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- W4310303162 abstract "Tremendous efforts have been made to study the theoretical and algorithmic aspects of sparse recovery and low-rank matrix recovery. This paper fills a theoretical gap in matrix recovery: the optimal sample complexity for stable recovery without constants or log factors. We treat sparsity, low-rankness, and potentially other parsimonious structures within the same framework: constraint sets that have small covering numbers or Minkowski dimensions. We consider three types of random measurement matrices (unstructured, rank-1, and symmetric rank-1 matrices), following probability distributions that satisfy some mild conditions. In all these cases, we prove a fundamental result -- the recovery of matrices with parsimonious structures, using an optimal (or near optimal) number of measurements, is stable with high probability." @default.
- W4310303162 created "2022-12-03" @default.
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- W4310303162 date "2017-12-05" @default.
- W4310303162 modified "2023-10-16" @default.
- W4310303162 title "Optimal Sample Complexity for Stable Matrix Recovery" @default.
- W4310303162 doi "https://doi.org/10.48550/arxiv.1712.01915" @default.
- W4310303162 hasPublicationYear "2017" @default.
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