Robust Matrix Completion with Deterministic Sampling via Convex Optimization
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912062663294976 |
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| author | Wang, Yinjian |
| author_facet | Wang, Yinjian |
| contents | This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the compressed matrix in our case is sampled in a deterministic pattern instead of those random ones on which existing studies depend. In fact, deterministic sampling is much more hardware-friendly than random ones. The limited resources on many platforms leave deterministic sampling the only choice to sense a matrix, resulting in the significance of investigating robust matrix completion with deterministic pattern. In such spirit, this paper proposes \textit{restricted approximate $\infty$-isometry property} and proves that, if a \textit{low-rank} and \textit{incoherent} square matrix and certain deterministic sampling pattern satisfy such property and two existing conditions called \textit{isomerism} and \textit{relative well-conditionedness}, the exact recovery from its sampled counterpart grossly corrupted by a small fraction of outliers via convex optimization happens with very high probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05412 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust Matrix Completion with Deterministic Sampling via Convex Optimization Wang, Yinjian Information Theory This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the compressed matrix in our case is sampled in a deterministic pattern instead of those random ones on which existing studies depend. In fact, deterministic sampling is much more hardware-friendly than random ones. The limited resources on many platforms leave deterministic sampling the only choice to sense a matrix, resulting in the significance of investigating robust matrix completion with deterministic pattern. In such spirit, this paper proposes \textit{restricted approximate $\infty$-isometry property} and proves that, if a \textit{low-rank} and \textit{incoherent} square matrix and certain deterministic sampling pattern satisfy such property and two existing conditions called \textit{isomerism} and \textit{relative well-conditionedness}, the exact recovery from its sampled counterpart grossly corrupted by a small fraction of outliers via convex optimization happens with very high probability. |
| title | Robust Matrix Completion with Deterministic Sampling via Convex Optimization |
| topic | Information Theory |
| url | https://arxiv.org/abs/2410.05412 |