Dual Norms and Image Decomposition Models

By Jean-François Aujol, Antonin Chambolle. International Journal of Computer Vision, 2005

386 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/157e84997d4da963e89cf6f41c957f0f4437958b

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In Computational Mechanics

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Citations in the corpus

Structure-Texture Image Decomposition—Modeling, Algorithms, and Parameter Selection (2006, methodology): “(1998), we know that the solution of (45) is given by: û = W ST ( f − v, α), where W ST ( f − v, α) stands for the Wavelet Soft Thresholding of f-v with threshold α (Meyer, 2001; Aujol and Chambolle, 2005).”
Infimal convolution regularizations with discrete ℓ1-type functionals (2011, neutral): “, for image decomposition in [1, 2, 36].”
Edge and line oriented contour detection: State of the art (2011, background): “Other extensions concern vector-valued images [45,46], images defined on graphs [46], deblurring application [47,48], and decomposition of an image into three components (filtered image, texture, and noise) [37].”
An Iterative Regularization Method for Total Variation-Based Image Restoration (2005, background): “See also [3] for an explanation of this phenomenon.”
Signal Recovery by Proximal Forward-Backward Splitting (2005, background): “The variational formulations proposed in [5, 6, 7, 71, 72] to achieve this decomposition based on a noisy observation z ∈ H of the signal of interest are of the general form (4.10) minimize where ψ and φ are in Γ 0 ( H ) and ρ ∈ ]0 , + ∞ [.”
Proximal Splitting Methods in Signal Processing (2009, background): “This framework captures in particular probl em formulations found in [7,8,80,88,133].”
Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction (2010, methodology): “Minimization with respect to u corresponds to solving the ROF model, which is done using a gradient projection method [5, 15, 19], and the minimization for v can be solved using an explicit formula.”
Fast Global Minimization of the Active Contour/Snake Model (2007, background): “, smooth part, and a texture part as in [20, 21].”
Primal-Dual Splitting Algorithm for Solving Inclusions with Mixtures of Composite, Lipschitzian, and Parallel-Sum Type Monotone Operators (2011, background): “…the primal-dual problem (we drop the subscript ‘1’ for brevity) investigated in [9]. which can be rewritten as (1.10) In the special case when h = 0, G = H , L = Id , and ℓ is a quadratic coupling function, such formulations have been investigated in [1, 4, 6, 12, 15]. x 7→ { 0 } , and z = r 1 = 0.”