A theory of optimal convex regularization for low-dimensional recovery

Convex programming (90C25) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Decoding (94B35)

Cites Work

A mathematical introduction to compressive sensing
Simple bounds for recovering low-complexity models
Sparsest solutions of underdetermined linear systems via $ \ell _q$-minimization for $0<q\leqslant 1$
Towards minimal assumptions for the infimal convolution regularization
Convexification procedures and decomposition methods for nonconvex optimization problems
Stable recovery of low-dimensional cones in Hilbert spaces: one RIP to rule them all
The convex geometry of linear inverse problems
A first-order primal-dual algorithm for convex problems with applications to imaging
Stable restoration and separation of approximately sparse signals
Robust multi-image processing with optimal sparse regularization
Compressed sensing of low-rank plus sparse matrices
Estimation in High Dimensions: A Geometric Perspective
Fundamental Performance Limits for Ideal Decoders in High-Dimensional Linear Inverse Problems
Global Solutions of Variational Models with Convex Regularization
A Continuous Exact $\ell_0$ Penalty (CEL0) for Least Squares Regularized Problem
The Convex Envelope of (n–1)-Convex Functions
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
Atomic Decomposition by Basis Pursuit
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Model selection with low complexity priors
Nuclear norm of higher-order tensors
Restricted Isometry Constants Where $\ell ^{p}$ Sparse Recovery Can Fail for $0≪ p \leq 1$
The basins of attraction of the global minimizers of the non-convex sparse spike estimation problem
Effective Condition Number Bounds for Convex Regularization
Living on the edge: phase transitions in convex programs with random data
Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
Recipes for Stable Linear Embeddings From Hilbert Spaces to $ {\mathbb {R}}^{m}$
Learning with Submodular Functions: A Convex Optimization Perspective
Model Selection and Estimation in Regression with Grouped Variables
For most large underdetermined systems of linear equations the minimal 𝓁₁‐norm solution is also the sparsest solution
Convex Analysis
The basins of attraction of the global minimizers of non-convex inverse problems with low-dimensional models in infinite dimension
A unified framework for high-dimensional analysis of $M$-estimators with decomposable regularizers
Sampling rates for $\ell^1$-synthesis

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