Fast dual minimization of the vectorial total variation norm and applications to color image processing

By Xavier Bresson, Tony F. Chan. 2008

424 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/90dcb872fcf15505322a6a466c0881e856a78b9a

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In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

An introduction to continuous optimization for imaging (2016, background): “If p = 2, the resulting norm is equivalent to the Frobenius norm, which corresponds to one of the most classical choices (Bresson and Chan 2008), though other choices might also be interesting (Sapiro and Ringach 1996, Chambolle 1994).”
Hyperspectral Pansharpening: A Review (2015, methodology): “The VTV regularizer (see [68]) is given by φ ( U ) = n∑ j=1 √√√√ m̃λ∑ k=1 {[ (UDh)kj ]2 + [ (UDv)kj ]2} , (14) where Akj denotes the element in the kth row and jth column of matrix A, and the products by matrices Dh and Dv compute the horizontal and vertical discrete differences of an image, respect”
Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models (2010, methodology): “The CGM dual method for color image restoration is still missing in the literature, as pointed out in [ 4 ] that \the question of extension is open for the CGM’s model".”
A Convex Formulation for Hyperspectral Image Superresolution via Subspace-Based Regularization (2014, background): “Let the matrix representing the observed hyperspectral data be Y h ∈ R L h × n h , with L h bands and spatial dimension n h , and let Y m ∈ R L m × n m denote the observed multispectral data, with L m < L h bands and spatial dimension n m > n h .”
Hyperspectral Image Denoising Employing a Spectral–Spatial Adaptive Total Variation Model (2012, methodology): “To make the denoising process spectrally adaptive, we extend the CTV model proposed in [27] to de-ﬁne the hyperspectral TV model, which has the following formation: where MN is the total number of pixels in one hyperspectral band and B is the total number of bands.”