Statistical Modeling Of Wavelet Coefficients Research Articles

Closed-form shrinkage function based on mixture of Gauss–Laplace distributions for dropping ambient noise

Removing the ambient noise and increasing the signal-to-noise ratio are very important for detecting defects and corrosions of conductive material by using the electromagnetic acoustic transducer. It is still an issue to remove the ambient noise without losing the original signal information. The aim of this paper is to solve the issue by using a new closed-form shrinkage function based on Gauss–Laplace mixture distribution in wavelet domain. First, we prove that Gauss–Laplace mixture distribution is well fitted to the statistical model for wavelet coefficients of noise-free signal of electromagnetic acoustic transducer. As well, we use Gauss–Laplace mixture distribution and Gauss distribution for statistical modeling on the wavelet coefficients of noise-free signal and ambient noise, respectively. Using these distributions, we derive a new closed-form shrinkage function that is an analytical solution of a Bayesian maximum a posteriori estimator. Next, we evaluate the denoising performance of new shrinkage function compared with various shrinkage functions in terms of the improved signal-to-noise ratio, root mean squared error and entropy. The experiment results show that the wavelet denoising method using the proposed shrinkage function effectively removes the ambient noise than the other existing denoising methods for noisy signal of electromagnetic acoustic transducer.

Effective EMG denoising using a hybrid model based on WAT and GARCH

Abstract EMG is the recording of electrical activity of the muscles that can be used in diagnosing muscular diseases like myopathy and neuropathy and in generating control signals for operating artificial prosthetic arms and limbs. Various forms of artifacts get introduced into the EMG during the acquisition process that limits its proper analysis and characterization. This paper proposes a novel noise suppression method for EMG signals employing orthogonal Wave Atom Transform (WAT) followed by statistical modelling of wavelet coefficients by using a Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model with maximum a-posteriori (MAP) estimator for signal recovery from noisy EMG signals. The proposed algorithm was evaluated on signals taken from the standard Physionet ATM database that was manually corrupted by different levels of Additive White Gaussian Noise (AWGN) noise. The efficiency of the proposed algorithm is studied using the standard metrics namely, Signal to Noise Ratio (SNR) in dB, and Percent Root Mean Square Deviation (PRD). Results indicate that the hybrid denoising scheme was able to reduce noise from EMG signals more effectively quantified by average SNR of 22.98 dB and PRD of 0.00029, across different datasets, in comparison with the currently employed noise reduction algorithms.

Statistical modeling and Gaussianization procedure based de-speckling algorithm for retinal OCT images

This paper presents a de-noising method for speckle noise removal called de-speckling, retinal optical coherence tomography image by combining the features of wavelet transform, statistical modeling, Bayesian estimators and Gaussianization procedure. De-speckling methods based on statistical modeling of wavelet coefficients depend on the correct estimation of probability density function (PDF). The density estimation problem has been solved by using the Gaussianization procedure. The dynamic range capability of Gaussian PDF has been used for sharp estimation of density. A Cauchy PDF is used for modeling wavelet coefficients and finding the cumulative distribution function (CDF) of wavelet coefficients. This CDF is used as the input to the Gaussianization procedure, where it equalizes with the Gaussian CDF to estimate the density function of wavelet coefficients. Finally, the wavelet coefficients are recovered using Bayesian minimum mean square error estimator. Both visual and quantitative comparisons are performed for demonstrating the prominence of the proposed method. From simulation result it is seen that the proposed method outperforms the state-of-the-art methods in terms of peak signal-to-noise ratio (PSNR), structural similarity, correlation coefficient (CoC) and edge preservation index (EPI). The proposed method has been achieved improvement of 5.13% in PSNR, 2.44% in SSIM, 2.11% in CoC and 3.45% in EPI over the well accepted existing method.

Comparative study of statistical modeling of wavelet coefficients for SAR image despeckling

The work is concentrated to get good despeckled performance under non-homomorphic framework by involving simple distributions to obtain closed form Maximum-a-Posteriori probability (MAP) solutions. To estimate noise-free wavelet coefficient, distributions with lesser number of parameters allied Laplacian/Gaussian probability density function (pdf) for signal reflectivity and Rayleigh/Gaussian pdf for noisy signal are employed. Thus, the four despeckling methods are formed, namely LRMAP, GRMAP, LGMAP and GGMAP to despeckle SAR images and the effectiveness of different distributions is studied. The despeckling method is made adaptive by estimating the local variance of high frequency image using wavelet sub-band coefficient statistics. Also, the parameter space used in the proposed methods does not involve initialization, iterative search and convergence problems. The performances of the proposed methods are evaluated in terms of Equivalent Number of Looks (ENL), Peak Signal to Noise Ratio (PSNR), Edge Preservation ([Formula: see text] and Mean Structural Similarity Index Measure (MSSIM). Experimental results show that LRMAP yields good results over all methods and GGMAP does not perform good for all images in terms of all quality metrics. Also, the proposed methods yield good quality metrics in less computing time as compared with the method available in the literature.

Automatic contrast enhancement of low-light images based on local statistics of wavelet coefficients

This paper describes a new method for contrast enhancement in images and image sequences of low-light or unevenly illuminated scenes based on statistical modelling of wavelet coefficients of the image. A non-linear enhancement function has been designed based on the local dispersion of the wavelet coefficients modelled as a bivariate Cauchy distribution. Within the same statistical framework, a simultaneous noise reduction in the image is performed by means of a shrinkage function, thus preventing noise amplification. The proposed enhancement method has been shown to perform very well with insufficiently illuminated and noisy imagery, outperforming other conventional methods, in terms of contrast enhancement and noise reduction in the output data.

Wavelet domain Bayesian processor for speckle removal in medical ultrasound images

Speckle reduction is a prerequisite for many ultrasound image processing tasks. In this study, the authors introduce a novel speckle suppression method for ultrasound images, based on statistical modelling of wavelet coefficients. First, the authors demonstrate that the wavelet coefficients of log-transformed ultrasound images have significantly non-Gaussian statistics and a two-dimensional heteroscedasticity exists in them. Previously, they described the overall multiscale wavelet transform of the log-transformed ultrasound images using two-dimensional generalised autoregressive conditional heteroscedastic (2D GARCH) model. In this study, they introduce a new heteroscedastic model, that is, 2D-GARCH generalised Gaussian (2D-GARCH-GG) as an extension of 2D-GARCH model. This new model can capture heavy-tailed marginal distribution and the intrascale dependencies of wavelet coefficients. Also, 2D-GARCH-GG model introduces additional flexibility in the model formulation in comparison with 2D-GARCH model, which results in better characterisation of ultrasound images subbands and improved restoration in noisy environments. In consequence, the authors introduce maximum a-posteriori estimator, based on GARCH-GG modelling to estimate the clean wavelet coefficients. In order to evaluate the performance of the proposed method in speckle suppression, they compare it with other denoising methods applied on some artificially speckled and actual ultrasound images and we verify the performance improvement in utilising the new strategies.

Image resolution enhancement using statistical estimation in wavelet domain

The goal of medical image resolution enhancement is to reconstruct a higher-resolution image from its lower-resolution counterpart. This paper proposes a Bayesian approach in the wavelet domain by exploiting a Bayesian inference framework to mathematically formulate the image interpolation problem. Furthermore, the proposed approach jointly estimates both the unknown wavelet coefficients of the high-resolution image and the unknown parameters of the statistical model for wavelet coefficients. Experiments are conducted to demonstrate the superior performance of the proposed approach.

Wavelet Thresholding Approach For Image Denoising

The original image corrupted by Gaussian noise is a long established problem in signal or image processing .This noise is removed by using wavelet thresholding by focused on statistical modelling of wavelet coefficients and the optimal choice of thresholds called as image denoising . For the first part, threshold is driven in a Bayesian technique to use probabilistic model of the image wavelet coefficients that are dependent on the higher order moments of generalized Gaussian distribution (GGD) in image processing applications. The proposed threshold is very simple. Experimental results show that the proposed method is called BayesShrink, is typically within 5% of the MSE of the best soft-thresholding benchmark with the image. It outperforms Donoho and Johnston Sure Shrink. The second part of the paper is attempt to claim on lossy compression can be used for image denoising .thus achieving the image compression & image denoising simultaneously. The parameter is choosing based on a criterion derived from Rissanen’s minimum description length (MDL) principle. Experiments show that this compression & denoise method does indeed remove noise significantly, especially for large noise power.

Image fusion technique using multivariate statistical model for wavelet coefficients

Wavelet-based image fusion techniques have been highly successful in combining important features such as edges and textures of source images. In this work, a new discrete wavelet transform (DWT)-based fusion algorithm is proposed using a locally-adaptive multivariate statistical model for the wavelet coefficients of the source images as well as that of the fused image. The multivariate model is proposed based on the fact that the DWT coefficients of source images are correlated not only with each other but also with the fused image. By using this model as a joint prior function, an estimate of the fused coefficients is derived via the Bayesian maximum a posteriori estimation technique. Experimental results show that performance of the proposed fusion method is better than that of the other methods in terms of commonly-used metrics such as structural similarity, peak signal-to-noise ratio, and cross-entropy.

A Novel Image Denoising using Matched Partial Biorthogonal Wavelets and Adaptive Thresholding

denoising of a natural image corrupted by Gaussian noise is a problem in signal or image processing Even though much work has been done in the field of wavelet thresholding, most of it was focused on statistical modeling of wavelet coefficients and the optimal choice of thresholds. This paper describes a new method for suppression of noise in image by fusing the wavelet Denoising technique with optimized thresholding function, improving the denoised results significantly by using partial biorthogonal wavelets. In today's scenario denoising techniques use the classical orthonormal wavelets for decomposition of an image corrupted with additive white Gaussian noise, upon which various thresholding strategies are built. We present a method to design partial biorthogonal wavelet bases and report on their potential for denoising. This paper describes a new method for suppression of noise in image by fusing the wavelet Denoising technique with optimized thresholding function, improving the denoised results significantly. Simulated noise images are used to evaluate the denoising performance of proposed algorithm along with another wavelet-based denoising algorithm. Experimental result shows that the proposed denoising method outperforms standard wavelet denoising techniques in terms of the PSNR and the preservation of edge information. The use of available biorthogonal wavelets in image denoising is less common because of their poor performance. But when we combine the approach of fusion with partial biorthogonal wavelets then the performance is increases in comparison of traditional methodology. This point to the importance of matching when using wavelet-based denoising.

Non-Gaussian model-based fusion of noisy images in the wavelet domain

This paper describes a new methodology for multimodal image fusion based on non-Gaussian statistical modelling of wavelet coefficients. Special emphasis is placed on the fusion of noisy images. The use of families of generalised Gaussian and alpha-stable distributions for modelling image wavelet coefficients is investigated and methods for estimating distribution parameters are proposed. Improved techniques for image fusion are developed, by incorporating these models into a weighted average image fusion algorithm. The proposed method has been shown to perform very well with both noisy and noise-free images from multimodal datasets, outperforming conventional methods in terms of fusion quality and noise reduction in the fused output.

EFFICIENT STATISTICAL MODELING OF WAVELET COEFFICIENTS FOR IMAGE DENOISING

Statistical modeling of wavelet coefficients is a critical issue in wavelet domain signal processing. By analyzing the defects of other existing methods, and exploiting the local dependency of wavelet coefficients, an efficient statistical model is proposed. Improved variance estimation of the local wavelet coefficients can be obtained using the new model. Then we apply an approximate minimum mean squared error (MMSE) estimation procedure to restore the wavelet image coefficients. The modeling process is computational cost saving, and the denoising experiments show the algorithm outperforms other approaches in peak-signal-to-noise ratio (PSNR).

Iterative PET Image Reconstruction Using Translation Invariant Wavelet Transform

The present work describes a Bayesian maximum a posteriori (MAP) method using a statistical multiscale wavelet prior model. Rather than using the orthogonal discrete wavelet transform (DWT), this prior is built on the translation invariant wavelet transform (TIWT). The statistical modeling of wavelet coefficients relies on the generalized Gaussian distribution. Image reconstruction is performed in spatial domain with a fast block sequential iteration algorithm. We study theoretically the TIWT MAP method by analyzing the Hessian of the prior function to provide some insights on noise and resolution properties of image reconstruction. We adapt the key concept of local shift invariance and explore how the TIWT MAP algorithm behaves with different scales. It is also shown that larger support wavelet filters do not offer better performance in contrast recovery studies. These theoretical developments are confirmed through simulation studies. The results show that the proposed method is more attractive than other MAP methods using either the conventional Gibbs prior or the DWT-based wavelet prior.

Machine condition diagnosis using hidden Markov tree

As a statistical model of wavelet coefficients,hidden Markov tree(HMT) can consider the statistical dependencies and non-Gaussian statistics of wavelet coefficients.Due to shift-variance of discrete wavelet transform(DWT),if DWT-based HMT model is used for machine condition diagnosis,it is likely to get incorrect results.To obtain shift-invariance,DT CWT-based(dual-tree complex wavelet transform) HMT model is developed.Experiments show that DT CWT-based HMT model can get much higher recognition rates in comparison with DWT-based HMT model.

SAR Images Despeckling Based on Bayesian Estimation and Fuzzy Shrinkage in Wavelet Domains

An efficient despeckling algorithm is proposed based on stationary wavelet transform (SWT) for synthetic aperture radar (SAR) images. The statistical model of wavelet coefficients is analyzed and its performance is modeled with a mixture density of two zero-mean Gaussian distributions. A fuzzy shrinkage factor is derived based on the minimum mean square error (MMSE) criteria with Bayesian estimation. In the case above, the ideas of region division and fuzzy shrinkage are adopted according to the interscale dependencies among wavelet coefficients. The noise-free wavelet coefficients are estimated accurately. Experimental results show that the algorithm proposed is superior to the refined Lee filter, wavelet soft thresholding shrinkage and SWT shrinkage algorithms in terms of smoothing effects and edges preservation.

Detecting abnormal process trends by wavelet‐domain hidden Markov models

AbstractA novel method for detection of abnormal conditions during plant operation uses wavelet‐domain hidden Markov models (HMMs) as a powerful tool for statistical modeling of wavelet coefficients. By capturing the interdependence of wavelet coefficients of a measured process variable, a classification strategy is developed that can detect abnormal conditions and classify the process behavior on‐line. The method is extended to include multiple measured variables in detection and classification. Two case studies illustrate the potential of this method.

Low-complexity image denoising based on statistical modeling of wavelet coefficients

We introduce a simple spatially adaptive statistical model for wavelet image coefficients and apply it to image denoising. Our model is inspired by a recent wavelet image compression algorithm, the estimation-quantization (EQ) coder. We model wavelet image coefficients as zero-mean Gaussian random variables with high local correlation. We assume a marginal prior distribution on wavelet coefficients variances and estimate them using an approximate maximum a posteriori probability rule. Then we apply an approximate minimum mean squared error estimation procedure to restore the noisy wavelet image coefficients. Despite the simplicity of our method, both in its concept and implementation, our denoising results are among the best reported in the literature.