An Introduction to Compressed Sensing

DOI10.1007/978-3-319-73074-5_1zbMath1453.94028OpenAlexW2968692945MaRDI QIDQ3296174

Arash Behboodi, Niklas Koep, Rudolf Mathar

Publication date: 7 July 2020

Published in: Applied and Numerical Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-73074-5_1

zbMATH Keywords

signal recoverycompressed sensing, sparsityconic integral geometry

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Uses Software

• CVX
• NESTA
• SPGL1
• L1-MAGIC
• CVXPY

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• A mathematical introduction to compressive sensing
• Oracle inequalities in empirical risk minimization and sparse recovery problems. École d'Été de Probabilités de Saint-Flour XXXVIII-2008.
• The Gelfand widths of \(\ell_p\)-balls for \(0 < p \leq 1\)
• Restricted isometry property of matrices with independent columns and neighborly polytopes by random sampling
• Geometry of log-concave ensembles of random matrices and approximate reconstruction
• Shearlets. Multiscale analysis for multivariate data.
• Discrete uncertainty principles and sparse signal processing
• Uniform recovery of fusion frame structured sparse signals
• Near-ideal model selection by \(\ell _{1}\) minimization
• The restricted isometry property and its implications for compressed sensing
• A simple proof of the restricted isometry property for random matrices
• Gabor analysis and algorithms. Theory and applications
• Introductory lectures on convex optimization. A basic course.
• The convex geometry of linear inverse problems
• The Lasso problem and uniqueness
• Necessary and sufficient conditions of solution uniqueness in 1-norm minimization
• The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).
• Estimation in High Dimensions: A Geometric Perspective
• CVXPY: A Python-Embedded Modeling Language for Convex Optimization
• Suprema of Chaos Processes and the Restricted Isometry Property
• From Denoising to Compressed Sensing
• The Generalized Lasso With Non-Linear Observations
• Accurate Prediction of Phase Transitions in Compressed Sensing via a Connection to Minimax Denoising
• Robust 1-bit Compressed Sensing and Sparse Logistic Regression: A Convex Programming Approach
• Theta Bodies for Polynomial Ideals
• NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
• Compressed sensing and best 𝑘-term approximation
• Extensions of Lipschitz mappings into a Hilbert space
• Quantization and Compressive Sensing
• On sparse reconstruction from Fourier and Gaussian measurements
• Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
• Decoding by Linear Programming
• Stable recovery of sparse overcomplete representations in the presence of noise
• Greed is Good: Algorithmic Results for Sparse Approximation
• Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
• Probing the Pareto Frontier for Basis Pursuit Solutions
• Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing
• Sparse and Redundant Representations
• Compressed Sensing and Redundant Dictionaries
• Lower bounds on the maximum cross correlation of signals (Corresp.)
• New tight frames of curvelets and optimal representations of objects with piecewise C² singularities
• Sparse Reconstruction by Separable Approximation
• Blind Multiband Signal Reconstruction: Compressed Sensing for Analog Signals
• Atomic Norm Denoising With Applications to Line Spectral Estimation
• Flavors of Compressive Sensing
• Sparsity and Smoothness Via the Fused Lasso
• On the Gap Between Restricted Isometry Properties and Sparse Recovery Conditions
• An elementary proof of a theorem of Johnson and Lindenstrauss
• Sparse Approximate Solutions to Linear Systems
• Compressive Sensing
• Introduction to Finite Frame Theory
• Subspace Pursuit for Compressive Sensing Signal Reconstruction
• Living on the edge: phase transitions in convex programs with random data
• Vector Approximate Message Passing
• An Improved Estimate in the Restricted Isometry Problem
• Introduction to Compressed Sensing and Sparse Filtering
• Sparse Recovery From Combined Fusion Frame Measurements
• The Restricted Isometry Property of Subsampled Fourier Matrices
• A Simple Tool for Bounding the Deviation of Random Matrices on Geometric Sets
• Corrupted Sensing: Novel Guarantees for Separating Structured Signals
• The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing
• Compressed Sensing Off the Grid
• New constructions of RIP matrices with fast multiplication and fewer rows
• Restricted Isometry of Fourier Matrices and List Decodability of Random Linear Codes
• Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ ¹ minimization
• Learning Theory
• Stable signal recovery from incomplete and inaccurate measurements
• Compressed sensing
• Noiselets

This page was built for publication: An Introduction to Compressed Sensing