A New Performance Measure Using $k$-Set Correlation for Compressed Sensing Matrices

Abstract

In this letter, a new performance measure for compressed sensing matrices is proposed. This new measure is based on the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -set correlation vectors whose components consist of the correlation values between two columns in the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -column submatrices of a sensing matrix. This measure is highly related to the restricted isometry property (RIP). And the proposed measure has less computational complexity than the condition number approach which is a typical approach for performance prediction with RIP check. It is shown by simulation that the proposed scheme works well as a performance measure for the compressed sensing matrices.