Dynamic Orthogonal Matching Pursuit for Sparse Data Reconstruction

TL;DR

This paper introduces the DOMP and EDOMP algorithms, which improve the efficiency of sparse data reconstruction over traditional OMP, with theoretical error bounds and convergence guarantees.

Contribution

It proposes novel dynamic variants of OMP that enhance efficiency and provides rigorous analysis of their error bounds and convergence properties.

Findings

DOMP outperforms OMP in numerical efficiency.

Reconstruction error is bounded by iterations, sparsity, and noise.

Finite convergence is established for large-scale problems.

Abstract

The orthogonal matching pursuit (OMP) is one of the mainstream algorithms for sparse data reconstruction or approximation. It acts as a driving force for the development of several other greedy methods for sparse data reconstruction, and it also plays a vital role in the development of compressed sensing theory for sparse signal and image reconstruction. In this paper, we propose the so-called dynamic orthogonal matching pursuit (DOMP) and enhanced dynamic orthogonal matching pursuit (EDOMP) algorithms which are more efficient than OMP for sparse data reconstruction from a numerical point of view. We carry out a rigorous analysis to establish the reconstruction error bound for DOMP under the restricted isometry property of the measurement matrix. The main result claims that the reconstruction error via DOMP can be controlled and measured in terms of the number of iterations, sparsity level of data, and the noise level of measurements. Moveover, the finite convergence of DOMP for a class of large-scale compressed sensing problems is also shown.