Learning-Based Design of Measurement Matrix with Inter-Column Correlation for Compressive Sensing

Abstract

In this paper, a new approach for the design of measurement matrix, Φ, for compressive sensing (CS) in a generic context is proposed. In accordance with well-known classical CS theory, we take the elements of Φ to be random, yet, we include correlations within the elements of the individual columns of Φ. To this end, a new structure for Φ is proposed where the correlations of interest are controlled by a selectable parameter. We aim at optimizing the proposed Φ with respect to the latter correlation parameter by leveraging an appropriate criterion in a learning-based framework. We evaluate the performance of the proposed Φ and compare it with the state-of-the-art literature including random Φ with independent and identically distributed (i.i.d.) elements. Performance advantage of the proposed approach is validated in different CS scenarios.