The $L^1$-Potts Functional for Robust Jump-Sparse Reconstruction

DOI10.1137/120896256zbMath1312.65097arXiv1207.4642OpenAlexW3105073607MaRDI QIDQ5253560

Martin Storath, Laurent Demaret, Andreas Weinmann

Publication date: 27 May 2015

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.4642

zbMATH Keywords

adaptive estimationPotts functionalnonconvex functionaljump-sparse reconstructionpenalized absolute deviation

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Numerical mathematical programming methods (65K05) Numerical optimization and variational techniques (65K10) Nonsmooth analysis (49J52) Dynamic programming (90C39) Complexity and performance of numerical algorithms (65Y20)

Related Items (9)

Constrained energy variation for change point detection ⋮ Nonsmoothness in machine learning: specific structure, proximal identification, and applications ⋮ Mumford-Shah and Potts regularization for manifold-valued data ⋮ Model-based reconstruction for magnetic particle imaging in 2D and 3D ⋮ Recursive reconstruction of piecewise constant signals by minimization of an energy function ⋮ Jump-penalized least absolute values estimation of scalar or circle-valued signals ⋮ Non-smooth Variational Regularization for Processing Manifold-Valued Data ⋮ Exact Algorithms for $L^1$-TV Regularization of Real-Valued or Circle-Valued Signals ⋮ Smoothing for signals with discontinuities using higher order Mumford-Shah models

Cites Work

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• Consistencies and rates of convergence of jump-penalized least squares estimators
• Don't shed tears over breaks
• Wedgelets: Nearly minimax estimation of edges
• A first-order primal-dual algorithm for convex problems with applications to imaging
• Jump estimation in inverse regression
• A Duality-Based Splitting Method for $\ell^1$-$TV$ Image Restoration with Automatic Regularization Parameter Choice
• Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
• Sparse and Redundant Representations
• An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise
• Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
• Reconstruction of a Piecewise Constant Function from Noisy Fourier Coefficients by Padé Method
• Jump-Sparse and Sparse Recovery Using Potts Functionals
• Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms. Application to the Processing of Outliers
• Image Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximations
• Beitrag zur Theorie des Ferromagnetismus
• Scale space consistency of piecewise constant least squares estimators – another look at the regressogram
• Complexity penalized least squares estimators: Analytical results
• Efficient Moment Computation over Polygonal Domains with an Application to Rapid Wedgelet Approximation

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