Structured Bayesian compressive sensing with spatial location dependence via variational Bayesian inference

Wu, Qisong; Fang, Shiliang

doi:10.1016/j.dsp.2017.08.007

Cited by 9 publications

(11 citation statements)

References 29 publications

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“…We refer to the algorithm associated with this Bayesian modeling based on VB inference as SBL(BGiG). SBL using VB inference for the clustered pattern of sparse signals has already been investigated in the recent literature [ 45 , 50 , 51 , 58 ]. In this paper, however, we intend to focus on the ordinary SBL using VB inference modeling without promoting any structure on the supports other than sparsity itself.…”

Section: Bernoulli–gaussian-inverse Gamma Modeling and Sbl(bgig) Algo...mentioning

confidence: 99%

“…The measurement matrix can be defined as

, where

is the sensing design matrix and

is a proper sparsifying basis. There exist various approaches to solve for

in ( 1 ) including greedy-based, convex-based, thresholding-based and sparse Bayesian learning (SBL) algorithms [ 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 ]. Typically, the performance of CS reconstruction is determined in terms of the mean-squared reconstruction error.…”

Section: Introductionmentioning

confidence: 99%

“…A prior favoring the sparsity or compressibility in

can be represented in the SBL framework via Gaussian-inverse Gamma (GiG), Laplace-inverse Gamma (LiG), Bernoulli–Gaussian-inverse Gamma (BGiG), often referred to as spike-and-slab prior, etc. [ 27 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 ]. The inference on parameters and hidden variables in these models is usually made using Markov chain Monte Carlo (MCMC) and variational Bayes (VB) [ 27 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 ].…”

Section: Introductionmentioning

confidence: 99%

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Compressive Sensing via Variational Bayesian Inference under Two Widely Used Priors: Modeling, Comparison and Discussion

Shekaramiz

Moon

2023

Entropy

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Compressive sensing is a sub-Nyquist sampling technique for efficient signal acquisition and reconstruction of sparse or compressible signals. In order to account for the sparsity of the underlying signal of interest, it is common to use sparsifying priors such as Bernoulli–Gaussian-inverse Gamma (BGiG) and Gaussian-inverse Gamma (GiG) priors on the components of the signal. With the introduction of variational Bayesian inference, the sparse Bayesian learning (SBL) methods for solving the inverse problem of compressive sensing have received significant interest as the SBL methods become more efficient in terms of execution time. In this paper, we consider the sparse signal recovery problem using compressive sensing and the variational Bayesian (VB) inference framework. More specifically, we consider two widely used Bayesian models of BGiG and GiG for modeling the underlying sparse signal for this problem. Although these two models have been widely used for sparse recovery problems under various signal structures, the question of which model can outperform the other for sparse signal recovery under no specific structure has yet to be fully addressed under the VB inference setting. Here, we study these two models specifically under VB inference in detail, provide some motivating examples regarding the issues in signal reconstruction that may occur under each model, perform comparisons and provide suggestions on how to improve the performance of each model.

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Section: Bernoulli–gaussian-inverse Gamma Modeling and Sbl(bgig) Algo...mentioning

confidence: 99%

“…The measurement matrix can be defined as

, where

is the sensing design matrix and

is a proper sparsifying basis. There exist various approaches to solve for

Section: Introductionmentioning

confidence: 99%

“…A prior favoring the sparsity or compressibility in

Section: Introductionmentioning

confidence: 99%

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Compressive Sensing via Variational Bayesian Inference under Two Widely Used Priors: Modeling, Comparison and Discussion

Shekaramiz

Moon

2023

Entropy

View full text Add to dashboard Cite

show abstract

“…This mitigates information loss between wireless sensor nodes and the base station [19][20][21]. An extension of this, BCS, couples sparse Bayesian learning to reconstruct signals from a limited set of compressed measurements [22,23]. Multitask BCS techniques determine the relationship between compressive measurements and original signals, thereby improving signal reconstruction performance.…”

Section: Introductionmentioning

confidence: 99%

Novel measurement method for full-field bridge strain and displacement with limited long-gauge strain sensors

Zhang,

Li,

Yuan

2023

Meas. Sci. Technol.

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In efforts to resolve the limitations of incomplete bridge measurements in accurately identifying structural parameters, this study introduces a novel approach for precise measurement of full-field bridge strain and displacement using a limited number of long-gauge fiber bragg grating (FBG) strain sensors. This method consists of two algorithms: a double reconstruction algorithm for strain reconstruction and an improved conjugate beam algorithm for displacement identification. The dual reconstruction algorithm exploits proper orthogonal decomposition (POD) to establish a comprehensive mapping relationship between units, thereby achieving precise strain estimation. This intricate mapping process enables the algorithm to accurately compute strain responses. By leveraging the derived full-field strain data, the improved conjugate beam algorithm effectively captures complete displacement responses. The conventional sensor placement configuration monitors only a limited number of units. To enhance full-field measurement accuracy, this method categorizes unmonitored units into two levels based on sensor placement. The double reconstruction algorithm then estimates the strain response sequentially, contributing to enhanced precision. Numerical simulations validate the proposed method, which is demonstrated to be efficient and robust under various vehicle loads, impact loads, and noised levels. A physical experiment further demonstrates the efficacy of the proposed method in practice. The results underscore the potency of the proposed method as powerful theoretical and practical approach for full-field strain and displacement measurement.

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“…Therefore, this new technique presents an efficient signal processing paradigm by merging traditional signal sensing and compression into a single phase. Recently, much interest has been extended to CS methods, including Bayesian CS (BCS) [12][13][14], distributed CS [15,16], 1-bit CS [17,18], and others. As a novel signal processing technique for efficiently acquiring and reconstructing signals, CS had wide applications in many fields; e.g.…”

Section: Introductionmentioning

confidence: 99%

Diagnosis and accuracy enhancement of compressive-sensing signal reconstruction in structural health monitoring using multi-task sparse Bayesian learning

Huang¹,

Shao²,

Wu³

et al. 2019

Smart Mater. Struct.

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Bayesian compressive sensing (BCS) has provided algorithms to reconstruct underlying signals from far fewer compressed measurements by adopting the theory of sparse Bayesian learning (SBL). However, BCS lacks robustness when the number of measurements is much less than the length of the original signal because signal reconstruction accuracy is sensitive to the specific compressed measurements. As a result, signal reconstruction diagnosis and accuracy enhancement are necessary to tackle this problem. In this study, multi-task SBL is introduced for robust diagnosis and 'healing' of BCS signal reconstruction. A diagnosis technique is proposed to investigate whether the reconstructed (decompressed) signal representation is accurate, based on the phenomenon that inaccurate (suboptimal) signal models are much less stable than accurate (optimal) ones. For accuracy enhancement of compressive sensing signal reconstruction, a modified two-task learning algorithm is developed for potentially improving BCS reconstruction, and the corresponding 'healing' method is presented combined with the diagnosis technique. By applying these methods, the performance of BCS signal reconstruction can be monitored and, when necessary, improved. The real data collected from the structural health monitoring system of a bridge show that the accuracy of BCS reconstruction for automated recovery of data lost during wireless transmission is significantly enhanced by the proposed diagnosis and 'healing' methods.

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Structured Bayesian compressive sensing with spatial location dependence via variational Bayesian inference

Cited by 9 publications

References 29 publications

Compressive Sensing via Variational Bayesian Inference under Two Widely Used Priors: Modeling, Comparison and Discussion

Compressive Sensing via Variational Bayesian Inference under Two Widely Used Priors: Modeling, Comparison and Discussion

Novel measurement method for full-field bridge strain and displacement with limited long-gauge strain sensors

Diagnosis and accuracy enhancement of compressive-sensing signal reconstruction in structural health monitoring using multi-task sparse Bayesian learning

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