# Greedy Sparse Signal Reconstruction Using Matching Pursuit Based on Hope-tree

## TL;DR

This paper introduces GSRA, an iterative greedy algorithm for sparse signal reconstruction that combines support set estimation, hope-tree expansion, and subspace pursuit for improved accuracy in compressed sensing.

## Contribution

The paper proposes a novel GSRA algorithm that enhances support set estimation through hope-tree expansion and rectification, outperforming existing methods.

## Key findings

- GSRA achieves higher reconstruction accuracy for Gaussian, 0-1 sparse, and synthetic signals.
- Simulation results show GSRA outperforms typical existing methods.
- The method effectively combines multiple support estimation strategies for improved results.

## Abstract

The reconstruction of sparse signals requires the solution of an $\ell_0$-norm minimization problem in Compressed Sensing. Previous research has focused on the investigation of a single candidate to identify the support (index of nonzero elements) of a sparse signal. To ensure that the optimal candidate can be obtained in each iteration, we propose here an iterative greedy reconstruction algorithm (GSRA). First, the intersection of the support sets estimated by the Orthogonal Matching Pursuit (OMP) and Subspace Pursuit (SP) is set as the initial support set. Then, a hope-tree is built to expand the set. Finally, a developed decreasing subspace pursuit method is used to rectify the candidate set. Detailed simulation results demonstrate that GSRA is more accurate than other typical methods in recovering Gaussian signals, 0--1 sparse signals, and synthetic signals.