Localization of More Sources Than Sensors via Jointly-Sparse Bayesian Learning

Balkan, Ozgur; Kreutz-Delgado, Kenneth; Makeig, Scott

doi:10.1109/lsp.2013.2294862

Cited by 30 publications

(14 citation statements)

References 11 publications

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“…Lemma 1. Let the estimator λ be as defined in (4). Then, under Assumptions 1 and 2 with c = c ′ = c ′′ = 1, we have that…”

Section: A the Estimatormentioning

confidence: 99%

“…However, none of the above works addresses the question of tradeoff between m and n when m < k. Initial works considering the m < k regime were [21] and [4], followed by [18] and [23], where it was empirically demonstrated that when multiple samples are available, it is possible to operate in the m < k regime. However, the analysis in [4] is done under two fairly restrictive conditions. The first condition is an orthogonality assumption on the data vectors that requires n i=1 X i X ⊤ i to be diagonal.…”

Section: Introductionmentioning

confidence: 99%

“…Also, several algorithms from the single sample setting have been generalized to work with multiple samples that include convex programming methods [20], [28], [11], thresholding-based methods [13], [14], Bayesian methods [34] and greedy methods [29], [30]. However, none of the above works addresses the question of tradeoff between m and n when m < k. Initial works considering the m < k regime were [21] and [4], followed by [18] and [23], where it was empirically demonstrated that when multiple samples are available, it is possible to operate in the m < k regime. However, the analysis in [4] is done under two fairly restrictive conditions.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Lemma 1. Let the estimator λ be as defined in (4). Then, under Assumptions 1 and 2 with c = c ′ = c ′′ = 1, we have that…”

Section: A the Estimatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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show abstract

“…Recently it was shown that given the true dictionary A, and a data segment Y s ∈ R M ×Ls , where L s is the length of the segment in data frames, M-SBL (multiple measurement Sparse Bayesian Learning) applied directly on Y s can identify active sources under the assumption that sources are uncorrelated in the time segment [22]. The number of sources identified in this case is not limited by the number of channels M , 1 ≤ k ≤ M (M + 1)/2.…”

Section: Related Workmentioning

confidence: 99%

Covariance-domain Dictionary Learning for Overcomplete EEG Source Identification

Balkan,

Kreutz-Delgado,

Makeig

2015

Preprint

Self Cite

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We propose an algorithm targeting the identification of more sources than channels for electroencephalography (EEG). Our overcomplete source identification algorithm, Cov-DL, leverages dictionary learning methods applied in the covariancedomain. Assuming that EEG sources are uncorrelated within moving time-windows and the scalp mixing is linear, the forward problem can be transferred to the covariance domain which has higher dimensionality than the original EEG channel domain. This allows for learning the overcomplete mixing matrix that generates the scalp EEG even when there may be more sources than sensors active at any time segment, i.e. when there are nonsparse sources. This is contrary to straight-forward dictionary learning methods that are based on the assumption of sparsity, which is not a satisfied condition in the case of low-density EEG systems. We present two different learning strategies for Cov-DL, determined by the size of the target mixing matrix. We demonstrate that Cov-DL outperforms existing overcomplete ICA algorithms under various scenarios of EEG simulations and real EEG experiments.

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“…Under the frame of BCS, signal reconstruction is mainly achieved by sparse Bayesian learning (SBL) [6]. The SBL has obtained great development in the recent researches, such as root SBL [7], variational SBL [8], jointly SBL [9] and grid evolution method [15]. SBL has a multilayered assumption frame which is designed to iterate to "learn" new information and update the hyperparameters.…”

Section: Introductionmentioning

confidence: 99%

Direction-of-Arrival Method Based on Randomize-Then-Optimize Approach

Tang

Wang

Zhao

et al. 2020

Preprint

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Sparse Bayesian learning (SBL) has been successfully applied in solving the problem of direction-of-arrival (DOA) estimation. However, SBL needs multiple snapshots to ensure accuracy and costs huge computational workload. To reduce the requirement of snapshot and computational burden, a DOA estimation method based on the randomize-then-optimize (RTO) algorithm is first time introduced. RTO algorithm uses the optimization and Metropolis-Hastings approach to avoid the “learning” process of SBL in updating hyperparameters. And in order to apply RTO algorithm in the circumstance of signal with Laplace prior, a prior transformation technique is first induced. Compared with conventional CS based DOA methods, the proposed method has a better accuracy with single snapshot and shorter processing time. Some simulations are conducted to demonstrate the effectiveness of the proposed method.

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Localization of More Sources Than Sensors via Jointly-Sparse Bayesian Learning

Cited by 30 publications

References 11 publications

Sample-Measurement Tradeoff in Support Recovery Under a Subgaussian Prior

Sample-Measurement Tradeoff in Support Recovery Under a Subgaussian Prior

Covariance-domain Dictionary Learning for Overcomplete EEG Source Identification

Direction-of-Arrival Method Based on Randomize-Then-Optimize Approach

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