DeepAI AI Chat
Log In Sign Up

Deterministic partial binary circulant compressed sensing matrices

by   Arman Arian, et al.

Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representation. This is achieved by collecting linear, non-adaptive measurements of a signal, which can be formalized as multiplying the signal with a "measurement matrix". Most of matrices used in CS are random matrices as they satisfy the restricted isometry property (RIP) in an optimal regime of number of measurements with high probability. However, these matrices have their own caveats and for this reason, deterministic measurement matrices have been proposed. While there is a wide classes of deterministic matrices in the literature, we propose a novel class of deterministic matrices using the Legendre symbol. This construction has a simple structure, it enjoys being a binary matrix, and having a partial circulant structure which provides a fast matrix-vector multiplication and a fast reconstruction algorithm. We will derive a bound on the sparsity level of signals that can be measured (and be reconstructed) with this class of matrices. We perform quantization using these matrices, and we verify the performance of these matrices (and compare with other existing constructions) numerically.


page 1

page 2

page 3

page 4


RIP constants for deterministic compressed sensing matrices-beyond Gershgorin

Compressed sensing (CS) is a signal acquisition paradigm to simultaneous...

On one-stage recovery for ΣΔ-quantized compressed sensing

Compressed sensing (CS) is a signal acquisition paradigm to simultaneous...

Limits on Sparse Data Acquisition: RIC Analysis of Finite Gaussian Matrices

One of the key issues in the acquisition of sparse data by means of comp...

Fast Fourier-Based Generation of the Compression Matrix for Deterministic Compressed Sensing

The primary goal of this work is to review the importance of data compre...

Estimating Unknown Sparsity in Compressed Sensing

In the theory of compressed sensing (CS), the sparsity ||x||_0 of the un...

Deep Compressed Sensing

Compressed sensing (CS) provides an elegant framework for recovering spa...

Generalized Tensor Summation Compressive Sensing Network (GTSNET): An Easy to Learn Compressive Sensing Operation

In CS literature, the efforts can be divided into two groups: finding a ...