Nonlinear total variation based noise removal algorithms

Rudin, Leonid; Osher, Stanley; Fatemi, Emad

doi:10.1016/0167-2789(92)90242-f

Cited by 13,553 publications

(8,280 citation statements)

References 9 publications

Supporting

Mentioning

8,211

Contrasting

Unclassified

Order By: Relevance

“…latest Laplacian matrix pre-conditioner by Krishnan et al [26], we have noticed that solving equation (20) takes in general only one iteration, and two iterations for very small λ values. This is very fast processing : for two iterations of the proposed method, around 2 × 3 = 6 pre-conditioned conjugate gradient iterations in total are required to perform edge-aware smoothing of a full-color image.…”

Section: Fast Numerical Solutionmentioning

confidence: 99%

“…(a) Input (b) BLF [1] (c) NCF [11] (d) TV [20] (e) Extrema [27] (f) GF [28] (g) WLS [16] (h) L0 [21] (i) Proposed [21]). The proposed method produces high-quality smoothing while being flexible and computationally efficient.…”

Section: Image Smoothingmentioning

confidence: 99%

“…We propose a simple method to extend the proposed fast edge-processing method to large-scale processing and can fully take advantage of parallel processing. The idea consists in transforming the deconvolution operation in equation (20) first to a convolution operation, then estimating the convolution kernel with separable filters. Equation (20) can be written as the following convolution :…”

Section: Fast Numerical Solutionmentioning

confidence: 99%

“…These methods are based on optimization, contrary to local filtering methods such as the bilateral filter. The first method introduced in this category is the Total Variation (TV) method [20]. This approach consists in minimizing an energy regularized by a convex gradient function (l 1 -norm).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fast Edge-Aware Processing via First Order Proximal Approximation

Badri

Yahia

Aboutajdine³

2015

IEEE Trans. Visual. Comput. Graphics

View full text Add to dashboard Cite

Abstract-We present a new framework for fast edge-aware processing of images and videos. The proposed smoothing method is based on an optimization formulation with a non-convex sparse regularization for a better smoothing behavior near strong edges. We develop mathematical tools based on first order approximation of proximal operators to accelerate the proposed method while maintaining high-quality smoothing. The first order approximation is used to estimate a solution of the proximal form in a half-quadratic solver, and also to derive a warm-start solution that can be calculated quickly when the image is loaded by the user. We extend the method to large-scale processing by estimating the smoothing operation with independent 1D convolution operations. This approach linearly scales to the size of the image and can fully take advantage of parallel processing. The method supports full color filtering and turns out to be temporally coherent for fast video processing. We demonstrate the performance of the proposed method on various applications including image smoothing, detail manipulation, HDR tone-mapping, fast edge simplification and video edge-aware processing.

show abstract

Section: Fast Numerical Solutionmentioning

confidence: 99%

Section: Image Smoothingmentioning

confidence: 99%

Section: Fast Numerical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fast Edge-Aware Processing via First Order Proximal Approximation

Badri

Yahia

Aboutajdine³

2015

IEEE Trans. Visual. Comput. Graphics

View full text Add to dashboard Cite

show abstract

“…Interestingly, researchers in image restoration had proposed over the years solutions to Strang's dual problem, that of minimizing the total variation (TV) of a functional. Initial solutions used level-set formulations [60], and later ones convex optimization methods [11,58]. Nonetheless, it is thought that primal maximum flow methods are better suited to segmentation than TV formulations [18].…”

Section: Maximal Continuous Flows and Total Variationmentioning

confidence: 99%

Seeded Segmentation Methods for Medical Image Analysis

Najman

Talbot

2011

Medical Image Processing

View full text Add to dashboard Cite

Chapter 3International audienceSegmentation is one of the key tools in medical image analysis. The objective of segmentation is to provide reliable, fast, and effective organ delineation. While traditionally, particularly in computer vision, segmentation is seen as an early vision tool used for subsequent recognition, in medical imaging the opposite is often true. Recognition can be performed interactively by clinicians or automatically using robust techniques, while the objective of segmentation is to precisely delineate contours and surfaces. This can lead to effective techniques known as "intelligent scissors" in 2D and their equivalent in 3D

show abstract

Wavelet‐Based Image Deconvolution and Reconstruction

Pustelnik

Benazza-Benhayia²,

Zheng

et al. 2016

Wiley Encyclopedia of Electrical and Electronics Engineering

View full text Add to dashboard Cite

Image deconvolution and reconstruction are inverse problems which are encountered in a wide array of applications. Due to the ill-posedness of such problems, their resolution generally relies on the incorporation of prior information through regularizations, which may be formulated in the original data space or through a suitable linear representation. In this article, we show the benefits which can be drawn from frame representations, such as wavelet transforms. We present an overview of recovery methods based on these representations: (i) variational formulations and non-smooth convex optimization strategies, (ii) Bayesian approaches, especially Monte Carlo Markov Chain methods and variational Bayesian approximation techniques, and (iii) Stein-based approaches. A brief introduction to blind deconvolution is also provided.

show abstract

Nonlinear total variation based noise removal algorithms

Cited by 13,553 publications

References 9 publications

Fast Edge-Aware Processing via First Order Proximal Approximation

Fast Edge-Aware Processing via First Order Proximal Approximation

Seeded Segmentation Methods for Medical Image Analysis

Wavelet‐Based Image Deconvolution and Reconstruction

Contact Info

Product

Resources

About