Removing multiplicative noise using l1 data-fidelity term and nonlocal total variation

2012 ◽  
Author(s):  
Xiao Bing Shang ◽  
Zhi long Zhao ◽  
Lin Yang
Keyword(s):  
Total Variation ◽  
Multiplicative Noise ◽  
L1 Data ◽  
Nonlocal Total Variation ◽  
Data Fidelity ◽  
Fidelity Term

scholarly journals Adaptive Sparse Norm and Nonlocal Total Variation Methods for Image Smoothing

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Qiegen Liu ◽  
Biao Xiong ◽  
Minghui Zhang
Keyword(s):  
Total Variation ◽  
Image Smoothing ◽  
Penalty Term ◽  
Feature Structure ◽  
Nonlocal Total Variation ◽  
Data Fidelity ◽  
Spatially Varying ◽  
Penalty Weight ◽  
Structure Patterns

In computer vision and graphics, it is challenging to decompose various texture/structure patterns from input images. It is well recognized that how edges are defined and how this prior information guides smoothing are two keys in determining the quality of image smoothing. While many different approaches have been reported in the literature, sparse norm and nonlocal schemes are two promising tools. In this study, by integrating a texture measure as the spatially varying data-fidelity/smooth-penalty weight into the sparse norm and nonlocal total variation models, two new methods are presented for feature/structure-preserving filtering. The first one is a generalized relative total variation (i.e., GRTV) method, which improves the contrast-preserving and edge stiffness-enhancing capabilities of the RTV by extending the range of the penalty function’s norm from 1 to [0, 1]. The other one is a nonlocal version of generalized RTV (i.e., NLGRTV) for which the key idea is to use a modified texture-measure as spatially varying penalty weight and to replace the local candidate pixels with the nonlocal set in the smooth-penalty term. It is shown that NLGRTV substantially improves the performance of decomposition for regions with faint pixel-boundary.

scholarly journals Exact solutions for the total variation denoising problem of piecewise constant images in dimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Riccardo Cristoferi
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Total Variation ◽  
Piecewise Constant ◽  
Geometrical Properties ◽  
Total Variation Denoising ◽  
Fidelity Term ◽  
Dimension One

AbstractA method for obtaining the exact solution for the total variation denoising problem of piecewise constant images in dimension one is presented. The validity of the algorithm relies on some results concerning the behavior of the solution when the parameter λ in front of the fidelity term varies. Albeit some of them are well-known in the community, here they are proved with simple techniques based on qualitative geometrical properties of the solutions.

The nonlocal total variation flow

2010 ◽  
pp. 163-189 ◽  
Author(s):  
Fuensanta Andreu-Vaillo ◽  
José Mazón ◽  
Julio Rossi ◽  
J. Julián Toledo-Melero
Keyword(s):  
Total Variation ◽  
Total Variation Flow ◽  
Nonlocal Total Variation
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