Correspondence between Multiwavelet Shrinkage/Multiple Wavelet Frame Shrinkage and Nonlinear Diffusion

There are numerous methodologies for signal and image denoising. Wavelet, wavelet frame shrinkage, and nonlinear diffusion are effective ways for signal and image denoising. Also, multiwavelet transforms and multiple wavelet frame transforms have been used for signal and image denoising. Multiwavelets have important property that they can possess the orthogonality, short support, good performance at the boundaries, and symmetry simultaneously. The advantage of multiwavelet transform for signal and image denoising was illustrated by Bui et al. in 1998. They showed that the evaluation of thresholding on a multiwavelet basis has produced good results. Further, Strela et al. have showed that the decimated multiwavelet denoising provides superior results than decimated conventional (scalar) wavelet denoising. Mrazek, Weickert, and Steidl in 2003 examined the association between one-dimensional nonlinear diffusion and undecimated Haar wavelet shrinkage. They proved that nonlinear diffusion could be presented by using wavelet shrinkage. High-order nonlinear diffusion in terms of one-dimensional frame shrinkage and two-dimensional frame shrinkage were presented in 2012 by Jiang, and in 2013 by Dong, Jiang, and Shen, respectively. They obtained that the correspondence between both approaches leads to a different form of diffusion equation that mixes benefits from both approaches. The objective of this dissertation is to study the correspondence between one-dimensional multiwavelet shrinkage and high-order nonlinear diffusion, and to study high-order nonlinear diffusion in terms of one-dimensional multiple frame shrinkage also well. Further, this dissertation formulates nonlinear diffusion in terms of 2D multiwavelet shrinkage and 2D multiple wavelet frame shrinkage. From the experiment results, it can be inferred that nonlinear diffusion in terms of multiwavelet shrinkage/multiple frame shrinkage gives better results than a scalar case. On the whole, this dissertation expands nonlinear diffusion in terms of wavelet shrinkage and nonlinear diffusion in terms of frame shrinkage from the scalar wavelets and frames to the multiwavelets and multiple frames

Parameter optimization for local polynomial approximation based intersection confidence interval filter using genetic algorithm: an application for brain MRI image de-noising

Magnetic resonance imaging (MRI) is extensively exploited for more accuratepathological changes as well as diagnosis. Conversely, MRI suffers from variousshortcomings such as ambient noise from the environment, acquisition noise from theequipment, the presence of background tissue, breathing motion, body fat, etc.Consequently, noise reduction is critical as diverse types of the generated noise limit the efficiency of the medical image diagnosis. Local polynomial approximation basedintersection confidence interval (LPA-ICI) filter is one of the effective de-noising filters.This filter requires an adjustment of the ICI parameters for efficient window size selection.From the wide range of ICI parametric values, finding out the best set of tunes values is itselfan optimization problem. The present study proposed a novel technique for parameteroptimization of LPA-ICI filter using genetic algorithm (GA) for brain MR imagesde-noising. The experimental results proved that the proposed method outperforms theLPA-ICI method for de-noising in terms of various performance metrics for different noisevariance levels. Obtained results reports that the ICI parameter values depend on the noisevariance and the concerned under test image

Reconfigurable Wavelet Thresholding for Image Denoising while Keeping Edge Detection

Summary This paper proposes an reconfigurable adaptive threshold estimation method for image denoising in the wavelet domain based on the generalized Guassian distribution (GGD) modeling of sub-band coefficients. The proposed method called RegularShrink is computationally more efficient and adaptive because the parameters required for estimating the threshold depend on sub-band data Edge information is the most important high frequency information of an image, so we should try to maintain more edge information while denoising. In order to preserve image details as well as canceling image noise, we present a new image denoising method: image denoising based on edge detection. Before denoising, image's edges are first detected, and then the noised image is divided into two parts: edge part and smooth part. We can therefore set high denoising threshold to smooth part of the image and low Denoising threshold to edge part. The theoretical analyzes and experimental results presented in this paper show that, compared to commonly used wavelet threshold denoising methods, the proposed algorithm could not only keep edge information of an image, but also could improve signal-to-noise ratio of the denoised image

Wavelet Shrinkage Based Image Denoising using Soft Computing

Noise reduction is an open problem and has received considerable attention in the literature for several decades. Over the last two decades, wavelet based methods have been applied to the problem of noise reduction and have been shown to outperform the traditional Wiener filter, Median filter, and modified Lee filter in terms of root mean squared error (MSE), peak signal noise ratio (PSNR) and other evaluation methods. In this research, two approaches for the development of high performance algorithms for de-noising are proposed, both based on soft computing tools, such as fuzzy logic, neural networks, and genetic algorithms. First, an improved additive noise reduction method for digital grey scale nature images, which uses an interval type-2 fuzzy logic system to shrink wavelet coefficients, is proposed. This method is an extension of a recently published approach for additive noise reduction using a type-1 fuzzy logic system based wavelet shrinkage. Unlike the type-1 fuzzy logic system based wavelet shrinkage method, the proposed approach employs a thresholding filter to adjust the wavelet coefficients according to the linguistic uncertainty in neighborhood values, inter-scale dependencies and intra-scale correlations of wavelet coefficients at different resolutions by exploiting the interval type-2 fuzzy set theory. Experimental results show that the proposed approach can efficiently and rapidly remove additive noise from digital grey scale images. Objective analysis and visual observations show that the proposed approach outperforms current fuzzy non-wavelet methods and fuzzy wavelet based methods, and is comparable with some recent but more complex wavelet methods, such as Hidden Markov Model based additive noise de-noising method. The main differences between the proposed approach and other wavelet shrinkage based approaches and the main improvements of the proposed approach are also illustrated in this thesis. Second, another improved method of additive noise reduction is also proposed. The method is based on fusing the results of different filters using a Fuzzy Neural Network (FNN). The proposed method combines the advantages of these filters and has outstanding ability of smoothing out additive noise while preserving details of an image (e.g. edges and lines) effectively. A Genetic Algorithm (GA) is applied to choose the optimal parameters of the FNN. The experimental results show that the proposed method is powerful for removing noise from natural images, and the MSE of this approach is less, and the PSNR of is higher, than that of any individual filters which are used for fusion. Finally, the two proposed approaches are compared with each other from different point of views, such as objective analysis in terms of mean squared error(MSE), peak signal to noise ratio (PSNR), image quality index (IQI) based on quality assessment of distorted images, and Information Theoretic Criterion (ITC) based on a human vision model, computational cost, universality, and human observation. The results show that the proposed FNN based algorithm optimized by GA has the best performance among all testing approaches. Important considerations for these proposed approaches and future work are discussed

PHM survey: implementation of signal processing methods for monitoring bearings and gearboxes

The reliability and safety of industrial equipments are one of the main objectives of companies to remain competitive in sectors that are more and more exigent in terms of cost and security. Thus, an unexpected shutdown can lead to physical injury as well as economic consequences. This paper aims to show the emergence of the Prognostics and Health Management (PHM) concept in the industry and to describe how it comes to complement the different maintenance strategies. It describes the benefits to be expected by the implementation of signal processing, diagnostic and prognostic methods in health-monitoring. More specifically, this paper provides a state of the art of existing signal processing techniques that can be used in the PHM strategy. This paper allows showing the diversity of possible techniques and choosing among them the one that will define a framework for industrials to monitor sensitive components like bearings and gearboxes

Mathematical Approaches for Image Enhancement Problems

This thesis develops novel techniques that can solve some image enhancement problems using theoretically and technically proven and very useful mathematical tools to image processing such as wavelet transforms, partial differential equations, and variational models. Three subtopics are mainly covered. First, color image denoising framework is introduced to achieve high quality denoising results by considering correlations between color components while existing denoising approaches can be plugged in flexibly. Second, a new and efficient framework for image contrast and color enhancement in the compressed wavelet domain is proposed. The proposed approach is capable of enhancing both global and local contrast and brightness as well as preserving color consistency. The framework does not require inverse transform for image enhancement since linear scale factors are directly applied to both scaling and wavelet coefficients in the compressed domain, which results in high computational efficiency. Also contaminated noise in the image can be efficiently reduced by introducing wavelet shrinkage terms adaptively in different scales. The proposed method is able to enhance a wavelet-coded image computationally efficiently with high image quality and less noise or other artifact. The experimental results show that the proposed method produces encouraging results both visually and numerically compared to some existing approaches. Finally, image inpainting problem is discussed. Literature review, psychological analysis, and challenges on image inpainting problem and related topics are described. An inpainting algorithm using energy minimization and texture mapping is proposed. Mumford-Shah energy minimization model detects and preserves edges in the inpainting domain by detecting both the main structure and the detailed edges. This approach utilizes faster hierarchical level set method and guarantees convergence independent of initial conditions. The estimated segmentation results in the inpainting domain are stored in segmentation map, which is referred by a texture mapping algorithm for filling textured regions. We also propose an inpainting algorithm using wavelet transform that can expect better global structure estimation of the unknown region in addition to shape and texture properties since wavelet transforms have been used for various image analysis problems due to its nice multi-resolution properties and decoupling characteristics

30th International Conference on Condition Monitoring and Diagnostic Engineering Management (COMADEM 2017)

Proceedings of COMADEM 201

Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters

Some spatial-domain and transform-domain digital image filtering algorithms have been developed in this thesis to suppress additive white Gaussian noise (AWGN). In many occasions, noise in digital images is found to be additive in nature with uniform power in the whole bandwidth and with Gaussian probability distribution. Such a noise is referred to as Additive White Gaussian Noise (AWGN). It is difficult to suppress AWGN since it corrupts almost all pixels in an image. The arithmetic mean filter, commonly known as Mean filter, can be employed to suppress AWGN but it introduces a blurring effect. Image denoising is usually required to be performed before display or further processing like segmentation, feature extraction, object recognition, texture analysis, etc. The purpose of denoising is to suppress the noise quite efficiently while retaining the edges and other detailed features as much as possible