Signal recovery from multiple measurement vectors via tunable random projection and boost

Gai, Jianxin; Fu, Ping; Li, Zhen; Qiao, Jiaqing

doi:10.1016/j.sigpro.2012.05.022

Cited by 6 publications

(8 citation statements)

References 20 publications

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“…It is showed that [20] (15) Lemma 2 [8]: Let be an arbitrary orthogonal basis matrix, let be the measurement matrix defined by formula (12). Choose , then with probability at least , the coherence will obey (16) Remark: suppose , it is obviously that and then (17) Which means that the measurements guarantee reconstruction grows linearly with and . Formula (17) guarantees that this design of measurement matrix presented by this letter is optimal for signals sparse in frequency domain and achieves the minimal measurements.…”

Section: Theoretical Analysismentioning

confidence: 99%

“…However, owing to the independence of mixing functions between channels, the MWC exhibits high degree of freedom, which, results in high complexity in realistic hardware design. Unfortunately, most of the recently presented papers concerning MWC focus on the problem of joint sparse signal recovery which resolves simultaneous signal recovery from multiple measurements [16], [17]. We furthermore fully investigate the design of novel architecture with low hardware complexity in this letter.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Compressive Circulant Matrix Based Analog to Information Conversion

Peng

2014

IEEE Signal Process. Lett.

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Compressive Sampling is an attractive way implementing analog to information conversion (AIC), of which the most successful hardware architecture is modulated wideband converter (MWC). Unfortunately, the MWC has high hardware complexity owing to high degree of freedom of the random waveforms constructing the measurement matrix. To reduce the complexity, in this letter, we present a novel Compressive Circulant Matrix based AIC (CCM-AIC) generating random waveforms by cyclic shift of a special sequence with unit amplitude and random phase in frequency domain. Theoretical analysis shows this scheme is optimal for signals sparse in frequency. CCM-AIC outperforms MWC and is more robust. Simulations classify the above analysis.Index Terms-Analog to information conversion, circulant matrix, compressive sampling, joint sparse recovery.

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Section: Theoretical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Compressive Circulant Matrix Based Analog to Information Conversion

Peng

2014

IEEE Signal Process. Lett.

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“…In a previous study, Wei et al [1] treated direction of arrival estimation as a multiple measurement vectors (MMV) model involving the measurement of a set of vectors that share a joint sparsity pattern [2][3][4][5]. Wei et al [1] proposed the greedy block coordinate descent (GBCD) algorithm and discussed the following ℓ 1, 2 -norm minimisation formulation for jointly sparse signal recovery…”

Section: Introductionmentioning

confidence: 99%

Sufficient condition for exact support recovery of sparse signals through greedy block coordinate descent

Liu

Zou

2019

IET signal process.

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In the underdetermined model Ŷ = AX + N, where X is a K-group sparse matrix (i.e. it has no more than K non-zero rows), the matrix A may be also perturbed. Theoretically, a more relaxed condition means that fewer measurements are required to ensure sparse recovery. In this study, a relaxed sufficient condition is proposed for greedy block coordinate descent (GBCD) under total perturbations based on the restricted isometry property in order to guarantee that the support of X is recovered. We also show that GBCD fails in a more general case when 1/(K + 1) ≤ δ K + 1 < 1. A′ denotes the transpose of A, and x i is the ith row of X. The cardinality of a finite set Γ is denoted by |Γ|. Let Ω := {1, 2, …, n}, Γ c = Ω∖Γ = {i | i ∈ Ω, and i ∉ Γ}. The support of X is denoted by supp(X) (supp(X) = {i | x i ≠ 0}). ∥ A ∥ 2 (K) denotes the largest spectral norm taken over all K-column submatrices of A. ∥ ⋅ ∥ F denotes the Frobenius norm. I d ∈ ℝ d × d is an identity matrix. The

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“…The non‐zero rows of

bold-italicP

correspond to the angles of incident signals. Equation (2) is also studied from other perspectives in [17–22]. Especially, random projection [21, 22] is adopted to find the support of

bold-italicP

in (2) and it reduces the MMV problem to the SMV problem.…”

Section: Introductionmentioning

confidence: 99%

“…Equation (2) is also studied from other perspectives in [17–22]. Especially, random projection [21, 22] is adopted to find the support of

bold-italicP

in (2) and it reduces the MMV problem to the SMV problem. Mishali and Eldar [21] have proposed the reduce MMV and boost (ReMBo) algorithm which utilises a random right vector to boost the recovery performance.…”

Section: Introductionmentioning

confidence: 99%