Deterministic Compressed Sensing Matrices From Sequences With Optimal Correlation

Abstract

Compressed sensing (CS) is a new method of data acquisition which aims at recovering higher dimensional sparse vectors from considerably smaller linear measurements. One of the key problems in CS is the construction of sensing matrices. In this paper, we construct deterministic sensing matrices, using Zhou-Helleseth-Udaya sequences and Udaya-Siddiqi sequences. We also construct deterministic sensing matrices using quaternary sequence families A and D. With the orthogonal matching pursuit, numerical simulations show that some of our proposed sensing matrices outperform several typical known sensing matrices in terms of the rate of exact reconstruction.

Keywords

• Compressed sensing
• coherence
• deterministic sensing matrices
• optimal sequence