On the Design of Deterministic Matrices for Fast Recovery of Fourier Compressible Functions

TL;DR

This paper introduces a new class of deterministic compressed sensing matrices that enable fast, sublinear-time sparse Fourier approximation, improving sampling efficiency for Fourier compressible functions.

Contribution

The paper develops a general class of deterministic matrices with fast recovery algorithms and constructs specialized sparse matrices that enhance Fourier transform sampling efficiency.

Findings

Achieved sublinear-time sparse Fourier approximation algorithms.

Reduced sampling requirements compared to previous deterministic methods.

Constructed matrices that are sparse when multiplied with Fourier transform matrices.

Abstract

We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are sparse when multiplied with a discrete Fourier transform matrix. Ultimately, these considerations improve previous sampling requirements for deterministic sparse Fourier transform methods.