Deterministic Construction of Binary Measurement Matrices with Various Sizes

TL;DR

This paper presents a deterministic method to construct binary measurement matrices for compressed sensing, using permutation blocks and Johnson bound-based coherence optimization, achieving sizes and performance comparable to Gaussian matrices.

Contribution

A new deterministic framework for constructing binary measurement matrices with optimized coherence and flexible sizes, suitable for hardware implementation.

Findings

Constructed matrices have coherence close to theoretical bounds.

Matrices show empirical performance comparable to Gaussian matrices.

Framework allows various sizes and easy hardware realization.

Abstract

We introduce a general framework to deterministically construct binary measurement matrices for compressed sensing. The proposed matrices are composed of (circulant) permutation submatrix blocks and zero submatrix blocks, thus making their hardware realization convenient and easy. Firstly, using the famous Johnson bound for binary constant weight codes, we derive a new lower bound for the coherence of binary matrices with uniform column weights. Afterwards, a large class of binary base matrices with coherence asymptotically achieving this new bound are presented. Finally, by choosing proper rows and columns from these base matrices, we construct the desired measurement matrices with various sizes and they show empirically comparable performance to that of the corresponding Gaussian matrices