2D Sparse Signal Recovery via 2D Orthogonal Matching Pursuit

TL;DR

This paper introduces 2D-OMP, an efficient extension of 1D orthogonal matching pursuit for 2D signals, reducing complexity and memory usage in compressive sampling recovery.

Contribution

The paper develops a novel 2D-OMP algorithm that extends 1D-OMP to 2D signals, significantly lowering computational complexity and memory requirements.

Findings

2D-OMP reduces recovery complexity compared to traditional methods.

2D-OMP significantly decreases memory usage at the decoder.

The methodology can be extended to higher-dimensional OMP algorithms.

Abstract

Recovery algorithms play a key role in compressive sampling (CS). Most of current CS recovery algorithms are originally designed for one-dimensional (1D) signal, while many practical signals are two-dimensional (2D). By utilizing 2D separable sampling, 2D signal recovery problem can be converted into 1D signal recovery problem so that ordinary 1D recovery algorithms, e.g. orthogonal matching pursuit (OMP), can be applied directly. However, even with 2D separable sampling, the memory usage and complexity at the decoder is still high. This paper develops a novel recovery algorithm called 2D-OMP, which is an extension of 1D-OMP. In the 2D-OMP, each atom in the dictionary is a matrix. At each iteration, the decoder projects the sample matrix onto 2D atoms to select the best matched atom, and then renews the weights for all the already selected atoms via the least squares. We show that 2D-OMP is in fact equivalent to 1D-OMP, but it reduces recovery complexity and memory usage significantly. What's more important, by utilizing the same methodology used in this paper, one can even obtain higher dimensional OMP (say 3D-OMP, etc.) with ease.