Correlation-aware techniques for sparse support recovery

Abstract

Sparse support recovery techniques guarantee successful recovery of sparse solutions to linear underdetermined systems provided the measurement matrix satisfies certain conditions. The maximum level of sparsity that can be recovered with existing algorithms is O(M) where M denotes the size of the measurement vector. This paper shows how this can be improved to O(M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) by assuming certain prior knowledge about the correlation structure of the measurements. The theory for correlation aware framework for support recovery is developed, which involves the Khatri-Rao (KR) product of the measurement matrix. Necessary and sufficient conditions for unique recovery of the sparse support are provided for this new framework which outperforms the more traditional CS techniques in terms of required size of the measurement vector. It also gives rise to interesting questions of constructing classes of measurement matrices which can exploit the prior correlation knowledge in an effective way. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>