References & Further Reading
References
- E. J. Candes, J. Romberg, and T. Tao, Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information, 2006
The foundational $\ell_1$ recovery result.
- E. J. Candes, J. Romberg, and T. Tao, Stable Signal Recovery from Incomplete and Inaccurate Measurements, 2006
Stable recovery under noise; proves the $\delta_{2s}<\sqrt{2}-1$ condition.
- E. J. Candes and T. Tao, Decoding by Linear Programming, 2005
Connects CS recovery to error correction.
- E. J. Candes, The Restricted Isometry Property and Its Implications for Compressed Sensing, 2008
Improved RIP constant $\delta_{2s}<\sqrt{2}-1$.
- D. L. Donoho, Compressed Sensing, 2006
Parallel foundational paper to Candes-Romberg-Tao.
- S. S. Chen, D. L. Donoho, and M. A. Saunders, Atomic Decomposition by Basis Pursuit, 1998
Originates the Basis Pursuit formulation.
- R. Tibshirani, Regression Shrinkage and Selection via the Lasso, 1996
Defines the LASSO.
- D. L. Donoho and X. Huo, Uncertainty Principles and Ideal Atomic Decomposition, 2001
Coherence-based guarantees for sparse recovery.
- D. L. Donoho and M. Elad, Optimally Sparse Representation in General (Nonorthogonal) Dictionaries via $\ell_1$ Minimization, 2003
Mutual-coherence recovery guarantee.
- S. Foucart and H. Rauhut, A Mathematical Introduction to Compressive Sensing, Birkhauser, 2013
The definitive graduate text on CS theory.
- B. K. Natarajan, Sparse Approximate Solutions to Linear Systems, 1995
Proves $\ell_0$ minimization is NP-hard.
- L. R. Welch, Lower Bounds on the Maximum Cross Correlation of Signals, 1974
The Welch bound on coherence.
- R. G. Baraniuk, M. Davenport, R. A. DeVore, and M. B. Wakin, A Simple Proof of the Restricted Isometry Property for Random Matrices, 2008
Gaussian/Bernoulli sensing matrices satisfy RIP with $M=O(s\log(N/s))$.
- D. L. Donoho, For Most Large Underdetermined Systems of Linear Equations the Minimal $\ell_1$-Norm Solution Is Also the Sparsest Solution, 2006
Geometric/probabilistic justification of $\ell_1$ recovery.
- E. J. Candes and T. Tao, The Dantzig Selector: Statistical Estimation When $p$ Is Much Larger Than $n$, 2007
Linear-programming alternative to LASSO with sharp risk bounds.
- M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing, Springer, 2010
Book-length treatment of sparse modeling.
- P. J. Bickel, Y. Ritov, and A. B. Tsybakov, Simultaneous Analysis of Lasso and Dantzig Selector, 2009
Oracle inequalities for LASSO.
- G. Caire, CommIT group, Sparse Recovery with Reconfigurable Intelligent Surfaces in the Near Field, 2024