On Fundamental Limits of Joint Sparse Support Recovery Using Certain Correlation Priors

Koochakzadeh, Ali; Qiao, Heng; Pal, Piya

doi:10.1109/tsp.2018.2858211

Cited by 33 publications

(13 citation statements)

References 49 publications

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“…The second condition is that m 2 ≥ d, which is much stronger than our m ≥ (log k) 2 condition 1 In [21], a LASSO-based approach is proposed to recover the common support using correlation among the X i s. The authors empirically show that support recovery is possible using the same measurement matrix across samples (with large n) for support size k ≥ m and conjecture that k can be as large as O(m 2 ). In another recent work closely related to ours [19], the authors demonstrate the possibility of operating in the m < k regime. Their results are for the same measurement matrix across samples and for {X i } n i=1 drawn from a certain prior.…”

Section: Introductionsupporting

confidence: 59%

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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Section: Introductionsupporting

confidence: 59%

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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“…In space and air communication, the relative highspeed motion of the transceivers increases the complexity of beam alignment. Therefore, the accurate direction of arrival (DoA) and direction of departure (DoD) estimation is a key issue in MIMO communication [90][91][92]. Solutions have been proposed not only through the implementation of estimation algorithms such as Multiple Signal Classification (MU-SIC) and Estimation of Signal Parameters via Rational Invariance Techniques (ESPRIT), the implemen- tations of customized circuit blocks can also improve the speed and accuracy of alignment significantly [93].…”

Section: Space and Satellite Communicationmentioning

confidence: 99%

A review on applications of integrated terahertz systems

Venkatesh

Saeidi

2021

China Commun.

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A review on Terahertz end-to-end systems with an emphasis on integrated approaches is presented. Four major catalogs of THz integrated systems, including THz communication systems, THz imaging systems, THz radars, and THz spectroscopy systems, are reviewed in this article. The performance of integrated systems is compared with non-integrated solutions, followed by a discussion on the trend in future research avenues and applications.

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“…Both ℓ 1 -SVD and ℓ 1 -SRACV require reduced computational cost than the well-known ℓ 2,1 mixed norm, and are capable of handling coherent signals. The theoretical guarantees for this joint sparse recovery problem from MMVs developed in [26] (the overdetermined case) and [27], [28] (the underdetermined case with sparse arrays and uncorrelated sources) are based on a fixed deterministic measurement matrix representing the steering matrix of an array structure, which deviates from usual scenarios in compressed sensing relying on the randomness of the measurement matrix, while the support recovery for both the deterministic and random measurement matrix is discussed in [29]. Based on the fundamental ℓ 2,1 mixed norm, the MMV atomic norm approach [30] focusing mainly on the noiseless case and the SPARROW approach [31] are proposed as variants capable of incorporating the gridless optimization.…”

Section: Introductionmentioning

confidence: 99%