Phase transition of joint-sparse recovery from multiple measurements via convex optimization

Hu, Shih-Wei; Lin, Gang-Xuan; Hsieh, Sung-Hsien; Lu, Chun-Shien

doi:10.1109/icassp.2015.7178637

Cited by 5 publications

(5 citation statements)

References 19 publications

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“…By the definition of descent cone, the necessary and sufficient condition of the success of problem (ML1) is described and proved in our earlier work [9]. But in this paper, the main problem we are studying is not related to a norm function, so we need to modify the proof slightly to fit the problem (Mconvex) with general convex function as follows.…”

Section: Definition 21 (Descent Cone [10])mentioning

confidence: 97%

“…Since the nullity of A is n − m almost surely, the dimension of C 2 is δ (null(A, l)) = dim (null(A, l)) = (n − m)l. Then, the probability that (Mconvex) succeeds can be estimated by Theorem 2.5, which was derived in our earlier work [9].…”

Section: Definition 23 (Statistical Dimension [10])mentioning

confidence: 99%

“…They show that the performance can be improved provided good prior information can be available. In [9], we characterize when problem (ML1) succeeds and derive the phase transition of success rate inspired by the framework of conic geometry [10].…”

Section: Background and Problem Definitionmentioning

confidence: 99%

“…Then, the probability that (Mconvex) succeeds can be estimated by Theorem 2.5, which was derived in our earlier work [9].…”

Section: Definition 23 (Statistical Dimension [10])mentioning

confidence: 99%

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Performance analysis of joint-sparse recovery from multiple measurement vectors with prior information via convex optimization

Lin

Hsieh

et al. 2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We address the problem of compressed sensing with multiple measurement vectors associated with prior information in order to better reconstruct an original sparse signal. This problem is modeled via convex optimization with ℓ 2,1 − ℓ 2,1 minimization. We establish bounds on the number of measurements required for successful recovery. Our bounds and geometrical interpretations reveal that if the prior information can decrease the statistical dimension and make it lower than that under the case without prior information, ℓ 2,1 − ℓ 2,1 minimization improves the recovery performance dramatically. All our findings are further verified via simulations.

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Section: Definition 21 (Descent Cone [10])mentioning

confidence: 97%

Section: Definition 23 (Statistical Dimension [10])mentioning

confidence: 99%

Section: Background and Problem Definitionmentioning

confidence: 99%

“…Then, the probability that (Mconvex) succeeds can be estimated by Theorem 2.5, which was derived in our earlier work [9].…”

Section: Definition 23 (Statistical Dimension [10])mentioning

confidence: 99%

See 2 more Smart Citations

Performance analysis of joint-sparse recovery from multiple measurement vectors with prior information via convex optimization

Lin

Hsieh

et al. 2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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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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Performance Analysis of Joint-Sparse Recovery from Multiple Measurement Vectors via Convex Optimization: Which Prior Information is Better?

Lin

Hsieh

et al. 2018

IEEE Access

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Phase transition of joint-sparse recovery from multiple measurements via convex optimization

Cited by 5 publications

References 19 publications

Performance analysis of joint-sparse recovery from multiple measurement vectors with prior information via convex optimization

Performance analysis of joint-sparse recovery from multiple measurement vectors with prior information via convex optimization

Distributed Compressive Sensing: Performance Analysis With Diverse Signal Ensembles

Performance Analysis of Joint-Sparse Recovery from Multiple Measurement Vectors via Convex Optimization: Which Prior Information is Better?

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