Subspace Pursuit for Compressive Sensing Signal Reconstruction

TL;DR

The paper introduces the subspace pursuit algorithm for sparse signal reconstruction, offering low computational complexity and high accuracy, with proven exact recovery under certain conditions and bounded error in noisy or approximate cases.

Contribution

It presents a novel subspace pursuit algorithm that combines low complexity with high accuracy, extending sparse signal reconstruction capabilities.

Findings

Exact reconstruction in noiseless cases with restricted isometry property

Bounded mean squared error in noisy and approximately sparse cases

Comparable performance to LP optimization methods

Abstract

We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of orthogonal matching pursuit techniques when applied to very sparse signals, and reconstruction accuracy of the same order as that of LP optimization methods. The presented analysis shows that in the noiseless setting, the proposed algorithm can exactly reconstruct arbitrary sparse signals provided that the sensing matrix satisfies the restricted isometry property with a constant parameter. In the noisy setting and in the case that the signal is not exactly sparse, it can be shown that the mean squared error of the reconstruction is upper bounded by constant multiples of the measurement and signal perturbation energies.