Rank Awareness in Joint Sparse Recovery

By M. Davies, Yonina C. Eldar. IEEE Transactions on Information Theory, 2010

333 citations recorded by the source corpus.

This paper revisits the sparse multiple measurement vector (MMV) problem, where the aim is to recover a set of jointly sparse multichannel vectors from incomplete measurements. This problem is an extension of single channel sparse recovery, which lies at the heart of compressed sensing. Inspired by the links to array signal processing, a new family of MMV algorithms is considered that highlight the role of rank in determining the difficulty of the MMV recovery problem. The simplest such method is a discrete version of MUSIC which is guaranteed to recover the sparse vectors in the full rank MMV setting, under mild conditions. This idea is extended to a rank aware pursuit algorithm that naturally reduces to Order Recursive Matching Pursuit (ORMP) in the single measurement case while also providing guaranteed recovery in the full rank setting. In contrast, popular MMV methods such as Simultaneous Orthogonal Matching Pursuit (SOMP) and mixed norm minimization techniques are shown to be rank blind in terms of worst case analysis. Numerical simulations demonstrate that the rank aware techniques are significantly better than existing methods in dealing with multiple measurements.

Subfields: Computational Mechanics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/067bab300fad5dca329819194e551b4d808ea002

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Citations in the corpus

An Overview of Low-Rank Matrix Recovery From Incomplete Observations (2016, background): “To name just a few examples, we commonly encounter low-rank matrices in contexts as varied as: • ensembles of signals: the output of a sensor array or network, a collection of video frames, or a sequence of segments of a longer signal can often be highly correlated and represented using a low-rank m”
Sparse Methods for Direction-of-Arrival Estimation (2016, background): “Moreover, the condition in (9) or (10) is also necessary [19].”
Position and Orientation Estimation Through Millimeter-Wave MIMO in 5G Systems (2017, neutral): “We note that the algorithm is rank-blind as it does not assume knowledge of the number of the paths (i.e., K + 1 ) [45].”
Structured Compressed Sensing: From Theory to Applications (2011, methodology): “As shown in [110], [112], we can replace by in (31).”