Probability Theory

On the robustness of noise-blind low-rank recovery from rank-one measurements
We prove new results about the robustness of well-known convex noise-blind optimization formulations for the reconstruction of low-rank …
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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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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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