Shearlet-Based Total Variation Diffusion for Denoising

Easley, Glenn R.; Labate, Demetrio; Colonna, Flavia

doi:10.1109/tip.2008.2008070

Cited by 197 publications

(97 citation statements)

References 30 publications

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“…The sparsity of shearlet expansions is beneficial for various problems of data restoration and feature extraction. In particular, one class of imaging applications where shearlets have been proven very successful is image denoising problems and several shearlet-based image denoising algorithms were proposed, including those in [22,64], which adapt wavelet thresholding to the shearlet setting, and the method in [21], which combines thresholding with minimization of bounded variation. Extensions to these ideas to video denoising were proposed in [62,67].…”

Section: Shearlets In Applicationsmentioning

confidence: 99%

Introduction to Shearlets

Kutyniok

Labate

2012

Applied and Numerical Harmonic Analysis

116

124

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Shearlets emerged in recent years among the most successful frameworks for the efficient representation of multidimensional data. Indeed, after it was recognized that traditional multiscale methods are not very efficient at capturing edges and other anisotropic features which frequently dominate multidimensional phenomena, several methods were introduced to overcome their limitations. The shearlet representation stands out since it offers a unique combinations of some highly desirable properties: it has a single or finite set of generating functions, it provides optimally sparse representations for a large class of multidimensional data, it is possible to use compactly supported analyzing functions, it has fast algorithmic implementations and it allows a unified treatment of the continuum and digital realms. In this chapter, we present a self-contained overview of the main results concerning the theory and applications of shearlets.

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Section: Shearlets In Applicationsmentioning

confidence: 99%

Introduction to Shearlets

Kutyniok

Labate

2012

Applied and Numerical Harmonic Analysis

116

124

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“…Despite numerous advantages, theoretical justification [19], and numerous provisions of such a method, one can claim that it can not deal with image textures [21]. Following this work many alternative formulation of diffusion process have been formulated using a total variation approach [25] and iterative wavelet shrinkage [26,27]. Fattal et al [28] proposed using bilateral filtering to compute the smooth layer.…”

Section: Edge-aware Smoothing and Random Walksmentioning

confidence: 99%

Stochastic Capsule Endoscopy Image Enhancement

et al. 2018

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Abstract:Capsule endoscopy, which uses a wireless camera to take images of the digestive tract, is emerging as an alternative to traditional colonoscopy. The diagnostic values of these images depend on the quality of revealed underlying tissue surfaces. In this paper, we consider the problem of enhancing the visibility of detail and shadowed tissue surfaces for capsule endoscopy images. Using concentric circles at each pixel for random walks combined with stochastic sampling, the proposed method enhances the details of vessel and tissue surfaces. The framework decomposes the image into two detailed layers that contain shadowed tissue surfaces and detail features. The target pixel value is recalculated for the smooth layer using similarity of the target pixel to neighboring pixels by weighting against the total gradient variation and intensity differences. In order to evaluate the diagnostic image quality of the proposed method, we used clinical subjective evaluation with a rank order on selected KID image database and compared it to state-of-the-art enhancement methods. The result showed that the proposed method provides a better result in terms of diagnostic image quality and objective quality contrast metrics and structural similarity index.

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“…Such signals arise in geoscience, biophysics, and other areas [31]. The TV denoising technique is also used in conjunction with other methods in order to process more general types of signals [20], [23], [24], [26].…”

Section: Introductionmentioning

confidence: 99%

Total Variation Denoising Via the Moreau Envelope

Selesnick

2017

IEEE Signal Process. Lett.

104

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Abstract-Total variation denoising is a nonlinear filtering method well suited for the estimation of piecewise-constant signals observed in additive white Gaussian noise. The method is defined by the minimization of a particular non-differentiable convex cost function. This paper describes a generalization of this cost function that can yield more accurate estimation of piecewise constant signals. The new cost function involves a nonconvex penalty (regularizer) designed to maintain the convexity of the cost function. The new penalty is based on the Moreau envelope. The proposed total variation denoising method can be implemented using forward-backward splitting.

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Shearlet-Based Total Variation Diffusion for Denoising

Cited by 197 publications

References 30 publications

Introduction to Shearlets

Introduction to Shearlets

Stochastic Capsule Endoscopy Image Enhancement

Total Variation Denoising Via the Moreau Envelope

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