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- W3157639225 abstract "This paper considers theoretical analysis of recovering a low rank matrix given a few expansion coefficients with respect to any basis. The current approach generalizes the existing analysis for the low-rank matrix completion problem with sampling under entry sensing or with respect to a symmetric orthonormal basis. The analysis is based on dual certificates using a dual basis approach. We introduce a condition on the basis called the correlation condition. This condition can be computed in time O ( n 3 ) and holds for many cases of deterministic basis. If the correlation condition holds and the underlying low rank matrix obeys the coherence condition with parameter ν , under additional mild assumptions, our main result shows that the true matrix can be recovered with very high probability from O ( n r ν log 2 n ) uniformly random expansion coefficients." @default.
- W3157639225 created "2021-05-10" @default.
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- W3157639225 date "2021-09-01" @default.
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- W3157639225 title "Low-rank matrix completion in a general non-orthogonal basis" @default.
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- W3157639225 doi "https://doi.org/10.1016/j.laa.2021.05.001" @default.
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