Interscale Dependencies Of Wavelet Coefficients Research Articles

Mechanical Vibration Signal Denoising Using Quantum‐Inspired Standard Deviation Based on Subband Based Gaussian Mixture Model

Aiming at improving noise reduction effect for mechanical vibration signal, a Gaussian mixture model (SGMM) and a quantum‐inspired standard deviation (QSD) are proposed and applied to the denoising method using the thresholding function in wavelet domain. Firstly, the SGMM is presented and utilized as a local distribution to approximate the wavelet coefficients distribution in each subband. Then, within Bayesian framework, the maximum a posteriori (MAP) estimator is employed to derive a thresholding function with conventional standard deviation (CSD) which is calculated by the expectation‐maximization (EM) algorithm. However, the CSD has a disadvantage of ignoring the interscale dependency between wavelet coefficients. Considering this limit for the CSD, the quantum theory is adopted to analyze the interscale dependency between coefficients in adjacent subbands, and the QSD for noise‐free wavelet coefficients is presented based on quantum mechanics. Next, the QSD is constituted for the CSD in the thresholding function to shrink noisy coefficients. Finally, an application in the mechanical vibration signal processing is used to illustrate the denoising technique. The experimental study shows the SGMM can model the distribution of wavelet coefficients accurately and QSD can depict interscale dependency of wavelet coefficients of true signal quite successfully. Therefore, the denoising method utilizing the SGMM and QSD performs better than others.

Automated mitosis detection in histopathology based on non-gaussian modeling of complex wavelet coefficients

To diagnose breast cancer, the number of mitotic cells present in histology sections is an important indicator for examining and grading biopsy specimen. This study aims at improving the accuracy of automated mitosis detection by characterizing mitotic cells in wavelet based multi-resolution representations via a non-Gaussian modeling method. The potential mitosis candidates were decomposed into multi-scale forms by an undecimated dual-tree complex wavelet transform. Two non-Gaussian models (the generalized Gaussian distribution (GGD) and the symmetric alpha-stable (SαS) distributions) were used to accurately model the heavy-tailed behavior of wavelet marginal distributions. The method was evaluated on two independent data cohorts, including the benchmark dataset (MITOS), via a support vector machine classifier. The quantitative results shows that the bivariate SαS model achieved superior classification performance with the area under the curve value of 0.82 in comparison with 0.79 for bivariate GGD, 0.77 for univariate SαS, 0.72 for univariate GGD, and 0.59 for Gaussian model. Since both mitotic and non-mitotic cells appear as small objects with a large variety of shapes, characterization of mitosis is a hard problem. The inter-scale dependencies of wavelet coefficients allowing extraction of salient features within the cells that are more likely to appear at all different scales were captured by the bivariate non-Gaussian models, leading to more accurate detection results. The presented automated mitosis detection method might assist pathologists in enhancing the operational efficiency and productivity as well as improving diagnostic confidence.

Adaptive redundant multiwavelet denoising with improved neighboring coefficients for gearbox fault detection

Gearbox fault detection under strong background noise is a challenging task. It is feasible to make the fault feature distinct through multiwavelet denoising. In addition to the advantage of multi-resolution analysis, multiwavelet with several scaling functions and wavelet functions can detect the different fault features effectively. However, the fixed basis functions not related to the given signal may lower the accuracy of fault detection. Moreover, the multiwavelet transform may result in Gibbs phenomena in the step of reconstruction. Furthermore, both traditional term-by-term threshold and neighboring coefficients do not consider the direct spatial dependency of wavelet coefficients at adjacent scale. To overcome these deficiencies, adaptive redundant multiwavelet (ARM) denoising with improved neighboring coefficients (NeighCoeff) is proposed. Based on symmetric multiwavelet lifting scheme (SMLS), taking kurtosis—partial envelope spectrum entropy as the evaluation objective and genetic algorithms as the optimization method, ARM is proposed. Considering the intra-scale and inter-scale dependency of wavelet coefficients, the improved NeighCoeff method is developed and incorporated into ARM. The proposed method is applied to both the simulated signal and the practical gearbox vibration signal under different conditions. The results show its effectiveness and reliance for gearbox fault detection.

Segmentation of noisy colour images using Cauchy distribution in the complex wavelet domain

This study proposes a novel image segmentation technique for noisy colour images, in which the heavy-tailed characteristics of the image are modelled by Cauchy distributions. First, the RGB colour bands of the noisy image are decomposed into multiresolution representations using the dual-tree complex wavelet transform. For each wavelet subband, a model is built assuming that the input coefficients are contaminated with signal-independent additive white Gaussian noise. Hence, the authors derive an estimation rule in the wavelet domain to obtain the noise-free coefficients based on the bivariate Cauchy distribution. The bivariate model makes it possible to exploit the inter-scale dependencies of wavelet coefficients. Subsequently, the image is roughly segmented into textured and non-textured regions using the bivariate model parameters corresponding to the denoised coefficients. A multiscale segmentation is then applied to the resulting regions. Finally, a novel statistical region merging algorithm is introduced by measuring the Kullback-Leibler distance between the estimated Cauchy models for the neighbouring segments. The experiments demonstrate that the authors algorithm yields robust segmentation results for noisy images containing artificial or natural noise.

ECG denoising on bivariate shrinkage function exploiting interscale dependency of wavelet coefficients

This paper presents a new method for electrocardiogram (ECG) denoising based on bivariate shrinkage functions exploiting the interscale dependency of wavelet coefficients. Most nonlinear thresholding methods based on wavelet transform denoising assume that the wavelet coefficients are independent. However, wavelet coefficients of ECG signals have significant dependencies. In this paper, we proposed a new method by considering the dependencies between the coefficients and their parents in detail on a bivariate shrinkage function for denoising of an ECG signal corrupted by different types of noises, such as muscle artifact noise, electrode motion, and white noise. In real-time applications, reduction of computational time is very crucial, so we constructed the wavelet transform by lifting scheme. The lifting scheme is a new technique to construct wavelet transform; namely, second generation wavelet transform is an alternative and faster algorithm for a classical wavelet transform. The overall denoising performance of our proposed method was considered in relation to several measuring parameters, including types of wavelet filters (Daubechies 4 (DB4), Daubechies 6 (DB6), and Daubechies 8 (DB8)) and decomposition depth. Global performance was evaluated by means of the signal-to-noise ratio (SNR) and visual inspection. We used a set of MIT-BIH arrhythmia database ECG records. To evaluate our method, a comparative study was carried out that referred to effective data-driven techniques in the literature, namely VisuShrink, SureShrink, BayesShrink, and level-dependent threshold estimation. The experimental results indicated that the proposed methods in the paper were better than the compared methods in terms of retaining the geometrical characteristics of the ECG signal, SNR. Due to its simplicity and its fast implementation, the method can easily be used in clinical medicine.

A New Interscale and Intrascale Orthonormal Wavelet Thresholding for SURE-Based Image Denoising

The interscale Stein's unbiased risk estimator (SURE)-based approach introduced by Luisier is a recent state of the art in orthonormal wavelet denoising, but it is not very effective for those images that have substantial high-frequency contents. To solve this problem, we introduce an effective integration of the intrascale correlations within the interscale SURE-based approach. We show that the consideration of both the intrascale and interscale dependencies of wavelet coefficients brings more denoising gains than those obtained with the interscale SURE-based approach, especially for denoising of images that have substantial textures such as the Barbara image.

Customized wavelet denoising using intra- and inter-scale dependency for bearing fault detection

Bearing fault detection is a challenging task, especially at the incipient stage. Wavelet denoising is widely recognized as an effective tool for signal processing and feature extraction. The wavelet denoising method by incorporating neighboring coefficients (NeighCoeff), which is proposed by Cai and Silverman, gives the better results than the traditional term-by-term approaches. However, this method only exploits intra-scale dependency of wavelet coefficients. It does not consider the inter-scale dependency of wavelet coefficients. In this paper, customized wavelet denoising using intra- and inter-scale dependency of wavelet coefficients is proposed for bearing fault detection. By designing the prediction operator and update operator, a customized wavelet based on the lifting scheme is constructed directly to match the transient properties of a given signal. The NeighCoeff denoising algorithm is improved by taking into account the intra- and inter-scale dependency of wavelet coefficients. The results of the application to bearing fault detection show that the proposed method is very effective.

Image denoising using bivariate α-stable distributions in the complex wavelet domain

Recently, the dual-tree complex wavelet transform has been proposed as an analysis tool featuring near shift-invariance and improved directional selectivity compared to the standard wavelet transform. Within this framework, we describe a novel technique for removing noise from digital images. We design a bivariate maximum a posteriori estimator, which relies on the family of isotropic α-stable distributions. Using this relatively new statistical model we are able to better capture the heavy-tailed nature of the data as well as the interscale dependencies of wavelet coefficients. We test our algorithm for the Cauchy case, in comparison with several recently published methods. The simulation results show that our proposed technique achieves state-of-the-art performance in terms of root mean squared (RMS) error.