Low-Rank Matrix Recovery

Authored by: Angshul Majumdar

Compressed Sensing for Engineers

Print publication date:  December  2018
Online publication date:  December  2018

Print ISBN: 9780815365563
eBook ISBN: 9781351261364
Adobe ISBN:

10.1201/9781351261364-7

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Abstract

There is a matrix X n × n (it can be rectangular as well), but all the entries ( x i , j , ( i , j ) = 1… n ) are not available. Only a subset ( Ω ) ​ of entries is observed. Now, the question is, is it possible to estimate all the entries of the matrix, given the set of partially observed samples? In general, the answer is NO. However, in a special situation, when the matrix is of low rank, it is possible to estimate the entire matrix, provided “enough” samples are available.

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