macedo, E. C. T.; Araújo, D. B.; da Costa, E. G.; Freire, R. C. S.; Lopes, W. T. A.; Torres, I. S. M.; de Souza Neto, J. M. R.; Bhatti, S. A.; Glover, I. A.
2012-05-01
Partial Discharge (PD) is characterized by high frequency current pulses that occur in high voltage (HV) electrical equipments originated from gas ionization process when damaged insulation is submitted to high values of electric field [1]. PD monitoring is a useful method of assessing the aging degree of the insulation, manufacturing defects or chemical/mechanical damage. Many sources of noise (e.g. radio transmissions, commutator noise from rotating machines, power electronics switching circuits, corona discharge, etc.) can directly affect the PD estimation. Among the many mathematical techniques that can be applied to de-noise PD signals, the wavelet transform is one of the most powerful. It can simultaneously supply information about the pulse occurrence, time and pulse spectrum, and also de-noise in-field measured PD signals. In this paper is described the application of wavelet transform in the suppression of the main types of noise that can affect the observation and analysis of PD signals in high voltage apparatus. In addition, is presented a study that indicates the appropriated mother-wavelet for this application based on the cross-correlation factor.
Multiwavelets on the interval and divergence-free wavelets
NASA Astrophysics Data System (ADS)
Lakey, Joseph D.; Pereyra, M. Cristina
1999-10-01
This manuscript gives a construction of divergence-free multiwavelets which combines the Hardin-Marasovich (HM) construction with a recipe of Strela for increasing or decreasing regularity of biorthogonal wavelets. Strela's process preserves symmetry of the HM wavelets. This enables the divergence-free wavelets to be suitably adapted to the analysis of divergence-free vector fields whose boundary traces are tangent vectors.
A Decomposition Framework for Image Denoising Algorithms.
Ghimpeteanu, Gabriela; Batard, Thomas; Bertalmio, Marcelo; Levine, Stacey
2016-01-01
In this paper, we consider an image decomposition model that provides a novel framework for image denoising. The model computes the components of the image to be processed in a moving frame that encodes its local geometry (directions of gradients and level lines). Then, the strategy we develop is to denoise the components of the image in the moving frame in order to preserve its local geometry, which would have been more affected if processing the image directly. Experiments on a whole image database tested with several denoising methods show that this framework can provide better results than denoising the image directly, both in terms of Peak signal-to-noise ratio and Structural similarity index metrics.
2015-01-01
Hybridisation of the bi-dimensional empirical mode decomposition (BEMD) with denoising techniques has been proposed in the literature as an effective approach for image denoising. In this Letter, the Student's probability density function is introduced in the computation of the mean envelope of the data during the BEMD sifting process to make it robust to values that are far from the mean. The resulting BEMD is denoted tBEMD. In order to show the effectiveness of the tBEMD, several image denoising techniques in tBEMD domain are employed; namely, fourth order partial differential equation (PDE), linear complex diffusion process (LCDP), non-linear complex diffusion process (NLCDP), and the discrete wavelet transform (DWT). Two biomedical images and a standard digital image were considered for experiments. The original images were corrupted with additive Gaussian noise with three different levels. Based on peak-signal-to-noise ratio, the experimental results show that PDE, LCDP, NLCDP, and DWT all perform better in the tBEMD than in the classical BEMD domain. It is also found that tBEMD is faster than classical BEMD when the noise level is low. When it is high, the computational cost in terms of processing time is similar. The effectiveness of the presented approach makes it promising for clinical applications. PMID:27222723
Lahmiri, Salim
2016-03-01
Hybridisation of the bi-dimensional empirical mode decomposition (BEMD) with denoising techniques has been proposed in the literature as an effective approach for image denoising. In this Letter, the Student's probability density function is introduced in the computation of the mean envelope of the data during the BEMD sifting process to make it robust to values that are far from the mean. The resulting BEMD is denoted tBEMD. In order to show the effectiveness of the tBEMD, several image denoising techniques in tBEMD domain are employed; namely, fourth order partial differential equation (PDE), linear complex diffusion process (LCDP), non-linear complex diffusion process (NLCDP), and the discrete wavelet transform (DWT). Two biomedical images and a standard digital image were considered for experiments. The original images were corrupted with additive Gaussian noise with three different levels. Based on peak-signal-to-noise ratio, the experimental results show that PDE, LCDP, NLCDP, and DWT all perform better in the tBEMD than in the classical BEMD domain. It is also found that tBEMD is faster than classical BEMD when the noise level is low. When it is high, the computational cost in terms of processing time is similar. The effectiveness of the presented approach makes it promising for clinical applications.
NASA Astrophysics Data System (ADS)
Chen, Jinglong; Wan, Zhiguo; Pan, Jun; Zi, Yanyang; Wang, Yu; Chen, Binqiang; Sun, Hailiang; Yuan, Jing; He, Zhengjia
2016-02-01
Fault identification timely of rolling mill drivetrain is significant for guaranteeing product quality and realizing long-term safe operation. So, condition monitoring system of rolling mill drivetrain is designed and developed. However, because compound fault and weak fault feature information is usually sub-merged in heavy background noise, this task still faces challenge. This paper provides a possibility for fault identification of rolling mills drivetrain by proposing customized maximal-overlap multiwavelet denoising method. The effectiveness of wavelet denoising method mainly relies on the appropriate selections of wavelet base, transform strategy and threshold rule. First, in order to realize exact matching and accurate detection of fault feature, customized multiwavelet basis function is constructed via symmetric lifting scheme and then vibration signal is processed by maximal-overlap multiwavelet transform. Next, based on spatial dependency of multiwavelet transform coefficients, spatial neighboring coefficient data-driven group threshold shrinkage strategy is developed for denoising process by choosing the optimal group length and threshold via the minimum of Stein's Unbiased Risk Estimate. The effectiveness of proposed method is first demonstrated through compound fault identification of reduction gearbox on rolling mill. Then it is applied for weak fault identification of dedusting fan bearing on rolling mill and the results support its feasibility.
NASA Astrophysics Data System (ADS)
Jones, B. J. T.
Wavelet analysis has become a major tool in many aspects of data handling, whether it be statistical analysis, noise removal or image reconstruction. Wavelet analysis has worked its way into fields as diverse as economics, medicine, geophysics, music and cosmology.
Visibility of wavelet quantization noise
NASA Technical Reports Server (NTRS)
Watson, A. B.; Yang, G. Y.; Solomon, J. A.; Villasenor, J.
1997-01-01
The discrete wavelet transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that we call DWT uniform quantization noise; it is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2-lambda, where r is display visual resolution in pixels/degree, and lambda is the wavelet level. Thresholds increase rapidly with wavelet spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from lowpass to horizontal/vertical to diagonal. We construct a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.
Wavelet Approximation in Data Assimilation
NASA Technical Reports Server (NTRS)
Tangborn, Andrew; Atlas, Robert (Technical Monitor)
2002-01-01
Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.
Nonlocal means image denoising using orthogonal moments.
Kumar, Ahlad
2015-09-20
An image denoising method in moment domain has been proposed. The denoising involves the development and evaluation based on the modified nonlocal means (NLM) algorithm. It uses the similarity of the neighborhood, evaluated using Krawtchouk moments. The results of the proposed denoising method have been validated using peak signal-to-noise ratio (PSNR), a well-known quality measure such as structural similarity (SSIM) index and blind/referenceless image spatial quality evaluator (BRISQUE). The denoising algorithm has been evaluated for synthetic and real clinical images contaminated by Gaussian, Poisson, and Rician noise. The algorithm performs well compared to the Zernike based denoising as indicated by the PSNR, SSIM, and BRISQUE scores of the denoised images with an improvement of 3.1 dB, 0.1285, and 4.23, respectively. Further, comparative analysis of the proposed work with the existing techniques has also been performed. It has been observed that the results are competitive in terms of PSNR, SSIM, and BRISQUE scores when evaluated for varying levels of noise.
Review of wavelet transforms for pattern recognitions
NASA Astrophysics Data System (ADS)
Szu, Harold H.
1996-03-01
After relating the adaptive wavelet transform to the human visual and hearing systems, we exploit the synergism between such a smart sensor processing with brain-style neural network computing. The freedom of choosing an appropriate kernel of a linear transform, which is given to us by the recent mathematical foundation of the wavelet transform, is exploited fully and is generally called the adaptive wavelet transform (WT). However, there are several levels of adaptivity: (1) optimum coefficients: adjustable transform coefficients chosen with respect to a fixed mother kernel for better invariant signal representation, (2) super-mother: grouping different scales of daughter wavelets of same or different mother wavelets at different shift location into a new family called a superposition mother kernel for better speech signal classification, (3) variational calculus to determine ab initio a constraint optimization mother for a specific task. The tradeoff between the mathematical rigor of the complete orthonormality and the speed of order (N) with the adaptive flexibility is finally up to the user's needs. Then, to illustrate (1), a new invariant optoelectronic architecture of a wedge- shape filter in the WT domain is given for scale-invariant signal classification by neural networks.
Transient Detection Using Wavelets.
1995-03-01
signaL and transients are nonstationary. A new technique for the analysis of this type of signal, called the Wavelet Transform , was applied to artificial...and real signals. A brief theoretical comparison between the Short Time Fourier Transform and the Wavelet Transform is introduced A multisolution...analysis approach for implementing the transform was used. Computer code for the Discrete Wavelet Transform was implemented. Different types of wavelets to use as basis functions were evaluated. (KAR) P. 2
Wavelet treatment of the intrachain correlation functions of homopolymers in dilute solutions
NASA Astrophysics Data System (ADS)
Fedorov, M. V.; Chuev, G. N.; Kuznetsov, Yu. A.; Timoshenko, E. G.
2004-11-01
Discrete wavelets are applied to the parametrization of the intrachain two-point correlation functions of homopolymers in dilute solutions obtained from Monte Carlo simulations. Several orthogonal and biorthogonal basis sets have been investigated for use in the truncated wavelet approximation. The quality of the approximation has been assessed by calculation of the scaling exponents obtained from the des Cloizeaux ansatz for the correlation functions of homopolymers with different connectivities in a good solvent. The resulting exponents are in better agreement with those from recent renormalization group calculations as compared to the data without the wavelet denoising. We also discuss how the wavelet treatment improves the quality of data for correlation functions from simulations of homopolymers at varied solvent conditions and of heteropolymers.
2012-01-01
Background High-density oligonucleotide microarray is an appropriate technology for genomic analysis, and is particulary useful in the generation of transcriptional maps, ChIP-on-chip studies and re-sequencing of the genome.Transcriptome analysis of tiling microarray data facilitates the discovery of novel transcripts and the assessment of differential expression in diverse experimental conditions. Although new technologies such as next-generation sequencing have appeared, microarrays might still be useful for the study of small genomes or for the analysis of genomic regions with custom microarrays due to their lower price and good accuracy in expression quantification. Results Here, we propose a novel wavelet-based method, named ZCL (zero-crossing lines), for the combined denoising and segmentation of tiling signals. The denoising is performed with the classical SUREshrink method and the detection of transcriptionally active regions is based on the computation of the Continuous Wavelet Transform (CWT). In particular, the detection of the transitions is implemented as the thresholding of the zero-crossing lines. The algorithm described has been applied to the public Saccharomyces cerevisiae dataset and it has been compared with two well-known algorithms: pseudo-median sliding window (PMSW) and the structural change model (SCM). As a proof-of-principle, we applied the ZCL algorithm to the analysis of the custom tiling microarray hybridization results of a S. aureus mutant deficient in the sigma B transcription factor. The challenge was to identify those transcripts whose expression decreases in the absence of sigma B. Conclusions The proposed method archives the best performance in terms of positive predictive value (PPV) while its sensitivity is similar to the other algorithms used for the comparison. The computation time needed to process the transcriptional signals is low as compared with model-based methods and in the same range to those based on the use of
An Improved Brain Tumour Classification System using Wavelet Transform and Neural Network.
Dhas, DAS; Madheswaran, M
2015-06-09
An improved brain tumour classification system using wavelet transform and neural network is developed and presented in this paper. The anisotropic diffusion filter is used for image denoising and the performance of oriented rician noise reducing anisotropic diffusion (ORNRAD) filter is validated. The segmentation of the denoised image is carried out by Fuzzy C-means clustering. The features are extracted using Symlet and Coiflet Wavelet transform and Levenberg Marquardt algorithm based neural network is used to classify the magnetic resonance imaging (MRI) images. This MRI classification technique is tested and analysed with the existing methodologies and its performance is found to be satisfactory with a classification accuracy of 93.02%. The developed system can assist the physicians for classifying the MRI images for better decision-making.
Rotation and Scale Invariant Wavelet Feature for Content-Based Texture Image Retrieval.
ERIC Educational Resources Information Center
Lee, Moon-Chuen; Pun, Chi-Man
2003-01-01
Introduces a rotation and scale invariant log-polar wavelet texture feature for image retrieval. The underlying feature extraction process involves a log-polar transform followed by an adaptive row shift invariant wavelet packet transform. Experimental results show that this rotation and scale invariant wavelet feature is quite effective for image…
Projection space denoising with bilateral filtering and CT noise modeling for dose reduction in CT
Manduca, Armando; Yu Lifeng; Trzasko, Joshua D.; Khaylova, Natalia; Kofler, James M.; McCollough, Cynthia M.; Fletcher, Joel G.
2009-11-15
Purpose: To investigate a novel locally adaptive projection space denoising algorithm for low-dose CT data. Methods: The denoising algorithm is based on bilateral filtering, which smooths values using a weighted average in a local neighborhood, with weights determined according to both spatial proximity and intensity similarity between the center pixel and the neighboring pixels. This filtering is locally adaptive and can preserve important edge information in the sinogram, thus maintaining high spatial resolution. A CT noise model that takes into account the bowtie filter and patient-specific automatic exposure control effects is also incorporated into the denoising process. The authors evaluated the noise-resolution properties of bilateral filtering incorporating such a CT noise model in phantom studies and preliminary patient studies with contrast-enhanced abdominal CT exams. Results: On a thin wire phantom, the noise-resolution properties were significantly improved with the denoising algorithm compared to commercial reconstruction kernels. The noise-resolution properties on low-dose (40 mA s) data after denoising approximated those of conventional reconstructions at twice the dose level. A separate contrast plate phantom showed improved depiction of low-contrast plates with the denoising algorithm over conventional reconstructions when noise levels were matched. Similar improvement in noise-resolution properties was found on CT colonography data and on five abdominal low-energy (80 kV) CT exams. In each abdominal case, a board-certified subspecialized radiologist rated the denoised 80 kV images markedly superior in image quality compared to the commercially available reconstructions, and denoising improved the image quality to the point where the 80 kV images alone were considered to be of diagnostic quality. Conclusions: The results demonstrate that bilateral filtering incorporating a CT noise model can achieve a significantly better noise-resolution trade
Two-dimensional wavelet mapping techniques for damage detection in structural systems
NASA Astrophysics Data System (ADS)
Amizic, Bruno; Amaravadi, Venkat; Rao, Vittal S.; Derriso, Mark M.
2002-07-01
Application of the wavelet transforms on the measured vibration data provides a new tool for the damage detection analysis of the two-dimensional structural systems. In this paper, a novel two-dimensional wavelet mapping technique for damage detection based on the wavelet transforms and residual mode shapes are proposed. After vibration data was collected, wavelet de-noising shrinkage was performed in order to reduce measurement noise. By performing wavelet decomposition of the residuals of mode shapes and by taking only detail coefficients, wavelet energy maps are constructed for all decomposition levels. The orthogonal property of the wavelet transforms has bee utilized to correlate energy at decomposition levels with the measured vibrational energy. After wavelet maps of interest are determined, they are mapped on top of each other to figure out damaged areas of the two-dimensional structural systems. The energy segmentation procedure is performed by using minimum homogeneity and uncertainty based thresholding methods. It has been shown that the proposed method can clearly locate the multiple damage locations on the two- dimensional structures. This method requires few sampling points, robust and independent of the type of damage or the material damaged. The proposed method is applied to detect multiple damage locations on a two-dimensional plate. The results are very satisfactory.
Discrete shearlet transform on GPU with applications in anomaly detection and denoising
NASA Astrophysics Data System (ADS)
Gibert, Xavier; Patel, Vishal M.; Labate, Demetrio; Chellappa, Rama
2014-12-01
Shearlets have emerged in recent years as one of the most successful methods for the multiscale analysis of multidimensional signals. Unlike wavelets, shearlets form a pyramid of well-localized functions defined not only over a range of scales and locations, but also over a range of orientations and with highly anisotropic supports. As a result, shearlets are much more effective than traditional wavelets in handling the geometry of multidimensional data, and this was exploited in a wide range of applications from image and signal processing. However, despite their desirable properties, the wider applicability of shearlets is limited by the computational complexity of current software implementations. For example, denoising a single 512 × 512 image using a current implementation of the shearlet-based shrinkage algorithm can take between 10 s and 2 min, depending on the number of CPU cores, and much longer processing times are required for video denoising. On the other hand, due to the parallel nature of the shearlet transform, it is possible to use graphics processing units (GPU) to accelerate its implementation. In this paper, we present an open source stand-alone implementation of the 2D discrete shearlet transform using CUDA C++ as well as GPU-accelerated MATLAB implementations of the 2D and 3D shearlet transforms. We have instrumented the code so that we can analyze the running time of each kernel under different GPU hardware. In addition to denoising, we describe a novel application of shearlets for detecting anomalies in textured images. In this application, computation times can be reduced by a factor of 50 or more, compared to multicore CPU implementations.
Improving the quality of the ECG signal by filtering in wavelet transform domain
NASA Astrophysics Data System (ADS)
DzierŻak, RóŻa; Surtel, Wojciech; Dzida, Grzegorz; Maciejewski, Marcin
2016-09-01
The article concerns the research methods of noise reduction occurring in the ECG signals. The method is based on the use of filtration in wavelet transform domain. The study was conducted on two types of signal - received during the rest of the patient and obtained during physical activity. For each of the signals 3 types of filtration were used. The study was designed to determine the effectiveness of various wavelets for de-noising signals obtained in both cases. The results confirm the suitability of the method for improving the quality of the electrocardiogram in case of both types of signals.
Signal Enhancement Using Time-Frequency Based Denoising
2003-03-01
algorithms on longer data segments. 15. NUMBER OF PAGES 125 14. SUBJECT TERMS Discrete Wavelet Transform , Soft and Hard...5 B. WAVELET TRANSFORM ............................................................................7...1. Continuous Wavelet Transform .........................................................7 2. Discrete Wavelet Transform .............................................................10
NASA Astrophysics Data System (ADS)
Nguyen van Ye, Romain; Del-Castillo-Negrete, Diego; Spong, D.; Hirshman, S.; Farge, M.
2008-11-01
A limitation of particle-based transport calculations is the noise due to limited statistical sampling. Thus, a key element for the success of these calculations is the development of efficient denoising methods. Here we discuss denoising techniques based on Proper Orthogonal Decomposition (POD) and Wavelet Decomposition (WD). The goal is the reconstruction of smooth (denoised) particle distribution functions from discrete particle data obtained from Monte Carlo simulations. In 2-D, the POD method is based on low rank truncations of the singular value decomposition of the data. For 3-D we propose the use of a generalized low rank approximation of matrices technique. The WD denoising is based on the thresholding of empirical wavelet coefficients [Donoho et al., 1996]. The methods are illustrated and tested with Monte-Carlo particle simulation data of plasma collisional relaxation including pitch angle and energy scattering. As an application we consider guiding-center transport with collisions in a magnetically confined plasma in toroidal geometry. The proposed noise reduction methods allow to achieve high levels of smoothness in the particle distribution function using significantly less particles in the computations.
Biorthogonal wavelet-based method of moments for electromagnetic scattering
NASA Astrophysics Data System (ADS)
Zhang, Qinke
Wavelet analysis is a technique developed in recent years in mathematics and has found usefulness in signal processing and many other engineering areas. The practical use of wavelets for the solution of partial differential and integral equations in computational electromagnetics has been investigated in this dissertation, with the emphasis on development of biorthogonal wavelet based method of moments for the solution of electric and magnetic field integral equations. The fundamentals and numerical analysis aspects of wavelet theory have been studied. In particular, a family of compactly supported biorthogonal spline wavelet bases on the n-cube (0,1) n has been studied in detail. The wavelet bases were used in this work as a building block to construct biorthogonal wavelet bases on general domain geometry. A specific and practical way of adapting the wavelet bases to certain n- dimensional blocks or elements is proposed based on the domain decomposition and local transformation techniques used in traditional finite element methods and computer aided graphics. The element, with the biorthogonal wavelet base embedded in it, is called a wavelet element in this work. The physical domains which can be treated with this method include general curves, surfaces in 2D and 3D, and 3D volume domains. A two-step mapping is proposed for the purpose of taking full advantage of the zero-moments of wavelets. The wavelet element approach appears to offer several important advantages. It avoids the need of generating very complicated meshes required in traditional finite element based methods, and makes the adaptive analysis easy to implement. A specific implementation procedure for performing adaptive analysis is proposed. The proposed biorthogonal wavelet based method of moments (BWMoM) has been implemented by using object-oriented programming techniques. The main computational issues have been detailed, discussed, and implemented in the whole package. Numerical examples show
Wavelet based image visibility enhancement of IR images
NASA Astrophysics Data System (ADS)
Jiang, Qin; Owechko, Yuri; Blanton, Brendan
2016-05-01
Enhancing the visibility of infrared images obtained in a degraded visibility environment is very important for many applications such as surveillance, visual navigation in bad weather, and helicopter landing in brownout conditions. In this paper, we present an IR image visibility enhancement system based on adaptively modifying the wavelet coefficients of the images. In our proposed system, input images are first filtered by a histogram-based dynamic range filter in order to remove sensor noise and convert the input images into 8-bit dynamic range for efficient processing and display. By utilizing a wavelet transformation, we modify the image intensity distribution and enhance image edges simultaneously. In the wavelet domain, low frequency wavelet coefficients contain original image intensity distribution while high frequency wavelet coefficients contain edge information for the original images. To modify the image intensity distribution, an adaptive histogram equalization technique is applied to the low frequency wavelet coefficients while to enhance image edges, an adaptive edge enhancement technique is applied to the high frequency wavelet coefficients. An inverse wavelet transformation is applied to the modified wavelet coefficients to obtain intensity images with enhanced visibility. Finally, a Gaussian filter is used to remove blocking artifacts introduced by the adaptive techniques. Since wavelet transformation uses down-sampling to obtain low frequency wavelet coefficients, histogram equalization of low-frequency coefficients is computationally more efficient than histogram equalization of the original images. We tested the proposed system with degraded IR images obtained from a helicopter landing in brownout conditions. Our experimental results show that the proposed system is effective for enhancing the visibility of degraded IR images.
NASA Astrophysics Data System (ADS)
Zhang, Yao; Zheng, Lihua; Li, Minzan; Deng, Xiaolei; Sun, Hong
2012-11-01
The visible and NIR spectral reflectance were measured for apple leaves by using a spectrophotometer in fruit-bearing, fruit-falling and fruit-maturing period respectively, and the nitrogen content of each sample was measured in the lab. The analysis of correlation between nitrogen content of apple tree leaves and their hyperspectral data was conducted. Then the low frequency signal and high frequency noise reduction signal were extracted by using wavelet packet decomposition algorithm. At the same time, the original spectral reflectance was denoised taking advantage of the wavelet filtering technology. And then the principal components spectra were collected after PCA (Principal Component Analysis). It was known that the model built based on noise reduction principal components spectra reached higher accuracy than the other three ones in fruit-bearing period and physiological fruit-maturing period. Their calibration R2 reached 0.9529 and 0.9501, and validation R2 reached 0.7285 and 0.7303 respectively. While in the fruit-falling period the model based on low frequency principal components spectra reached the highest accuracy, and its calibration R2 reached 0.9921 and validation R2 reached 0.6234. The results showed that it was an effective way to improve ability of predicting apple tree nitrogen content based on hyperspectral analysis by using wavelet packet algorithm.
NASA Astrophysics Data System (ADS)
van den Berg, J. C.
1999-08-01
A guided tour J. C. van den Berg; 1. Wavelet analysis, a new tool in physics J.-P. Antoine; 2. The 2-D wavelet transform, physical applications J.-P. Antoine; 3. Wavelets and astrophysical applications A. Bijaoui; 4. Turbulence analysis, modelling and computing using wavelets M. Farge, N. K.-R. Kevlahan, V. Perrier and K. Schneider; 5. Wavelets and detection of coherent structures in fluid turbulence L. Hudgins and J. H. Kaspersen; 6. Wavelets, non-linearity and turbulence in fusion plasmas B. Ph. van Milligen; 7. Transfers and fluxes of wind kinetic energy between orthogonal wavelet components during atmospheric blocking A. Fournier; 8. Wavelets in atomic physics and in solid state physics J.-P. Antoine, Ph. Antoine and B. Piraux; 9. The thermodynamics of fractals revisited with wavelets A. Arneodo, E. Bacry and J. F. Muzy; 10. Wavelets in medicine and physiology P. Ch. Ivanov, A. L. Goldberger, S. Havlin, C.-K. Peng, M. G. Rosenblum and H. E. Stanley; 11. Wavelet dimension and time evolution Ch.-A. Guérin and M. Holschneider.
NASA Astrophysics Data System (ADS)
van den Berg, J. C.
2004-03-01
A guided tour J. C. van den Berg; 1. Wavelet analysis, a new tool in physics J.-P. Antoine; 2. The 2-D wavelet transform, physical applications J.-P. Antoine; 3. Wavelets and astrophysical applications A. Bijaoui; 4. Turbulence analysis, modelling and computing using wavelets M. Farge, N. K.-R. Kevlahan, V. Perrier and K. Schneider; 5. Wavelets and detection of coherent structures in fluid turbulence L. Hudgins and J. H. Kaspersen; 6. Wavelets, non-linearity and turbulence in fusion plasmas B. Ph. van Milligen; 7. Transfers and fluxes of wind kinetic energy between orthogonal wavelet components during atmospheric blocking A. Fournier; 8. Wavelets in atomic physics and in solid state physics J.-P. Antoine, Ph. Antoine and B. Piraux; 9. The thermodynamics of fractals revisited with wavelets A. Arneodo, E. Bacry and J. F. Muzy; 10. Wavelets in medicine and physiology P. Ch. Ivanov, A. L. Goldberger, S. Havlin, C.-K. Peng, M. G. Rosenblum and H. E. Stanley; 11. Wavelet dimension and time evolution Ch.-A. Guérin and M. Holschneider.
Compression of Ultrasonic NDT Image by Wavelet Based Local Quantization
NASA Astrophysics Data System (ADS)
Cheng, W.; Li, L. Q.; Tsukada, K.; Hanasaki, K.
2004-02-01
Compression on ultrasonic image that is always corrupted by noise will cause `over-smoothness' or much distortion. To solve this problem to meet the need of real time inspection and tele-inspection, a compression method based on Discrete Wavelet Transform (DWT) that can also suppress the noise without losing much flaw-relevant information, is presented in this work. Exploiting the multi-resolution and interscale correlation property of DWT, a simple way named DWCs classification, is introduced first to classify detail wavelet coefficients (DWCs) as dominated by noise, signal or bi-effected. A better denoising can be realized by selective thresholding DWCs. While in `Local quantization', different quantization strategies are applied to the DWCs according to their classification and the local image property. It allocates the bit rate more efficiently to the DWCs thus achieve a higher compression rate. Meanwhile, the decompressed image shows the effects of noise suppressed and flaw characters preserved.
Geodesic denoising for optical coherence tomography images
NASA Astrophysics Data System (ADS)
Shahrian Varnousfaderani, Ehsan; Vogl, Wolf-Dieter; Wu, Jing; Gerendas, Bianca S.; Simader, Christian; Langs, Georg; Waldstein, Sebastian M.; Schmidt-Erfurth, Ursula
2016-03-01
Optical coherence tomography (OCT) is an optical signal acquisition method capturing micrometer resolution, cross-sectional three-dimensional images. OCT images are used widely in ophthalmology to diagnose and monitor retinal diseases such as age-related macular degeneration (AMD) and Glaucoma. While OCT allows the visualization of retinal structures such as vessels and retinal layers, image quality and contrast is reduced by speckle noise, obfuscating small, low intensity structures and structural boundaries. Existing denoising methods for OCT images may remove clinically significant image features such as texture and boundaries of anomalies. In this paper, we propose a novel patch based denoising method, Geodesic Denoising. The method reduces noise in OCT images while preserving clinically significant, although small, pathological structures, such as fluid-filled cysts in diseased retinas. Our method selects optimal image patch distribution representations based on geodesic patch similarity to noisy samples. Patch distributions are then randomly sampled to build a set of best matching candidates for every noisy sample, and the denoised value is computed based on a geodesic weighted average of the best candidate samples. Our method is evaluated qualitatively on real pathological OCT scans and quantitatively on a proposed set of ground truth, noise free synthetic OCT scans with artificially added noise and pathologies. Experimental results show that performance of our method is comparable with state of the art denoising methods while outperforming them in preserving the critical clinically relevant structures.
Computed tomography perfusion imaging denoising using Gaussian process regression
NASA Astrophysics Data System (ADS)
Zhu, Fan; Carpenter, Trevor; Rodriguez Gonzalez, David; Atkinson, Malcolm; Wardlaw, Joanna
2012-06-01
Brain perfusion weighted images acquired using dynamic contrast studies have an important clinical role in acute stroke diagnosis and treatment decisions. However, computed tomography (CT) images suffer from low contrast-to-noise ratios (CNR) as a consequence of the limitation of the exposure to radiation of the patient. As a consequence, the developments of methods for improving the CNR are valuable. The majority of existing approaches for denoising CT images are optimized for 3D (spatial) information, including spatial decimation (spatially weighted mean filters) and techniques based on wavelet and curvelet transforms. However, perfusion imaging data is 4D as it also contains temporal information. Our approach using Gaussian process regression (GPR), which takes advantage of the temporal information, to reduce the noise level. Over the entire image, GPR gains a 99% CNR improvement over the raw images and also improves the quality of haemodynamic maps allowing a better identification of edges and detailed information. At the level of individual voxel, GPR provides a stable baseline, helps us to identify key parameters from tissue time-concentration curves and reduces the oscillations in the curve. GPR is superior to the comparable techniques used in this study.
Wavelet-Based Signal and Image Processing for Target Recognition
2002-01-01
in target recognition applications. Classical spatial and frequency domain image processing algorithms were generalized to process discrete wavelet ... transform (DWT) data. Results include adaptation of classical filtering, smoothing and interpolation techniques to DWT. From 2003 the research
Ladar range image denoising by a nonlocal probability statistics algorithm
NASA Astrophysics Data System (ADS)
Xia, Zhi-Wei; Li, Qi; Xiong, Zhi-Peng; Wang, Qi
2013-01-01
According to the characteristic of range images of coherent ladar and the basis of nonlocal means (NLM), a nonlocal probability statistics (NLPS) algorithm is proposed in this paper. The difference is that NLM performs denoising using the mean of the conditional probability distribution function (PDF) while NLPS using the maximum of the marginal PDF. In the algorithm, similar blocks are found out by the operation of block matching and form a group. Pixels in the group are analyzed by probability statistics and the gray value with maximum probability is used as the estimated value of the current pixel. The simulated range images of coherent ladar with different carrier-to-noise ratio and real range image of coherent ladar with 8 gray-scales are denoised by this algorithm, and the results are compared with those of median filter, multitemplate order mean filter, NLM, median nonlocal mean filter and its incorporation of anatomical side information, and unsupervised information-theoretic adaptive filter. The range abnormality noise and Gaussian noise in range image of coherent ladar are effectively suppressed by NLPS.
[Denoising and assessing method of additive noise in the ultraviolet spectrum of SO2 in flue gas].
Zhou, Tao; Sun, Chang-Ku; Liu, Bin; Zhao, Yu-Mei
2009-11-01
The problem of denoising and assessing method of the spectrum of SO2 in flue gas was studied based on DOAS. The denoising procedure of the additive noise in the spectrum was divided into two parts: reducing the additive noise and enhancing the useful signal. When obtaining the absorption feature of measured gas, a multi-resolution preprocessing method of original spectrum was adopted for denoising by DWT (discrete wavelet transform). The signal energy operators in different scales were used to choose the denoising threshold and separate the useful signal from the noise. On the other hand, because there was no sudden change in the spectra of flue gas in time series, the useful signal component was enhanced according to the signal time dependence. And the standard absorption cross section was used to build the ideal absorption spectrum with the measured gas temperature and pressure. This ideal spectrum was used as the desired signal instead of the original spectrum in the assessing method to modify the SNR (signal-noise ratio). There were two different environments to do the proof test-in the lab and at the scene. In the lab, SO2 was measured several times with the system using this method mentioned above. The average deviation was less than 1.5%, while the repeatability was less than 1%. And the short range experiment data were better than the large range. In the scene of a power plant whose concentration of flue gas had a large variation range, the maximum deviation of this method was 2.31% in the 18 groups of contrast data. The experimental results show that the denoising effect of the scene spectrum was better than that of the lab spectrum. This means that this method can improve the SNR of the spectrum effectively, which is seriously polluted by additive noise.
Speckle filtering of medical ultrasonic images using wavelet and guided filter.
Zhang, Ju; Lin, Guangkuo; Wu, Lili; Cheng, Yun
2016-02-01
Speckle noise is an inherent yet ineffectual residual artifact in medical ultrasound images, which significantly degrades quality and restricts accuracy in automatic diagnostic techniques. Speckle reduction is therefore an important step prior to the analysis and processing of the ultrasound images. A new de-noising method based on an improved wavelet filter and guided filter is proposed in this paper. According to the characteristics of medical ultrasound images in the wavelet domain, an improved threshold function based on the universal wavelet threshold function is developed. The wavelet coefficients of speckle noise and noise-free signal are modeled as Rayleigh distribution and generalized Gaussian distribution respectively. The Bayesian maximum a posteriori estimation is applied to obtain a new wavelet shrinkage algorithm. The coefficients of the low frequency sub-band in the wavelet domain are filtered by guided filter. The filtered image is then obtained by using the inverse wavelet transformation. Experiments with the comparison of the other seven de-speckling filters are conducted. The results show that the proposed method not only has a strong de-speckling ability, but also keeps the image details, such as the edge of a lesion.
Kernel regression based feature extraction for 3D MR image denoising.
López-Rubio, Ezequiel; Florentín-Núñez, María Nieves
2011-08-01
Kernel regression is a non-parametric estimation technique which has been successfully applied to image denoising and enhancement in recent times. Magnetic resonance 3D image denoising has two features that distinguish it from other typical image denoising applications, namely the tridimensional structure of the images and the nature of the noise, which is Rician rather than Gaussian or impulsive. Here we propose a principled way to adapt the general kernel regression framework to this particular problem. Our noise removal system is rooted on a zeroth order 3D kernel regression, which computes a weighted average of the pixels over a regression window. We propose to obtain the weights from the similarities among small sized feature vectors associated to each pixel. In turn, these features come from a second order 3D kernel regression estimation of the original image values and gradient vectors. By considering directional information in the weight computation, this approach substantially enhances the performance of the filter. Moreover, Rician noise level is automatically estimated without any need of human intervention, i.e. our method is fully automated. Experimental results over synthetic and real images demonstrate that our proposal achieves good performance with respect to the other MRI denoising filters being compared.
Higher-order graph wavelets and sparsity on circulant graphs
NASA Astrophysics Data System (ADS)
Kotzagiannidis, Madeleine S.; Dragotti, Pier Luigi
2015-08-01
The notion of a graph wavelet gives rise to more advanced processing of data on graphs due to its ability to operate in a localized manner, across newly arising data-dependency structures, with respect to the graph signal and underlying graph structure, thereby taking into consideration the inherent geometry of the data. In this work, we tackle the problem of creating graph wavelet filterbanks on circulant graphs for a sparse representation of certain classes of graph signals. The underlying graph can hereby be data-driven as well as fixed, for applications including image processing and social network theory, whereby clusters can be modelled as circulant graphs, respectively. We present a set of novel graph wavelet filter-bank constructions, which annihilate higher-order polynomial graph signals (up to a border effect) defined on the vertices of undirected, circulant graphs, and are localised in the vertex domain. We give preliminary results on their performance for non-linear graph signal approximation and denoising. Furthermore, we provide extensions to our previously developed segmentation-inspired graph wavelet framework for non-linear image approximation, by incorporating notions of smoothness and vanishing moments, which further improve performance compared to traditional methods.
Enhancement of the automatic onset time picking via wavelet thresholding
NASA Astrophysics Data System (ADS)
Gaci, Said
2013-04-01
Since arrival time-picking is a critical step in the analysis of geophysical data, many time picking algorithms have been developed. Nowadays, the ''short-time-average through long-time-average trigger'' (STA/LTA) in different forms are the most commonly used. This study aims at improving this algorithm in the presence of high amplitude noise. The suggested method consists of denoising the seismic trace using the discrete wavelet transform. Therefore, the STA/LTA curve obtained from the denoised trace displays a faster build up at the position of the wave arrival, and the picking error is reduced. The application of this technique is first demonstrated on synthetic seismic traces with varying noise levels, then extended to uphole seismic traces recorded in the Algerian Sahara. The results show that the picked first arrivals are more accurate than those yielded by the standard STA/LTA algorithm and this method can tolerate high noise levels. Keywords: picking, first arrival, seismic wave, wavelet thresholding.
Discrete wavelet transform core for image processing applications
NASA Astrophysics Data System (ADS)
Savakis, Andreas E.; Carbone, Richard
2005-02-01
This paper presents a flexible hardware architecture for performing the Discrete Wavelet Transform (DWT) on a digital image. The proposed architecture uses a variation of the lifting scheme technique and provides advantages that include small memory requirements, fixed-point arithmetic implementation, and a small number of arithmetic computations. The DWT core may be used for image processing operations, such as denoising and image compression. For example, the JPEG2000 still image compression standard uses the Cohen-Daubechies-Favreau (CDF) 5/3 and CDF 9/7 DWT for lossless and lossy image compression respectively. Simple wavelet image denoising techniques resulted in improved images up to 27 dB PSNR. The DWT core is modeled using MATLAB and VHDL. The VHDL model is synthesized to a Xilinx FPGA to demonstrate hardware functionality. The CDF 5/3 and CDF 9/7 versions of the DWT are both modeled and used as comparisons. The execution time for performing both DWTs is nearly identical at approximately 14 clock cycles per image pixel for one level of DWT decomposition. The hardware area generated for the CDF 5/3 is around 15,000 gates using only 5% of the Xilinx FPGA hardware area, at 2.185 MHz max clock speed and 24 mW power consumption.
Visibility of Wavelet Quantization Noise
NASA Technical Reports Server (NTRS)
Watson, Andrew B.; Yang, Gloria Y.; Solomon, Joshua A.; Villasenor, John; Null, Cynthia H. (Technical Monitor)
1995-01-01
The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp)-L , where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We describe a mathematical model to predict DWT noise detection thresholds as a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.
Analysis of de-noising methods to improve the precision of the ILSF BPM electronic readout system
NASA Astrophysics Data System (ADS)
Shafiee, M.; Feghhi, S. A. H.; Rahighi, J.
2016-12-01
In order to have optimum operation and precise control system at particle accelerators, it is required to measure the beam position with the precision of sub-μm. We developed a BPM electronic readout system at Iranian Light Source Facility and it has been experimentally tested at ALBA accelerator facility. The results show the precision of 0.54 μm in beam position measurements. To improve the precision of this beam position monitoring system to sub-μm level, we have studied different de-noising methods such as principal component analysis, wavelet transforms, filtering by FIR, and direct averaging method. An evaluation of the noise reduction was given to testify the ability of these methods. The results show that the noise reduction based on Daubechies wavelet transform is better than other algorithms, and the method is suitable for signal noise reduction in beam position monitoring system.
Statistical Methods for Image Registration and Denoising
2008-06-19
21 2.5.4 Nonlocal Means . . . . . . . . . . . . . . . . . 22 2.5.5 Patch -Based Denoising with Optimal Spatial Adap- tation...24 2.5.6 Other Patch -Based Methods . . . . . . . . . . 25 2.6 Chapter Summary...the nonlocal means [9], and an optimal patch -based algorithm [31]. These algorithms all include some measure of pixel similarity that allows the
Performance evaluation and optimization of BM4D-AV denoising algorithm for cone-beam CT images
NASA Astrophysics Data System (ADS)
Huang, Kuidong; Tian, Xiaofei; Zhang, Dinghua; Zhang, Hua
2015-12-01
The broadening application of cone-beam Computed Tomography (CBCT) in medical diagnostics and nondestructive testing, necessitates advanced denoising algorithms for its 3D images. The block-matching and four dimensional filtering algorithm with adaptive variance (BM4D-AV) is applied to the 3D image denoising in this research. To optimize it, the key filtering parameters of the BM4D-AV algorithm are assessed firstly based on the simulated CBCT images and a table of optimized filtering parameters is obtained. Then, considering the complexity of the noise in realistic CBCT images, possible noise standard deviations in BM4D-AV are evaluated to attain the chosen principle for the realistic denoising. The results of corresponding experiments demonstrate that the BM4D-AV algorithm with optimized parameters presents excellent denosing effect on the realistic 3D CBCT images.
Quadtree structured image approximation for denoising and interpolation.
Scholefield, Adam; Dragotti, Pier Luigi
2014-03-01
The success of many image restoration algorithms is often due to their ability to sparsely describe the original signal. Shukla proposed a compression algorithm, based on a sparse quadtree decomposition model, which could optimally represent piecewise polynomial images. In this paper, we adapt this model to the image restoration by changing the rate-distortion penalty to a description-length penalty. In addition, one of the major drawbacks of this type of approximation is the computational complexity required to find a suitable subspace for each node of the quadtree. We address this issue by searching for a suitable subspace much more efficiently using the mathematics of updating matrix factorisations. Algorithms are developed to tackle denoising and interpolation. Simulation results indicate that we beat state of the art results when the original signal is in the model (e.g., depth images) and are competitive for natural images when the degradation is high.
NASA Astrophysics Data System (ADS)
Li, Hong; Ding, Xue
2017-03-01
This paper combines wavelet analysis and wavelet transform theory with artificial neural network, through the pretreatment on point feature attributes before in intrusion detection, to make them suitable for improvement of wavelet neural network. The whole intrusion classification model gets the better adaptability, self-learning ability, greatly enhances the wavelet neural network for solving the problem of field detection invasion, reduces storage space, contributes to improve the performance of the constructed neural network, and reduces the training time. Finally the results of the KDDCup99 data set simulation experiment shows that, this method reduces the complexity of constructing wavelet neural network, but also ensures the accuracy of the intrusion classification.
Wavelet Analyses and Applications
ERIC Educational Resources Information Center
Bordeianu, Cristian C.; Landau, Rubin H.; Paez, Manuel J.
2009-01-01
It is shown how a modern extension of Fourier analysis known as wavelet analysis is applied to signals containing multiscale information. First, a continuous wavelet transform is used to analyse the spectrum of a nonstationary signal (one whose form changes in time). The spectral analysis of such a signal gives the strength of the signal in each…
Wavelet-based approach for detection and analysis of transient signal in distributed power system
NASA Astrophysics Data System (ADS)
Liao, Wei; Han, Pu
2008-10-01
By combining wavelet transform (WT) with neural network theory, a novel approach is put forward to detect transient fault and analyze voltage stability. The application of signal denoising based on the statistic rule is proposed to determine the threshold of each order of wavelet space. In a view of the inter relationship of wavelet transform and neural network, the whole and local fractal exponents obtained from WT coefficients as features are presented for extracting signal features. The effectiveness of the new algorithm used to extract the characteristic signal is described, which can be realized by the value of those types of transient signal. This model incorporates the advantages of morphological filter and multi-scale WT to extract the feature of fault signal meanwhile restraining various noises. Besides, it can be implemented in real time using the available hardware. The effectiveness of this model was verified with the voltage stability analysis of simulation results.
[Application of kalman filtering based on wavelet transform in ICP-AES].
Qin, Xia; Shen, Lan-sun
2002-12-01
Kalman filtering is a recursive algorithm, which has been proposed as an attractive alternative to correct overlapping interferences in ICP-AES. However, the noise in ICP-AES contaminates the signal arising from the analyte and hence limits the accuracy of kalman filtering. Wavelet transform is a powerful technique in signal denoising due to its multi-resolution characteristics. In this paper, first, the effect of noise on kalman filtering is discussed. Then we apply the wavelet-transform-based soft-thresholding as the pre-processing of kalman filtering. The simulation results show that the kalman filtering based on wavelet transform can effectively reduce the noise and increase the accuracy of the analysis.
NASA Astrophysics Data System (ADS)
Shen, Yan; Wang, Xin; Lou, Shuqin; Lian, Zhenggang; Zhao, Tongtong
2016-09-01
An evaluation method based on the total variation model (TV) in wavelet domain is proposed for modeling optical properties of real photonic crystal fibers (PCFs). The TV model in wavelet domain is set up to suppress the noise of the original image effectively and rebuild the cross section images of real PCFs with high accuracy. The optical properties of three PCFs are evaluated, including two kinds of PCFs that supplied from the Crystal Fiber A/S and a homemade side-leakage PCF, by using the combination of the proposed model and finite element method. Numerical results demonstrate that the proposed method can obtain high noise suppression ratio and effectively reduce the noise of cross section images of PCFs, which leads to an accurate evaluation of optical properties of real PCFs. To the best of our knowledge, it is the first time to denoise the cross section images of PCFs with the TV model in the wavelet domain.
Predictive depth coding of wavelet transformed images
NASA Astrophysics Data System (ADS)
Lehtinen, Joonas
1999-10-01
In this paper, a new prediction based method, predictive depth coding, for lossy wavelet image compression is presented. It compresses a wavelet pyramid composition by predicting the number of significant bits in each wavelet coefficient quantized by the universal scalar quantization and then by coding the prediction error with arithmetic coding. The adaptively found linear prediction context covers spatial neighbors of the coefficient to be predicted and the corresponding coefficients on lower scale and in the different orientation pyramids. In addition to the number of significant bits, the sign and the bits of non-zero coefficients are coded. The compression method is tested with a standard set of images and the results are compared with SFQ, SPIHT, EZW and context based algorithms. Even though the algorithm is very simple and it does not require any extra memory, the compression results are relatively good.
A stacked contractive denoising auto-encoder for ECG signal denoising.
Xiong, Peng; Wang, Hongrui; Liu, Ming; Lin, Feng; Hou, Zengguang; Liu, Xiuling
2016-12-01
As a primary diagnostic tool for cardiac diseases, electrocardiogram (ECG) signals are often contaminated by various kinds of noise, such as baseline wander, electrode contact noise and motion artifacts. In this paper, we propose a contractive denoising technique to improve the performance of current denoising auto-encoders (DAEs) for ECG signal denoising. Based on the Frobenius norm of the Jacobean matrix for the learned features with respect to the input, we develop a stacked contractive denoising auto-encoder (CDAE) to build a deep neural network (DNN) for noise reduction, which can significantly improve the expression of ECG signals through multi-level feature extraction. The proposed method is evaluated on ECG signals from the bench-marker MIT-BIH Arrhythmia Database, and the noises come from the MIT-BIH noise stress test database. The experimental results show that the new CDAE algorithm performs better than the conventional ECG denoising method, specifically with more than 2.40 dB improvement in the signal-to-noise ratio (SNR) and nearly 0.075 to 0.350 improvements in the root mean square error (RMSE).
Fractional-order TV-L2 model for image denoising
NASA Astrophysics Data System (ADS)
Chen, Dali; Sun, Shenshen; Zhang, Congrong; Chen, YangQuan; Xue, Dingyu
2013-10-01
This paper proposes a new fractional order total variation (TV) denoising method, which provides a much more elegant and effective way of treating problems of the algorithm implementation, ill-posed inverse, regularization parameter selection and blocky effect. Two fractional order TV-L2 models are constructed for image denoising. The majorization-minimization (MM) algorithm is used to decompose these two complex fractional TV optimization problems into a set of linear optimization problems which can be solved by the conjugate gradient algorithm. The final adaptive numerical procedure is given. Finally, we report experimental results which show that the proposed methodology avoids the blocky effect and achieves state-of-the-art performance. In addition, two medical image processing experiments are presented to demonstrate the validity of the proposed methodology.
[A novel denoising approach to SVD filtering based on DCT and PCA in CT image].
Feng, Fuqiang; Wang, Jun
2013-10-01
Because of various effects of the imaging mechanism, noises are inevitably introduced in medical CT imaging process. Noises in the images will greatly degrade the quality of images and bring difficulties to clinical diagnosis. This paper presents a new method to improve singular value decomposition (SVD) filtering performance in CT image. Filter based on SVD can effectively analyze characteristics of the image in horizontal (and/or vertical) directions. According to the features of CT image, we can make use of discrete cosine transform (DCT) to extract the region of interest and to shield uninterested region so as to realize the extraction of structure characteristics of the image. Then we transformed SVD to the image after DCT, constructing weighting function for image reconstruction adaptively weighted. The algorithm for the novel denoising approach in this paper was applied in CT image denoising, and the experimental results showed that the new method could effectively improve the performance of SVD filtering.
Denoising MR images using non-local means filter with combined patch and pixel similarity.
Zhang, Xinyuan; Hou, Guirong; Ma, Jianhua; Yang, Wei; Lin, Bingquan; Xu, Yikai; Chen, Wufan; Feng, Yanqiu
2014-01-01
Denoising is critical for improving visual quality and reliability of associative quantitative analysis when magnetic resonance (MR) images are acquired with low signal-to-noise ratios. The classical non-local means (NLM) filter, which averages pixels weighted by the similarity of their neighborhoods, is adapted and demonstrated to effectively reduce Rician noise without affecting edge details in MR magnitude images. However, the Rician NLM (RNLM) filter usually blurs small high-contrast particle details which might be clinically relevant information. In this paper, we investigated the reason of this particle blurring problem and proposed a novel particle-preserving RNLM filter with combined patch and pixel (RNLM-CPP) similarity. The results of experiments on both synthetic and real MR data demonstrate that the proposed RNLM-CPP filter can preserve small high-contrast particle details better than the original RNLM filter while denoising MR images.
Hermite cubic spline multi-wavelets on the cube
NASA Astrophysics Data System (ADS)
Cvejnová, Daniela; Černá, Dana; Finěk, Václav
2015-11-01
In 2000, W. Dahmen et al. proposed a construction of Hermite cubic spline multi-wavelets adapted to the interval [0, 1]. Later, several more simple constructions of wavelet bases based on Hermite cubic splines were proposed. We focus here on wavelet basis with respect to which both the mass and stiffness matrices are sparse in the sense that the number of non-zero elements in each column is bounded by a constant. Then, a matrix-vector multiplication in adaptive wavelet methods can be performed exactly with linear complexity for any second order differential equation with constant coefficients. In this contribution, we shortly review these constructions, use an anisotropic tensor product to obtain bases on the cube [0, 1]3, and compare their condition numbers.
Wavelet analysis in neurodynamics
NASA Astrophysics Data System (ADS)
Pavlov, Aleksei N.; Hramov, Aleksandr E.; Koronovskii, Aleksei A.; Sitnikova, Evgenija Yu; Makarov, Valeri A.; Ovchinnikov, Alexey A.
2012-09-01
Results obtained using continuous and discrete wavelet transforms as applied to problems in neurodynamics are reviewed, with the emphasis on the potential of wavelet analysis for decoding signal information from neural systems and networks. The following areas of application are considered: (1) the microscopic dynamics of single cells and intracellular processes, (2) sensory data processing, (3) the group dynamics of neuronal ensembles, and (4) the macrodynamics of rhythmical brain activity (using multichannel EEG recordings). The detection and classification of various oscillatory patterns of brain electrical activity and the development of continuous wavelet-based brain activity monitoring systems are also discussed as possibilities.
Bayesian wavelet PCA methodology for turbomachinery damage diagnosis under uncertainty
NASA Astrophysics Data System (ADS)
Xu, Shengli; Jiang, Xiaomo; Huang, Jinzhi; Yang, Shuhua; Wang, Xiaofang
2016-12-01
Centrifugal compressor often suffers various defects such as impeller cracking, resulting in forced outage of the total plant. Damage diagnostics and condition monitoring of such a turbomachinery system has become an increasingly important and powerful tool to prevent potential failure in components and reduce unplanned forced outage and further maintenance costs, while improving reliability, availability and maintainability of a turbomachinery system. This paper presents a probabilistic signal processing methodology for damage diagnostics using multiple time history data collected from different locations of a turbomachine, considering data uncertainty and multivariate correlation. The proposed methodology is based on the integration of three advanced state-of-the-art data mining techniques: discrete wavelet packet transform, Bayesian hypothesis testing, and probabilistic principal component analysis. The multiresolution wavelet analysis approach is employed to decompose a time series signal into different levels of wavelet coefficients. These coefficients represent multiple time-frequency resolutions of a signal. Bayesian hypothesis testing is then applied to each level of wavelet coefficient to remove possible imperfections. The ratio of posterior odds Bayesian approach provides a direct means to assess whether there is imperfection in the decomposed coefficients, thus avoiding over-denoising. Power spectral density estimated by the Welch method is utilized to evaluate the effectiveness of Bayesian wavelet cleansing method. Furthermore, the probabilistic principal component analysis approach is developed to reduce dimensionality of multiple time series and to address multivariate correlation and data uncertainty for damage diagnostics. The proposed methodology and generalized framework is demonstrated with a set of sensor data collected from a real-world centrifugal compressor with impeller cracks, through both time series and contour analyses of vibration
A wavelet approach to binary blackholes with asynchronous multitasking
NASA Astrophysics Data System (ADS)
Lim, Hyun; Hirschmann, Eric; Neilsen, David; Anderson, Matthew; Debuhr, Jackson; Zhang, Bo
2016-03-01
Highly accurate simulations of binary black holes and neutron stars are needed to address a variety of interesting problems in relativistic astrophysics. We present a new method for the solving the Einstein equations (BSSN formulation) using iterated interpolating wavelets. Wavelet coefficients provide a direct measure of the local approximation error for the solution and place collocation points that naturally adapt to features of the solution. Further, they exhibit exponential convergence on unevenly spaced collection points. The parallel implementation of the wavelet simulation framework presented here deviates from conventional practice in combining multi-threading with a form of message-driven computation sometimes referred to as asynchronous multitasking.
EEG Artifact Removal Using a Wavelet Neural Network
NASA Technical Reports Server (NTRS)
Nguyen, Hoang-Anh T.; Musson, John; Li, Jiang; McKenzie, Frederick; Zhang, Guangfan; Xu, Roger; Richey, Carl; Schnell, Tom
2011-01-01
!n this paper we developed a wavelet neural network. (WNN) algorithm for Electroencephalogram (EEG) artifact removal without electrooculographic (EOG) recordings. The algorithm combines the universal approximation characteristics of neural network and the time/frequency property of wavelet. We. compared the WNN algorithm with .the ICA technique ,and a wavelet thresholding method, which was realized by using the Stein's unbiased risk estimate (SURE) with an adaptive gradient-based optimal threshold. Experimental results on a driving test data set show that WNN can remove EEG artifacts effectively without diminishing useful EEG information even for very noisy data.
Image denoising by exploring external and internal correlations.
Yue, Huanjing; Sun, Xiaoyan; Yang, Jingyu; Wu, Feng
2015-06-01
Single image denoising suffers from limited data collection within a noisy image. In this paper, we propose a novel image denoising scheme, which explores both internal and external correlations with the help of web images. For each noisy patch, we build internal and external data cubes by finding similar patches from the noisy and web images, respectively. We then propose reducing noise by a two-stage strategy using different filtering approaches. In the first stage, since the noisy patch may lead to inaccurate patch selection, we propose a graph based optimization method to improve patch matching accuracy in external denoising. The internal denoising is frequency truncation on internal cubes. By combining the internal and external denoising patches, we obtain a preliminary denoising result. In the second stage, we propose reducing noise by filtering of external and internal cubes, respectively, on transform domain. In this stage, the preliminary denoising result not only enhances the patch matching accuracy but also provides reliable estimates of filtering parameters. The final denoising image is obtained by fusing the external and internal filtering results. Experimental results show that our method constantly outperforms state-of-the-art denoising schemes in both subjective and objective quality measurements, e.g., it achieves >2 dB gain compared with BM3D at a wide range of noise levels.
PRINCIPAL COMPONENTS FOR NON-LOCAL MEANS IMAGE DENOISING.
Tasdizen, Tolga
2008-01-01
This paper presents an image denoising algorithm that uses principal component analysis (PCA) in conjunction with the non-local means image denoising. Image neighborhood vectors used in the non-local means algorithm are first projected onto a lower-dimensional subspace using PCA. Consequently, neighborhood similarity weights for denoising are computed using distances in this subspace rather than the full space. This modification to the non-local means algorithm results in improved accuracy and computational performance. We present an analysis of the proposed method's accuracy as a function of the dimensionality of the projection subspace and demonstrate that denoising accuracy peaks at a relatively low number of dimensions.
Choi, Hyun Ho; Lee, Ju Hwan; Kim, Sung Min; Park, Sung Yun
2015-01-01
Here, the speckle noise in ultrasonic images is removed using an image fusion-based denoising method. To optimize the denoising performance, each discrete wavelet transform (DWT) and filtering technique was analyzed and compared. In addition, the performances were compared in order to derive the optimal input conditions. To evaluate the speckle noise removal performance, an image fusion algorithm was applied to the ultrasound images, and comparatively analyzed with the original image without the algorithm. As a result, applying DWT and filtering techniques caused information loss and noise characteristics, and did not represent the most significant noise reduction performance. Conversely, an image fusion method applying SRAD-original conditions preserved the key information in the original image, and the speckle noise was removed. Based on such characteristics, the input conditions of SRAD-original had the best denoising performance with the ultrasound images. From this study, the best denoising technique proposed based on the results was confirmed to have a high potential for clinical application.
Yuan, Tingbi; Wang, Zhe; Li, Zheng; Ni, Weidou; Liu, Jianmin
2014-01-07
A partial least squares (PLS) and wavelet transform hybrid model are proposed to analyze the carbon content of coal by using laser-induced breakdown spectroscopy (LIBS). The hybrid model is composed of two steps of wavelet analysis procedures, which include environmental denoising and background noise reduction, to pretreat the LIBS spectrum. The processed wavelet coefficients, which contain the discrete line information of the spectra, were taken as inputs for the PLS model for calibration and prediction of carbon element. A higher signal-to-noise ratio of carbon line was obtained after environmental denoising, and the best decomposition level was determined after background noise reduction. The hybrid model resulted in a significant improvement over the conventional PLS method under different ambient environments, which include air, argon, and helium. The average relative error of carbon decreased from 2.74 to 1.67% under an ambient helium environment, which indicated a significantly improved accuracy in the measurement of carbon in coal. The best results obtained under an ambient helium environment could be partly attributed to the smallest interference by noise after wavelet denoising. A similar improvement was observed in ambient air and argon environments, thereby proving the applicability of the hybrid model under different experimental conditions.
Postprocessing of Compressed Images via Sequential Denoising
NASA Astrophysics Data System (ADS)
Dar, Yehuda; Bruckstein, Alfred M.; Elad, Michael; Giryes, Raja
2016-07-01
In this work we propose a novel postprocessing technique for compression-artifact reduction. Our approach is based on posing this task as an inverse problem, with a regularization that leverages on existing state-of-the-art image denoising algorithms. We rely on the recently proposed Plug-and-Play Prior framework, suggesting the solution of general inverse problems via Alternating Direction Method of Multipliers (ADMM), leading to a sequence of Gaussian denoising steps. A key feature in our scheme is a linearization of the compression-decompression process, so as to get a formulation that can be optimized. In addition, we supply a thorough analysis of this linear approximation for several basic compression procedures. The proposed method is suitable for diverse compression techniques that rely on transform coding. Specifically, we demonstrate impressive gains in image quality for several leading compression methods - JPEG, JPEG2000, and HEVC.
Nonlocal Markovian models for image denoising
NASA Astrophysics Data System (ADS)
Salvadeo, Denis H. P.; Mascarenhas, Nelson D. A.; Levada, Alexandre L. M.
2016-01-01
Currently, the state-of-the art methods for image denoising are patch-based approaches. Redundant information present in nonlocal regions (patches) of the image is considered for better image modeling, resulting in an improved quality of filtering. In this respect, nonlocal Markov random field (MRF) models are proposed by redefining the energy functions of classical MRF models to adopt a nonlocal approach. With the new energy functions, the pairwise pixel interaction is weighted according to the similarities between the patches corresponding to each pair. Also, a maximum pseudolikelihood estimation of the spatial dependency parameter (β) for these models is presented here. For evaluating this proposal, these models are used as an a priori model in a maximum a posteriori estimation to denoise additive white Gaussian noise in images. Finally, results display a notable improvement in both quantitative and qualitative terms in comparison with the local MRFs.
NASA Astrophysics Data System (ADS)
Lazaro, D.; Barat, E.; Le Loirec, C.; Dautremer, T.; Montagu, T.; Guérin, L.; Batalla, A.
2013-05-01
This work investigates the possibility of combining Monte Carlo (MC) simulations to a denoising algorithm for the accurate prediction of images acquired using amorphous silicon (a-Si) electronic portal imaging devices (EPIDs). An accurate MC model of the Siemens OptiVue1000 EPID was first developed using the penelope code, integrating a non-uniform backscatter modelling. Two already existing denoising algorithms were then applied on simulated portal images, namely the iterative reduction of noise (IRON) method and the locally adaptive Savitzky-Golay (LASG) method. A third denoising method, based on a nonparametric Bayesian framework and called DPGLM (for Dirichlet process generalized linear model) was also developed. Performances of the IRON, LASG and DPGLM methods, in terms of smoothing capabilities and computation time, were compared for portal images computed for different values of the RMS pixel noise (up to 10%) in three different configurations, a heterogeneous phantom irradiated by a non-conformal 15 × 15 cm2 field, a conformal beam from a pelvis treatment plan, and an IMRT beam from a prostate treatment plan. For all configurations, DPGLM outperforms both IRON and LASG by providing better smoothing performances and demonstrating a better robustness with respect to noise. Additionally, no parameter tuning is required by DPGLM, which makes the denoising step very generic and easy to handle for any portal image. Concerning the computation time, the denoising of 1024 × 1024 images takes about 1 h 30 min, 2 h and 5 min using DPGLM, IRON, and LASG, respectively. This paper shows the feasibility to predict within a few hours and with the same resolution as real images accurate portal images, combining MC simulations with the DPGLM denoising algorithm.
Wavelet transforms with discrete-time continuous-dilation wavelets
NASA Astrophysics Data System (ADS)
Zhao, Wei; Rao, Raghuveer M.
1999-03-01
Wavelet constructions and transforms have been confined principally to the continuous-time domain. Even the discrete wavelet transform implemented through multirate filter banks is based on continuous-time wavelet functions that provide orthogonal or biorthogonal decompositions. This paper provides a novel wavelet transform construction based on the definition of discrete-time wavelets that can undergo continuous parameter dilations. The result is a transformation that has the advantage of discrete-time or digital implementation while circumventing the problem of inadequate scaling resolution seen with conventional dyadic or M-channel constructions. Examples of constructing such wavelets are presented.
Denoising forced-choice detection data.
García-Pérez, Miguel A
2010-02-01
Observers in a two-alternative forced-choice (2AFC) detection task face the need to produce a response at random (a guess) on trials in which neither presentation appeared to display a stimulus. Observers could alternatively be instructed to use a 'guess' key on those trials, a key that would produce a random guess and would also record the resultant correct or wrong response as emanating from a computer-generated guess. A simulation study shows that 'denoising' 2AFC data with information regarding which responses are a result of guesses yields estimates of detection threshold and spread of the psychometric function that are far more precise than those obtained in the absence of this information, and parallel the precision of estimates obtained with yes-no tasks running for the same number of trials. Simulations also show that partial compliance with the instructions to use the 'guess' key reduces the quality of the estimates, which nevertheless continue to be more precise than those obtained from conventional 2AFC data if the observers are still moderately compliant. An empirical study testing the validity of simulation results showed that denoised 2AFC estimates of spread were clearly superior to conventional 2AFC estimates and similar to yes-no estimates, but variations in threshold across observers and across sessions hid the benefits of denoising for threshold estimation. The empirical study also proved the feasibility of using a 'guess' key in addition to the conventional response keys defined in 2AFC tasks.
Gearbox diagnostics using wavelet-based windowing technique
NASA Astrophysics Data System (ADS)
Omar, F. K.; Gaouda, A. M.
2009-08-01
In extracting gear box acoustic signals embedded in excessive noise, the need for an online and automated tool becomes a crucial necessity. One of the recent approaches that have gained some acceptance within the research arena is the Wavelet multi-resolution analysis (WMRA). However selecting an accurate mother wavelet, defining dynamic threshold values and identifying the resolution levels to be considered in gearboxes fault detection and diagnosis are still challenging tasks. This paper proposes a novel wavelet-based technique for detecting, locating and estimating the severity of defects in gear tooth fracture. The proposed technique enhances the WMRA by decomposing the noisy data into different resolution levels while data sliding it into Kaiser's window. Only the maximum expansion coefficients at each resolution level are used in de-noising, detecting and measuring the severity of the defects. A small set of coefficients is used in the monitoring process without assigning threshold values or performing signal reconstruction. The proposed monitoring technique has been applied to a laboratory data corrupted with high noise level.
The Discrete Wavelet Transform
1991-06-01
Split- Band Coding," Proc. ICASSP, May 1977, pp 191-195. 12. Vetterli, M. "A Theory of Multirate Filter Banks ," IEEE Trans. ASSP, 35, March 1987, pp 356...both special cases of a single filter bank structure, the discrete wavelet transform, the behavior of which is governed by one’s choice of filters . In...B-1 ,.iii FIGURES 1.1 A wavelet filter bank structure ..................................... 2 2.1 Diagram illustrating the dialation and
Wavelets and Multifractal Analysis
2004-07-01
distribution unlimited 13. SUPPLEMENTARY NOTES See also ADM001750, Wavelets and Multifractal Analysis (WAMA) Workshop held on 19-31 July 2004., The original...f)] . . . 16 2.5.4 Detrended Fluctuation Analysis [DFA(m)] . . . . . . . . . . . . . . . 17 2.6 Scale-Independent Measures...18 2.6.1 Detrended -Fluctuation- Analysis Power-Law Exponent (αD) . . . . . . 18 2.6.2 Wavelet-Transform Power-Law Exponent
Field programmable gate arrays implementation of Dual Tree Complex Wavelet Transform.
Canbay, Ferhat; Levent, Vecdi Emre; Serbes, Gorkem; Goren, Sezer; Aydin, Nizamettin
2015-01-01
Due to the inherent time-varying characteristics of physiological systems, most biomedical signals (BSs) are expected to have non-stationary character. Therefore, any appropriate analysis method for dealing with BSs should exhibit adjustable time-frequency (TF) resolution. The wavelet transform (WT) provides a TF representation of signals, which has good frequency resolution at low frequencies and good time resolution at high frequencies, resulting in an optimized TF resolution. Discrete wavelet transform (DWT), which is used in various medical signal processing applications such as denoising and feature extraction, is a fast and discretized algorithm for classical WT. However, the DWT has some very important drawbacks such as aliasing, lack of directionality, and shift-variance. To overcome these drawbacks, a new improved discrete transform named as Dual Tree Complex Wavelet Transform (DTCWT) can be used. Nowadays, with the improvements in embedded system technology, portable real-time medical devices are frequently used for rapid diagnosis in patients. In this study, in order to implement DTCWT algorithm in FPGAs, which can be used as real-time feature extraction or denoising operator for biomedical signals, a novel hardware architecture is proposed. In proposed architecture, DTCWT is implemented with only one adder and one multiplier. Additionally, considering the multi-channel outputs of biomedical data acquisition systems, this architecture is capable of running N channels in parallel.
Riesz wavelets and multiresolution structures
NASA Astrophysics Data System (ADS)
Larson, David R.; Tang, Wai-Shing; Weber, Eric
2001-12-01
Multiresolution structures are important in applications, but they are also useful for analyzing properties of associated wavelets. Given a nonorthogonal (multi-) wavelet in a Hilbert space, we construct a core subspace. Subsequently, the dilates of the core subspace defines a ladder of nested subspaces. Of fundamental importance are two questions: 1) when is the core subspace shift invariant; and if yes, then 2) when is the core subspace generated by shifts of a single vector, i.e. there exists a scaling vector. If the wavelet generates a Riesz basis then the answer to question 1) is yes if and only if the wavelet is a biorthogonal wavelet. Additionally, if the wavelet generates a tight frame of arbitrary frame constant, then the core subspace is shift invariant. Question 1) is still open in case the wavelet generates a non-tight frame. We also present some known results to question 2) and provide some preliminary improvements. Our analysis here arises from investigating the dimension function and the multiplicity function of a wavelet. These two functions agree if the wavelet is orthogonal. Finally, we discuss how these questions are important for considering linear perturbation of wavelets. Utilizing the idea of the local commutant of a unitary system developed by Dai and Larson, we show that nearly all linear perturbations of two orthonormal wavelets form a Riesz wavelet. If in fact these wavelets correspond to a von Neumann algebra in the local commutant of a base wavelet, then the interpolated wavelet is biorthogonal. Moreover, we demonstrate that in this case the interpolated wavelets have a scaling vector if the base wavelet has a scaling vector.
Image Pretreatment Tools I: Algorithms for Map Denoising and Background Subtraction Methods.
Cannistraci, Carlo Vittorio; Alessio, Massimo
2016-01-01
One of the critical steps in two-dimensional electrophoresis (2-DE) image pre-processing is the denoising, that might aggressively affect either spot detection or pixel-based methods. The Median Modified Wiener Filter (MMWF), a new nonlinear adaptive spatial filter, resulted to be a good denoising approach to use in practice with 2-DE. MMWF is suitable for global denoising, and contemporary for the removal of spikes and Gaussian noise, being its best setting invariant on the type of noise. The second critical step rises because of the fact that 2-DE gel images may contain high levels of background, generated by the laboratory experimental procedures, that must be subtracted for accurate measurements of the proteomic optical density signals. Here we discuss an efficient mathematical method for background estimation, that is suitable to work even before the 2-DE image spot detection, and it is based on the 3D mathematical morphology (3DMM) theory.
NASA Astrophysics Data System (ADS)
Wen-Bo, Wang; Xiao-Dong, Zhang; Yuchan, Chang; Xiang-Li, Wang; Zhao, Wang; Xi, Chen; Lei, Zheng
2016-01-01
In this paper, a new method to reduce noises within chaotic signals based on ICA (independent component analysis) and EMD (empirical mode decomposition) is proposed. The basic idea is decomposing chaotic signals and constructing multidimensional input vectors, firstly, on the base of EMD and its translation invariance. Secondly, it makes the independent component analysis on the input vectors, which means that a self adapting denoising is carried out for the intrinsic mode functions (IMFs) of chaotic signals. Finally, all IMFs compose the new denoised chaotic signal. Experiments on the Lorenz chaotic signal composed of different Gaussian noises and the monthly observed chaotic sequence on sunspots were put into practice. The results proved that the method proposed in this paper is effective in denoising of chaotic signals. Moreover, it can correct the center point in the phase space effectively, which makes it approach the real track of the chaotic attractor. Project supported by the National Science and Technology, China (Grant No. 2012BAJ15B04), the National Natural Science Foundation of China (Grant Nos. 41071270 and 61473213), the Natural Science Foundation of Hubei Province, China (Grant No. 2015CFB424), the State Key Laboratory Foundation of Satellite Ocean Environment Dynamics, China (Grant No. SOED1405), the Hubei Provincial Key Laboratory Foundation of Metallurgical Industry Process System Science, China (Grant No. Z201303), and the Hubei Key Laboratory Foundation of Transportation Internet of Things, Wuhan University of Technology, China (Grant No.2015III015-B02).
Dual-domain denoising in three dimensional magnetic resonance imaging.
Peng, Jing; Zhou, Jiliu; Wu, Xi
2016-08-01
Denoising is a crucial preprocessing procedure for three dimensional magnetic resonance imaging (3D MRI). Existing denoising methods are predominantly implemented in a single domain, ignoring information in other domains. However, denoising methods are becoming increasingly complex, making analysis and implementation challenging. The present study aimed to develop a dual-domain image denoising (DDID) algorithm for 3D MRI that encapsulates information from the spatial and transform domains. In the present study, the DDID method was used to distinguish signal from noise in the spatial and frequency domains, after which robust accurate noise estimation was introduced for iterative filtering, which is simple and beneficial for computation. In addition, the proposed method was compared quantitatively and qualitatively with existing methods for synthetic and in vivo MRI datasets. The results of the present study suggested that the novel DDID algorithm performed well and provided competitive results, as compared with existing MRI denoising filters.
Patch-based near-optimal image denoising.
Chatterjee, Priyam; Milanfar, Peyman
2012-04-01
In this paper, we propose a denoising method motivated by our previous analysis of the performance bounds for image denoising. Insights from that study are used here to derive a high-performance practical denoising algorithm. We propose a patch-based Wiener filter that exploits patch redundancy for image denoising. Our framework uses both geometrically and photometrically similar patches to estimate the different filter parameters. We describe how these parameters can be accurately estimated directly from the input noisy image. Our denoising approach, designed for near-optimal performance (in the mean-squared error sense), has a sound statistical foundation that is analyzed in detail. The performance of our approach is experimentally verified on a variety of images and noise levels. The results presented here demonstrate that our proposed method is on par or exceeding the current state of the art, both visually and quantitatively.
A connection between score matching and denoising autoencoders.
Vincent, Pascal
2011-07-01
Denoising autoencoders have been previously shown to be competitive alternatives to restricted Boltzmann machines for unsupervised pretraining of each layer of a deep architecture. We show that a simple denoising autoencoder training criterion is equivalent to matching the score (with respect to the data) of a specific energy-based model to that of a nonparametric Parzen density estimator of the data. This yields several useful insights. It defines a proper probabilistic model for the denoising autoencoder technique, which makes it in principle possible to sample from them or rank examples by their energy. It suggests a different way to apply score matching that is related to learning to denoise and does not require computing second derivatives. It justifies the use of tied weights between the encoder and decoder and suggests ways to extend the success of denoising autoencoders to a larger family of energy-based models.
Wavelet-based functional mixed models
Morris, Jeffrey S.; Carroll, Raymond J.
2009-01-01
Summary Increasingly, scientific studies yield functional data, in which the ideal units of observation are curves and the observed data consist of sets of curves that are sampled on a fine grid. We present new methodology that generalizes the linear mixed model to the functional mixed model framework, with model fitting done by using a Bayesian wavelet-based approach. This method is flexible, allowing functions of arbitrary form and the full range of fixed effects structures and between-curve covariance structures that are available in the mixed model framework. It yields nonparametric estimates of the fixed and random-effects functions as well as the various between-curve and within-curve covariance matrices. The functional fixed effects are adaptively regularized as a result of the non-linear shrinkage prior that is imposed on the fixed effects’ wavelet coefficients, and the random-effect functions experience a form of adaptive regularization because of the separately estimated variance components for each wavelet coefficient. Because we have posterior samples for all model quantities, we can perform pointwise or joint Bayesian inference or prediction on the quantities of the model. The adaptiveness of the method makes it especially appropriate for modelling irregular functional data that are characterized by numerous local features like peaks. PMID:19759841
NASA Astrophysics Data System (ADS)
Chen, Binqiang; Zhang, Zhousuo; Sun, Chuang; Li, Bing; Zi, Yanyang; He, Zhengjia
2012-11-01
Gearbox fault diagnosis is very important for preventing catastrophic accidents. Vibration signals of gearboxes measured by sensors are useful and dependable as they carry key information related to the mechanical faults in gearboxes. Effective signal processing techniques are in necessary demands to extract the fault features contained in the collected gearbox vibration signals. Overcomplete rational dilation discrete wavelet transform (ORDWT) enjoys attractive properties such as better shift-invariance, adjustable time-frequency distributions and flexible wavelet atoms of tunable oscillation in comparison with classical dyadic wavelet transform (DWT). Due to these advantages, ORDWT is presented as a versatile tool that can be adapted to analysis of gearbox fault features of different types, especially in analyzing the non-stationary and transient characteristics of the signals. Aiming to extract the various types of fault features confronted in gearbox fault diagnosis, a fault feature extraction technique based on ORDWT is proposed in this paper. In the routine of the proposed technique, ORDWT is used as the pre-processing decomposition tool, and a corresponding post-processing method is combined with ORDWT to extract the fault feature of a specific type. For extracting periodical impulses in the signal, an impulse matching algorithm is presented. In this algorithm, ORDWT bases of varied time-frequency distributions and varied oscillatory natures are adopted, moreover an improved signal impulsiveness measure derived from kurtosis is developed for choosing optimal ORDWT bases that perfectly match the hidden periodical impulses. For demodulation purpose, an improved instantaneous time-frequency spectrum (ITFS), based on the combination of ORDWT and Hilbert transform, is presented. For signal denoising applications, ORDWT is enhanced by neighboring coefficient shrinkage strategy as well as subband selection step to reveal the buried transient vibration contents. The
Adaptive photoacoustic imaging quality optimization with EMD and reconstruction
NASA Astrophysics Data System (ADS)
Guo, Chengwen; Ding, Yao; Yuan, Jie; Xu, Guan; Wang, Xueding; Carson, Paul L.
2016-10-01
Biomedical photoacoustic (PA) signal is characterized with extremely low signal to noise ratio which will yield significant artifacts in photoacoustic tomography (PAT) images. Since PA signals acquired by ultrasound transducers are non-linear and non-stationary, traditional data analysis methods such as Fourier and wavelet method cannot give useful information for further research. In this paper, we introduce an adaptive method to improve the quality of PA imaging based on empirical mode decomposition (EMD) and reconstruction. Data acquired by ultrasound transducers are adaptively decomposed into several intrinsic mode functions (IMFs) after a sifting pre-process. Since noise is randomly distributed in different IMFs, depressing IMFs with more noise while enhancing IMFs with less noise can effectively enhance the quality of reconstructed PAT images. However, searching optimal parameters by means of brute force searching algorithms will cost too much time, which prevent this method from practical use. To find parameters within reasonable time, heuristic algorithms, which are designed for finding good solutions more efficiently when traditional methods are too slow, are adopted in our method. Two of the heuristic algorithms, Simulated Annealing Algorithm, a probabilistic method to approximate the global optimal solution, and Artificial Bee Colony Algorithm, an optimization method inspired by the foraging behavior of bee swarm, are selected to search optimal parameters of IMFs in this paper. The effectiveness of our proposed method is proved both on simulated data and PA signals from real biomedical tissue, which might bear the potential for future clinical PA imaging de-noising.
Wavelet-Based Image Enhancement in X-Ray Imaging and Tomography
NASA Astrophysics Data System (ADS)
Bronnikov, Andrei V.; Duifhuis, Gerrit
1998-07-01
We consider an application of the wavelet transform to image processing in x-ray imaging and three-dimensional (3-D) tomography aimed at industrial inspection. Our experimental setup works in two operational modes digital radiography and 3-D cone-beam tomographic data acquisition. Although the x-ray images measured have a large dynamic range and good spatial resolution, their noise properties and contrast are often not optimal. To enhance the images, we suggest applying digital image processing by using wavelet-based algorithms and consider the wavelet-based multiscale edge representation in the framework of the Mallat and Zhong approach IEEE Trans. Pattern Anal. Mach. Intell. 14, 710 (1992) . A contrast-enhancement method by use of equalization of the multiscale edges is suggested. Several denoising algorithms based on modifying the modulus and the phase of the multiscale gradients and several contrast-enhancement techniques applying linear and nonlinear multiscale edge stretching are described and compared by use of experimental data. We propose the use of a filter bank of wavelet-based reconstruction filters for the filtered-backprojection reconstruction algorithm. Experimental results show a considerable increase in the performance of the whole x-ray imaging system for both radiographic and tomographic modes in the case of the application of the wavelet-based image-processing algorithms.
Wavelet-based SAR images despeckling using joint hidden Markov model
NASA Astrophysics Data System (ADS)
Li, Qiaoliang; Wang, Guoyou; Liu, Jianguo; Chen, Shaobo
2007-11-01
In the past few years, wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint probability density of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the deficiency for taking account of intrascale correlations that exist among neighboring wavelet coefficients. In this paper, we propose to develop a joint hidden Markov model by fusing the wavelet Bayesian denoising technique with an image regularization procedure based on HMT and Markov random field (MRF). The Expectation Maximization algorithm is used to estimate hyperparameters and specify the mixture model. The noise-free wavelet coefficients are finally estimated by a shrinkage function based on local weighted averaging of the Bayesian estimator. It is shown that the joint method outperforms lee filter and standard HMT techniques in terms of the integrative measure of the equivalent number of looks (ENL) and Pratt's figure of merit(FOM), especially when dealing with speckle noise in large variance.
Wavelet Approach for Operational Gamma Spectral Peak Detection - Preliminary Assessment
,
2012-02-01
Gamma spectroscopy for radionuclide identifications typically involves locating spectral peaks and matching the spectral peaks with known nuclides in the knowledge base or database. Wavelet analysis, due to its ability for fitting localized features, offers the potential for automatic detection of spectral peaks. Past studies of wavelet technologies for gamma spectra analysis essentially focused on direct fitting of raw gamma spectra. Although most of those studies demonstrated the potentials of peak detection using wavelets, they often failed to produce new benefits to operational adaptations for radiological surveys. This work presents a different approach with the operational objective being to detect only the nuclides that do not exist in the environment (anomalous nuclides). With this operational objective, the raw-count spectrum collected by a detector is first converted to a count-rate spectrum and is then followed by background subtraction prior to wavelet analysis. The experimental results suggest that this preprocess is independent of detector type and background radiation, and is capable of improving the peak detection rates using wavelets. This process broadens the doors for a practical adaptation of wavelet technologies for gamma spectral surveying devices.
Three-dimensional compression scheme based on wavelet transform
NASA Astrophysics Data System (ADS)
Yang, Wu; Xu, Hui; Liao, Mengyang
1999-03-01
In this paper, a 3D compression method based on separable wavelet transform is discussed in detail. The most commonly used digital modalities generate multiple slices in a single examination, which are normally anatomically or physiologically correlated to each other. 3D wavelet compression methods can achieve more efficient compression by exploring the correlation between slices. The first step is based on a separable 3D wavelet transform. Considering the difference between pixel distances within a slice and those between slices, one biorthogonal Antoninin filter bank is applied within 2D slices and a second biorthogonal Villa4 filter bank on the slice direction. Then, S+P transform is applied in the low-resolution wavelet components and an optimal quantizer is presented after analysis of the quantization noise. We use an optimal bit allocation algorithm, which, instead of eliminating the coefficients of high-resolution components in smooth areas, minimizes the system reconstruction distortion at a given bit-rate. Finally, to remain high coding efficiency and adapt to different properties of each component, a comprehensive entropy coding method is proposed, in which arithmetic coding method is applied in high-resolution components and adaptive Huffman coding method in low-resolution components. Our experimental results are evaluated by several image measures and our 3D wavelet compression scheme is proved to be more efficient than 2D wavelet compression.
NASA Astrophysics Data System (ADS)
Starosolski, Roman
2016-07-01
Reversible denoising and lifting steps (RDLS) are lifting steps integrated with denoising filters in such a way that, despite the inherently irreversible nature of denoising, they are perfectly reversible. We investigated the application of RDLS to reversible color space transforms: RCT, YCoCg-R, RDgDb, and LDgEb. In order to improve RDLS effects, we propose a heuristic for image-adaptive denoising filter selection, a fast estimator of the compressed image bitrate, and a special filter that may result in skipping of the steps. We analyzed the properties of the presented methods, paying special attention to their usefulness from a practical standpoint. For a diverse image test-set and lossless JPEG-LS, JPEG 2000, and JPEG XR algorithms, RDLS improves the bitrates of all the examined transforms. The most interesting results were obtained for an estimation-based heuristic filter selection out of a set of seven filters; the cost of this variant was similar to or lower than the transform cost, and it improved the average lossless JPEG 2000 bitrates by 2.65% for RDgDb and by over 1% for other transforms; bitrates of certain images were improved to a significantly greater extent.
Broom, Donald M
2006-01-01
The term adaptation is used in biology in three different ways. It may refer to changes which occur at the cell and organ level, or at the individual level, or at the level of gene action and evolutionary processes. Adaptation by cells, especially nerve cells helps in: communication within the body, the distinguishing of stimuli, the avoidance of overload and the conservation of energy. The time course and complexity of these mechanisms varies. Adaptive characters of organisms, including adaptive behaviours, increase fitness so this adaptation is evolutionary. The major part of this paper concerns adaptation by individuals and its relationships to welfare. In complex animals, feed forward control is widely used. Individuals predict problems and adapt by acting before the environmental effect is substantial. Much of adaptation involves brain control and animals have a set of needs, located in the brain and acting largely via motivational mechanisms, to regulate life. Needs may be for resources but are also for actions and stimuli which are part of the mechanism which has evolved to obtain the resources. Hence pigs do not just need food but need to be able to carry out actions like rooting in earth or manipulating materials which are part of foraging behaviour. The welfare of an individual is its state as regards its attempts to cope with its environment. This state includes various adaptive mechanisms including feelings and those which cope with disease. The part of welfare which is concerned with coping with pathology is health. Disease, which implies some significant effect of pathology, always results in poor welfare. Welfare varies over a range from very good, when adaptation is effective and there are feelings of pleasure or contentment, to very poor. A key point concerning the concept of individual adaptation in relation to welfare is that welfare may be good or poor while adaptation is occurring. Some adaptation is very easy and energetically cheap and
Wavelet differential neural network observer.
Chairez, Isaac
2009-09-01
State estimation for uncertain systems affected by external noises is an important problem in control theory. This paper deals with a state observation problem when the dynamic model of a plant contains uncertainties or it is completely unknown. Differential neural network (NN) approach is applied in this uninformative situation but with activation functions described by wavelets. A new learning law, containing an adaptive adjustment rate, is suggested to imply the stability condition for the free parameters of the observer. Nominal weights are adjusted during the preliminary training process using the least mean square (LMS) method. Lyapunov theory is used to obtain the upper bounds for the weights dynamics as well as for the mean squared estimation error. Two numeric examples illustrate this approach: first, a nonlinear electric system, governed by the Chua's equation and second the Lorentz oscillator. Both systems are assumed to be affected by external perturbations and their parameters are unknown.
Image denoising using a tight frame.
Shen, Lixin; Papadakis, Manos; Kakadiaris, Ioannis A; Konstantinidis, Ioannis; Kouri, Donald; Hoffman, David
2006-05-01
We present a general mathematical theory for lifting frames that allows us to modify existing filters to construct new ones that form Parseval frames. We apply our theory to design nonseparable Parseval frames from separable (tensor) products of a piecewise linear spline tight frame. These new frame systems incorporate the weighted average operator, the Sobel operator, and the Laplacian operator in directions that are integer multiples of 45 degrees. A new image denoising algorithm is then proposed, tailored to the specific properties of these new frame filters. We demonstrate the performance of our algorithm on a diverse set of images with very encouraging results.
NASA Astrophysics Data System (ADS)
Zielinski, B.; Patorski, K.
2008-12-01
The aim of this paper is to analyze the accuracy of 2D fringe pattern denoising performed by two chosen methods using quasi-1D two-arm spin filter and 2D Discrete Wavelet Transform (DWT) signal decomposition and thresholding. The ultimate aim of this comparison is to estimate which algorithm is better suited for high-accuracy interferometric measurements. In spite of the fact that both algorithms are designed to minimize possible fringe blur and distortion, the evaluation of errors introduced by each algorithm is essential for proper estimation of their performance.
A novel 3D wavelet based filter for visualizing features in noisy biological data
Moss, W C; Haase, S; Lyle, J M; Agard, D A; Sedat, J W
2005-01-05
We have developed a 3D wavelet-based filter for visualizing structural features in volumetric data. The only variable parameter is a characteristic linear size of the feature of interest. The filtered output contains only those regions that are correlated with the characteristic size, thus denoising the image. We demonstrate the use of the filter by applying it to 3D data from a variety of electron microscopy samples including low contrast vitreous ice cryogenic preparations, as well as 3D optical microscopy specimens.
Wavelets on Planar Tesselations
Bertram, M.; Duchaineau, M.A.; Hamann, B.; Joy, K.I.
2000-02-25
We present a new technique for progressive approximation and compression of polygonal objects in images. Our technique uses local parameterizations defined by meshes of convex polygons in the plane. We generalize a tensor product wavelet transform to polygonal domains to perform multiresolution analysis and compression of image regions. The advantage of our technique over conventional wavelet methods is that the domain is an arbitrary tessellation rather than, for example, a uniform rectilinear grid. We expect that this technique has many applications image compression, progressive transmission, radiosity, virtual reality, and image morphing.
Evolutionary Fuzzy Block-Matching-Based Camera Raw Image Denoising.
Yang, Chin-Chang; Guo, Shu-Mei; Tsai, Jason Sheng-Hong
2016-10-03
An evolutionary fuzzy block-matching-based image denoising algorithm is proposed to remove noise from a camera raw image. Recently, a variance stabilization transform is widely used to stabilize the noise variance, so that a Gaussian denoising algorithm can be used to remove the signal-dependent noise in camera sensors. However, in the stabilized domain, the existed denoising algorithm may blur too much detail. To provide a better estimate of the noise-free signal, a new block-matching approach is proposed to find similar blocks by the use of a type-2 fuzzy logic system (FLS). Then, these similar blocks are averaged with the weightings which are determined by the FLS. Finally, an efficient differential evolution is used to further improve the performance of the proposed denoising algorithm. The experimental results show that the proposed denoising algorithm effectively improves the performance of image denoising. Furthermore, the average performance of the proposed method is better than those of two state-of-the-art image denoising algorithms in subjective and objective measures.
Target profile identification of step frequency MMW radar based on wavelet neural network
NASA Astrophysics Data System (ADS)
Li, Yuehua; Gao, Duntang; Shen, Qinghong; Li, Xingguo
2001-11-01
With the increased availability of coherent wide band radar, there has been a renewed interest in the target recognition of MMW frequency step radar. A large bandwidth gives high resolution in range which means target recognition may be possible. In this paper, by integrating wavelet with neural network, a new adaptive wavelet function neural network is proposed. An artificial neural network with wavelet as weight coefficients is developed for pattern recognition. It is inspired by wavelet transform theory and feed forward neural network. The good localization characteristics of wavelet functions in both time and frequency space allow hierarchical multi-resolution learning of input-output data mappings. The wavelet shapes are adaptively computed to minimize an energy function for a specific application of radar targets. The mathematical frame of the neural network is introduced and error back propagation algorithm is used. The procedure of using wavelet neural network for identification is described in detail. Based on the target specific information offered by the range profiles of step frequency MMW radar targets, the wavelet neural network is applied to recognition of three kinds of practical radar targets. We find that we can reliably distinguish for three targets over a range of aspect angle. Experiment results indicate that the new feature vector in low dimension is valuable for target recognition, the wavelet neural network has faster convergence speed and higher correct recognition rate and the noise resistance character is good.