\(\ell^1\)-analysis minimization and generalized (co-)sparsity: when does recovery succeed?
From MaRDI portal
Publication:2659754
DOI10.1016/j.acha.2020.01.002zbMath1460.94021arXiv1710.04952OpenAlexW2765989888MaRDI QIDQ2659754
Maximilian März, Gitta Kutyniok, Martin Genzel
Publication date: 26 March 2021
Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1710.04952
total variationcompressed sensingstable recoveryanalysis sparsityGaussian mean widthredundant frames\(\ell^1\)-analysis basis pursuitcosparse modeling
Numerical mathematical programming methods (65K05) Convex programming (90C25) Applications of mathematical programming (90C90) Signal theory (characterization, reconstruction, filtering, etc.) (94A12)
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Cites Work
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- Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
- Nonlinear total variation based noise removal algorithms
- Sharp MSE bounds for proximal denoising
- A mathematical introduction to compressive sensing
- Finite frames. Theory and applications.
- Compressed sensing with coherent and redundant dictionaries
- Least squares problems with inequality constraints as quadratic constraints
- Intrinsic localization of frames
- Analysis \(\ell_1\)-recovery with frames and Gaussian measurements
- An algorithm for total variation minimization and applications
- The cosparse analysis model and algorithms
- Localization of frames, Banach frames, and the invertibility of the frame operator
- The convex geometry of linear inverse problems
- Sparse recovery with coherent tight frames via analysis Dantzig selector and analysis LASSO
- Stable recovery of analysis based approaches
- Stability and robustness of \(\ell_1\)-minimizations with Weibull matrices and redundant dictionaries
- Greedy-like algorithms for the cosparse analysis model
- Reconstruction and subgaussian operators in asymptotic geometric analysis
- Structure dependent sampling in compressed sensing: theoretical guarantees for tight frames
- Convex Recovery of a Structured Signal from Independent Random Linear Measurements
- ShearLab 3D
- Stable Image Reconstruction Using Total Variation Minimization
- On the Effective Measure of Dimension in the Analysis Cosparse Model
- Robust Sparse Analysis Regularization
- Robust 1-bit Compressed Sensing and Sparse Logistic Regression: A Convex Programming Approach
- Graph Implementations for Nonsmooth Convex Programs
- CURVELET-WAVELET REGULARIZED SPLIT BREGMAN ITERATION FOR COMPRESSED SENSING
- Sparsity and Nullity: Paradigms for Analysis Dictionary Learning
- Compressive Sensing with Redundant Dictionaries and Structured Measurements
- On sparse reconstruction from Fourier and Gaussian measurements
- Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
- Split Bregman Methods and Frame Based Image Restoration
- Compressed Sensing and Redundant Dictionaries
- A useful theorem for nonlinear devices having Gaussian inputs
- Atomic Decomposition by Basis Pursuit
- Ideal spatial adaptation by wavelet shrinkage
- Analysis K-SVD: A Dictionary-Learning Algorithm for the Analysis Sparse Model
- Learning Sparsifying Transforms
- Smoothing and Decomposition for Analysis Sparse Recovery
- Insights Into Analysis Operator Learning: From Patch-Based Sparse Models to Higher Order MRFs
- Robust analysis ℓ1-recovery from Gaussian measurements and total variation minimization
- Guarantees of total variation minimization for signal recovery
- Physics-Driven Inverse Problems Made Tractable With Cosparse Regularization
- Tradeoffs Between Convergence Speed and Reconstruction Accuracy in Inverse Problems
- High-Dimensional Probability
- Unified Theory for Recovery of Sparse Signals in a General Transform Domain
- Sampling Theorems for Signals From the Union of Finite-Dimensional Linear Subspaces
- Multi-Layer Sparse Coding: The Holistic Way
- Computational and statistical tradeoffs via convex relaxation
- Living on the edge: phase transitions in convex programs with random data
- Compressed Sensing With General Frames via Optimal-Dual-Based $\ell _{1}$-Analysis
- Recovering Compressively Sampled Signals Using Partial Support Information
- A Simple Tool for Bounding the Deviation of Random Matrices on Geometric Sets
- High-Dimensional Estimation of Structured Signals From Non-Linear Observations With General Convex Loss Functions
- Analysis versus synthesis in signal priors
- Wavelet footprints: theory, algorithms, and applications
- Analysis Operator Learning and its Application to Image Reconstruction
- Sharp Time–Data Tradeoffs for Linear Inverse Problems
- Stable signal recovery from incomplete and inaccurate measurements
- Understanding Machine Learning
- An extension of Price's theorem (Corresp.)
- Compressed sensing