Support Recovery of Sparse Signals in the Presence of Multiple Measurement Vectors

Jin, Yuzhe; Rao, Bhaskar D.

doi:10.1109/tit.2013.2238605

Cited by 45 publications

(29 citation statements)

References 65 publications

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“…In other words, DCS cannot accurately characterize the relationship between L and the performances of solvers such as SOMP. [9,10,11] focus on the performance analysis based on Eq. (2) and show that the performance is proportional to rank(Y ) with noiseless measurements.…”

Section: Background and Related Workmentioning

confidence: 99%

Distributed Compressive Sensing: Performance Analysis With Diverse Signal Ensembles

Hsieh

Liang

et al. 2020

IEEE Trans. Signal Process.

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Distributed compressive sensing is a framework considering jointly sparsity within signal ensembles along with multiple measurement vectors (MMVs). The current theoretical bound of performance for MMVs, however, is derived to be the same with that for single MV (SMV) because no assumption about signal ensembles is made.In this work, we propose a new concept of inducing the factor called "Euclidean distances between signals" for the performance analysis of MMVs. The novelty is that the size of signal ensembles will be taken into consideration in our analysis to theoretically show that MMVs indeed exhibit better performance than SMV. Although our concept can be broadly applied to CS algorithms with MMVs, the case study conducted on a well-known greedy solver called simultaneous orthogonal matching pursuit (SOMP) will be explored in this paper. We show that the performance of SOMP, when incorporated with our concept by modifying the steps of support detection and signal estimations, will be improved remarkably, especially when the Euclidean distances between signals are short. The performance of modified SOMP is verified to meet our theoretical prediction.

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Section: Background and Related Workmentioning

confidence: 99%

Distributed Compressive Sensing: Performance Analysis With Diverse Signal Ensembles

Hsieh

Liang

et al. 2020

IEEE Trans. Signal Process.

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“…Common choices of mixed-norms are the 2,1 norm [20], [37] and the ∞,1 norm [21], [22]. Similar to the SMV case, recovery guarantees for the MMV-based joint SSR problem have been derived [26]- [28], providing conditions for the noiseless case under which the sparse signal matrix X can be perfectly reconstructed. Moreover, it has been shown that rank-awareness in the signal reconstruction can additionally improve the reconstruction performance [29].…”

Section: Sparse Representation and Mixed-norm Minimizationmentioning

confidence: 99%

“…Similar to the SMV case, heuristics for the MMVbased SSR problem include convex relaxation by means of mixed-norm minimization [20]- [23], and greedy methods [24], [25]. Recovery guarantees for the MMV case have been established in [26]- [28], and it has been shown that rank awareness in MMV-based SSR can further enhance the recovery performance as compared to the SMV case [29]. An extension to the infinite-dimensional vector space for MMV-based SSR, using atomic norm minimization, has been proposed in [30]- [32].…”

Section: Introductionmentioning

confidence: 99%

A Compact Formulation for the $\ell _{2,1}$ Mixed-Norm Minimization Problem

Sandor

Pesavento

Pfetsch

2018

IEEE Trans. Signal Process.

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Abstract-Parameter estimation from multiple measurement vectors (MMVs) is a fundamental problem in many signal processing applications, e.g., spectral analysis and direction-ofarrival estimation. Recently, this problem has been address using prior information in form of a jointly sparse signal structure. A prominent approach for exploiting joint sparsity considers mixednorm minimization in which, however, the problem size grows with the number of measurements and the desired resolution, respectively. In this work we derive an equivalent, compact reformulation of the 2,1 mixed-norm minimization problem which provides new insights on the relation between different existing approaches for jointly sparse signal reconstruction. The reformulation builds upon a compact parameterization, which models the row-norms of the sparse signal representation as parameters of interest, resulting in a significant reduction of the MMV problem size. Given the sparse vector of row-norms, the jointly sparse signal can be computed from the MMVs in closed form. For the special case of uniform linear sampling, we present an extension of the compact formulation for gridless parameter estimation by means of semidefinite programming. Furthermore, we derive in this case from our compact problem formulation the exact equivalence between the 2,1 mixed-norm minimization and the atomic-norm minimization. Additionally, for the case of irregular sampling or a large number of samples, we present a low complexity, grid-based implementation based on the coordinate descent method.

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“…In particular, [22] showed a lower bound on sample complexity of support recovery of roughly (k/m), much weaker than our (k/m) 2 lower bound. Another related line of works [27], [17] studies this problem considering the same measurement matrix for all samples, under the assumption that the data vectors are deterministic. In [17], the authors connect the support recovery problem to communication over a single input multiple output MAC channel.…”

Section: Introductionmentioning

confidence: 99%

“…Another related line of works [27], [17] studies this problem considering the same measurement matrix for all samples, under the assumption that the data vectors are deterministic. In [17], the authors connect the support recovery problem to communication over a single input multiple output MAC channel. However, the performance guarantees are asymptotic in nature (d → ∞ and k, n fixed).…”

Section: Introductionmentioning

confidence: 99%

Sample-Measurement Tradeoff in Support Recovery Under a Subgaussian Prior

Ramesh

Murthy

Tyagi

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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Data samples from Ê d with a common support of size k are accessed through m random linear projections per sample. It is well-known that roughly k measurements from a single sample are sufficient to recover the support. In the multiple sample setting, do k overall measurements still suffice when only m < k measurements per sample are allowed? We answer this question in the negative by considering a generative model setting with independent samples drawn from a subgaussian prior. We show that n = Θ((k 2 /m 2 ) · log k(d − k)) samples are necessary and sufficient to recover the support exactly. In turn, this shows that k overall samples are insufficient for support recovery when m < k; instead we need about k 2 /m overall measurements. Our proposed sample-optimal estimator has a closed-form expression, has computational complexity of O(dnm), and is of independent interest.

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Support Recovery of Sparse Signals in the Presence of Multiple Measurement Vectors

Cited by 45 publications

References 65 publications

Distributed Compressive Sensing: Performance Analysis With Diverse Signal Ensembles

Distributed Compressive Sensing: Performance Analysis With Diverse Signal Ensembles

A Compact Formulation for the $\ell _{2,1}$ Mixed-Norm Minimization Problem

Sample-Measurement Tradeoff in Support Recovery Under a Subgaussian Prior

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