Near-Oracle Performance of Greedy Block-Sparse Estimation Techniques from Noisy Measurements

TL;DR

This paper analyzes the performance of greedy algorithms for estimating block sparse signals from noisy data, demonstrating near-optimal accuracy under various noise conditions and highlighting the benefits of block techniques.

Contribution

It provides theoretical performance guarantees for block sparse greedy algorithms under adversarial and Gaussian noise, including bounds close to the Cramer-Rao limit.

Findings

Estimation accuracy is within a constant factor of noise power in adversarial noise.

Greedy algorithms approach the Cramer-Rao bound at high SNR under Gaussian noise.

Block sparse techniques outperform non-block methods in noisy measurement scenarios.

Abstract

This paper examines the ability of greedy algorithms to estimate a block sparse parameter vector from noisy measurements. In particular, block sparse versions of the orthogonal matching pursuit and thresholding algorithms are analyzed under both adversarial and Gaussian noise models. In the adversarial setting, it is shown that estimation accuracy comes within a constant factor of the noise power. Under Gaussian noise, the Cramer-Rao bound is derived, and it is shown that the greedy techniques come close to this bound at high SNR. The guarantees are numerically compared with the actual performance of block and non-block algorithms, highlighting the advantages of block sparse techniques.