An Approach to 2D Signals Recovering in Compressive Sensing Context

TL;DR

This paper introduces a fast, single-iteration algorithm for reconstructing 2D signals in compressive sensing scenarios, leveraging an analytically derived threshold to accurately separate signal from noise, with promising results in ISAR imaging.

Contribution

A novel, efficient algorithm for 2D signal reconstruction in compressive sensing using an analytically determined threshold for separation.

Findings

Effective reconstruction with less than 10% data in ISAR imaging

Fast single-iteration algorithm based on analytic threshold

Robust performance even outside derivation constraints

Abstract

In this paper we study the compressive sensing effects on 2D signals exhibiting sparsity in 2D DFT domain. A simple algorithm for reconstruction of randomly under-sampled data is proposed. It is based on the analytically determined threshold that precisely separates signal and non-signal components in the 2D DFT domain. The algorithm operates fast in a single iteration providing the accurate signal reconstruction. In the situations that are not comprised by the analytic derivation and constrains, the algorithm is still efficient and need just a couple of iterations. The proposed solution shows promising results in ISAR imaging (simulated data are used), where the reconstruction is achieved even in the case when less than 10% of data is available.