Subspace Pursuit for Compressive Sensing Signal Reconstruction

Details Subspace Pursuit for Compressive Sensing Signal Reconstruction Subspace Pursuit for Compressive Sensing Signal Reconstruction

2008-03-06

arxiv.org/abs/0803.0811v3

Computer Science

Numerical Analysis

The first version was submitted on Mar. 6th, 2008. The 2nd version was updated on Mar. 10th, 2008. The 3rd version was submitt

Scientific paper

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.

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