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Compressed Sensing of Low-rank Plus Sparse Matrices by Jared Tanner; Simon Vary is a Computer Science article available to read on EtoBox.

What is Compressed Sensing of Low-rank Plus Sparse Matrices about?

Expressing a matrix as the sum of a low-rank matrix plus a sparse matrix is a flexible model capturing global and local features in data. This model is the foundation of robust principle component analysis [1,2], and popularized by dynamic-foreground/static-background separation [3]. Compressed sensing, matrix completion, and their variants [4,5] have established that data satisfying low complexity models can be efficiently measured and recovered from a number of measurements proportional to the model complexity rather than the ambient dimension. This manuscript develops similar guarantees showing that m × n matrices that can be expressed as the sum of a rank-r matrix and a s-sparse matrix can be recovered by computationally tractable methods from O ( r ( m + n − r ) + s ) log ⁡ ( m n / s ) linear measurements. More specifically, we establish that the low-rank plus sparse matrix set is closed provided the incoherence of the low-rank component is upper bounded as μ < m n / ( r s ) , and subsequently, the restricted isometry constants for the aforementioned matrices remain bounded independent of problem size provided p / m n , s / p , and r ( m + n − r ) / p remain fixed. Additionall

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Author

Jared Tanner; Simon Vary

Publisher

Elsevier BV

Published

2023

Language

EN

Field

Computer Science (Physical Sciences)