Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms. Application to the Processing of Outliers

By Mila Nikolova. SIAM Journal on Numerical Analysis, 2002

357 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/874a0e66ac0fe2207fe79d93b5e479d66b109753

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In Computational Mechanics

In Mathematical Physics

In Numerical Analysis

Citations in the corpus

Regularizing Flows for Constrained Matrix-Valued Images (2004, unknown): “If ψ is smooth at zero, the set h is empty for almost all y ∈ I R [24].”
Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations (2009, unknown): “Although this edge-preserving nonlinear function may take various forms [26]: φ(t) = |t|/α, 1 ≤ α ≤ 2, (31) φ(t) = √ α + t2, (32) φ(t) = 1+ |t|/α − log(1+ |t|/α), α > 0, (33) we restrict ourself to simple cases, where φ(t) = |t|/α for α = 1 or 2, andL is the derivative operator of the first or secon”
Split Bregman Methods and Frame Based Image Restoration (2009, background): “For example, the l1 norm term yields a solution with large strongly homogeneous zones, as shown in [55, 56].”
Aspects of Total Variation Regularized L[sup 1] Function Approximation (2005, methodology): “However, unlike the focus of this paper, results in [11, 12] mostly concern discrete versions of the denoising energies and depend on the discretization size; continuum analogues are not treated.”
Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models (2006, background): “It was previously introduced and studied in signal and image processing applications in [1, 2, 3, 17, 18, 6].”
Fast Global Minimization of the Active Contour/Snake Model (2007, background): “Hence, the energy functional (1) is actually a new length obtained by weighting the Euclidean element of length ds by the function g which contains information concerning the boundaries of objects [5].”
Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization (2005, result): “where Vi;j is the set of the four closest neighbors of (i;j), not including (i;j). It was shown in [ 18 ] and”
A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration (2009, background): “[1, 9, 26]) instead of the square of the 2-norm as in (1.”
A Combined First and Second Order Variational Approach for Image Reconstruction (2012, unknown): “Other examples for f are regularised versions of the total variation like f(x) = √ x2 + 2 for a positive 1 [1,41], the Huber-regulariser and alike [28,47,22,54].”