Compressive MUSIC with optimized partial support for joint sparse recovery

Abstract

The multiple measurement vector (MMV) problem addresses the identification of unknown input vectors that share common sparse support. The MMV problem has been traditionally addressed either by sensor array signal processing or compressive sensing. However, recent breakthroughs in this area such as compressive MUSIC (CS-MUSIC) or subspace-augumented MUSIC (SA-MUSIC) optimally combine the compressive sensing (CS) and array signal processing such that k−r supports are first found by CS and the remaining r supports are determined by a generalized MUSIC criterion, where k and r denote the sparsity and the number of independent snapshots, respectively. Even though such a hybrid approach significantly outperforms the conventional algorithms, its performance heavily depends on the correct identification of k − r partial support by the compressive sensing step, which often deteriorates the overall performance. The main contribution of this paper is, therefore, to show that as long as k − r + 1 correct supports are included in any ksparse CS solution, the optimal k − r partial support can be found using a subspace fitting criterion, significantly improving the overall performance of CS-MUSIC. Furthermore, unlike the single measurement CS counterpart that requires infinite SNR for a perfect support recovery, we can derive an information theoretic sufficient condition for the perfect recovery using CS-MUSIC under a finite SNR scenario.

Frequency selective millimeter‐wave channel estimation based on subspace enhancement algorithms

“…Since the length of δ is DL − r, then the selection rule introduced in Equation 19 will be repeatedDL − r times. After detection of the entries of δ, we can obtain the enhanced signal subspace as follows:…”

“…In the rank‐defective case, the conventional MMV approaches such as MOMP, MSBL, or MUSIC fail. Thus, Davies and Eldar and Kim et al proposed the rank‐aware subspace methods.…”

MUSIC-CSR: Hyperspectral Unmixing via Multiple Signal Classification and Collaborative Sparse Regression

“…This is the so-called multiple measurement vector (MMV) problem with applications, for example, in distributed compressive sensing, direction-of-arrival estimation in radar, magnetic resonance imaging with multiple coils, diffuse optical tomography using multiple illumination patterns (see [13]- [15] and references therein).…”

“…On the other hand, we have the MUSIC based approaches, which yield very good results, provided that the rank of the observations is no less than the number of elements of the support of the vectors. Very recently, the complementarity between MUSIC and sparse regression approaches to solve MMV problems has been exploited [13], [14] by first applying sparse regression methods that identify a subset of the support and then apply MUSIC based methods. In this paper, we also exploit MUSIC and sparse regression approaches to unmix hyperspectral data, but in a reversed order.…”

Dynamic sparse support tracking with multiple measurement vectors using compressive MUSIC

“…The breakthrough is based on our novel compressive multiple signal classification (CS-MUSIC) algorithm in MMV compressed sensing problem [7], in which a part of supports are found probabilistically using the conventional CS, after which the remaining supports are determined deterministically using the generalized MUSIC criterion. In addition, CS-MUSIC allows us to find all k support as long as at least k − r + 1 support out of any k-support estimate are correct [8],…”