Sparse Recovery

Sparse Recovery for Overcomplete Frames: Sensing Matrices and Recovery Guarantees
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame …
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On the geometry of polytopes generated by heavy-tailed random vectors
We study the geometry of centrally-symmetric random polytopes, generated by $N$ independent copies of a random vector $X$ taking values …
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Dictionary-Sparse Recovery From Heavy-Tailed Measurements
The recovery of signals that are sparse not in a given basis, but rather sparse with respect to an over-complete dictionary is one of …
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Iteratively Reweighted Least Squares for Basis Pursuit with Global Linear Convergence Rate
The recovery of sparse data is at the core of many applications in machine learning and signal processing. While such problems can be …
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Understanding and Enhancing Data Recovery Algorithms - From Noise-Blind Sparse Recovery to Reweighted Methods for Low-Rank Matrix Optimization
We prove new results about the robustness of noise-blind decoders for the problem of re- constructing a sparse vector from …
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A Quotient Property for Matrices with Heavy-Tailed Entries and its Application to Noise-Blind Compressed Sensing
For a large class of random matrices $A$ with i.i.d. entries we show that the $\ell_1$-quotient property holds with probability …
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