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About 406 papers for “Bayesian compressed sensing”

Bayesian online compressed sensing

パウロ ロッシ, Paulo V. Rossi, 樺島 祥介 et al. · Tokyo Tech Research Repository (Tokyo Institute of Technology) · 2016

Cited by 0

Bayesian online compressed sensing

Paulo Rossi, Yoshiyuki Kabashima, Jun‐ichi Inoue · Physical review. E · 2016

In this paper, we explore the possibilities and limitations of recovering sparse signals in an online fashion. Employing a mean field approximation to the Bayes recursion formula yields an online signal recovery algorithm that can be performed with a computational cost that is linearly proportional to the signal length per update. Analysis of the resulting algorithm indicates that the online algorithm asymptotically saturates the optimal performance limit achieved by the offline method in the presence of Gaussian measurement noise, while differences in the allowable computational costs may result in fundamental gaps of the achievable performance in the absence of noise.

Cited by 8Open access

Robust Bayesian Compressed sensing

Qian Wan, Huiping Duan, Jun Fang et al. · arXiv (Cornell University) · 2016

We consider the problem of robust compressed sensing whose objective is to recover a high-dimensional sparse signal from compressed measurements corrupted by outliers. A new sparse Bayesian learning method is developed for robust compressed sensing. The basic idea of the proposed method is to identify and remove the outliers from sparse signal recovery. To automatically identify the outliers, we employ a set of binary indicator hyperparameters to indicate which observations are outliers. These indicator hyperparameters are treated as random variables and assigned a beta process prior such that their values are confined to be binary. In addition, a Gaussian-inverse Gamma prior is imposed on the sparse signal to promote sparsity. Based on this hierarchical prior model, we develop a variational Bayesian method to estimate the indicator hyperparameters as well as the sparse signal. Simulation results show that the proposed method achieves a substantial performance improvement over existing robust compressed sensing techniques.

Cited by 1Open access

Bayesian Inference and Compressed Sensing

Solomon A. Tesfamicael, Faraz Barzideh · InTech eBooks · 2017

This chapter provides the use of Bayesian inference in compressive sensing (CS), a method in signal processing. Among the recovery methods used in CS literature, the convex relaxation methods are reformulated again using the Bayesian framework and this method is applied in different CS applications such as magnetic resonance imaging (MRI), remote sensing, and wireless communication systems, specifically on multipleinput multiple-output (MIMO) systems. The robustness of Bayesian method in incorporating prior information like sparse and structure among the sparse entries is shown in this chapter.

Cited by 0Open access

Clustered Compressed Sensing via Bayesian Framework

Solomon A. Tesfamicael, Faraz Barzideh · 2015

This paper provides clustered compressive sensing (CCS) based signal processing using Bayesian framework. Images like magnetic resonanse images (MRI) are usually very weak due to the presence of noise and due to the weak nature of the signal itself. Compressed sensing (CS) paradigm can be applied in order to boost such signal recoveries. We applied CS paradigm via Bayesian framework. That is incorporating the different prior information such as sparsity and the special structure that can be found in such sparse signal improves signal recovery. The method is applied on synthetic and medical images including MRI images. The results show that applying the clustered compressive sensing out performs the non clustered but only sparse counter parts when it comes to mean square error(MSE), pick signal to noise ratio (PSNR) and other performance metrics.

Cited by 2

Bayesian Experimental Design for Compressed Sensing

Hannes Nickisch, Matthias Seeger · 2008

Compressed sensing (CS) can be addressed as instance of Bayesian experimental design, which is based on similar models than common estimation (or energy minimisation) methods, but fundamentally differs from the latter, in that estimates of uncertainty and correlations of latent variables are maintained. The Bayesian computations are approximated by the expectation propagation fixed point alg orithm, which is scaled up to the application of interest here through a novel scheduling mechanism, exploiting the fact that marginal uncertainty estimates are available at all times. An important application of CS is the optimisation of architectures for measuring natural images. In a large study, we compare various CS reconstruction methods utilising random measurement filters from different ensembles to a number of techniques which sequentially search for these filters, including our own, and Bayesian projection optimisation [1]. We find that a simple heuristic of measuring wavelet coefficients in a fixed, top-down ordering significantly outperforms CS methods using random measurements; the approach of [1] performs even worse. In contrast, our Bayesian design method learns filters that o utperform the wavelet heuristic. Our results show that the property of incoherence of a measurement design, which plays a central role in the “unstructured except for random sparsity” theoretical CS setting, bears no significa nce for measuring real natural images. Our framework is not restricted to sparse signals, other notions of signal or noise structure can easily be accommodated. We give concrete ideas how our method can be scaled up to large signal representations. Part of this work has been presented at a conference [2].

Cited by 0

Multi‐contrast reconstruction with Bayesian compressed sensing

Berkin Bilgic̦, Vivek K Goyal, Elfar Adalsteinsson · Magnetic Resonance in Medicine · 2011

Clinical imaging with structural MRI routinely relies on multiple acquisitions of the same region of interest under several different contrast preparations. This work presents a reconstruction algorithm based on Bayesian compressed sensing to jointly reconstruct a set of images from undersampled k-space data with higher fidelity than when the images are reconstructed either individually or jointly by a previously proposed algorithm, M-FOCUSS. The joint inference problem is formulated in a hierarchical Bayesian setting, wherein solving each of the inverse problems corresponds to finding the parameters (here, image gradient coefficients) associated with each of the images. The variance of image gradients across contrasts for a single volumetric spatial position is a single hyperparameter. All of the images from the same anatomical region, but with different contrast properties, contribute to the estimation of the hyperparameters, and once they are found, the k-space data belonging to each image are used independently to infer the image gradients. Thus, commonality of image spatial structure across contrasts is exploited without the problematic assumption of correlation across contrasts. Examples demonstrate improved reconstruction quality (up to a factor of 4 in root-mean-square error) compared with previous compressed sensing algorithms and show the benefit of joint inversion under a hierarchical Bayesian model.

Cited by 138Open access

A cooperative spectrum sensing algorithm based on Bayesian Compressed sensing

Rikang Zhou, Yuyan Zhang, Xuekang Sun et al. · 2017

Compressed sensing (CS) has been applicably used in cognitive radio (CR) to sense wide-band spectrum, solving the wide-band sensing rate restriction problem. For a CR network which includes multiple nodes, it's considered that the received signals is high correlated. So in this paper, we focus on efficient compressed spectrum sensing reconstructions in CR network, proposing a probabilistic model called Cooperative Bayesian Compressed Spectrum Sensing (C-BCSS) algorithm. In the algorithm, node samples locally and a common sparse signal model is developed to the received signals where correlation exists. And then C-BCSS reconstruction is performed cooperatively at fusion center utilizing the information from all nodes. We compared C-BCSS with Multitask BCS and simulation results show that C-BCSS outperforms in condition of severe under-sampling and heavy noise.

Cited by 3

Bayesian Nonparametric Dictionary Learning for Compressed Sensing MRI

Huang, Yue, Paisley, John, Lin, Qin et al. · arXiv (Cornell University) · 2013

We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRI) from highly undersampled k-space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta process as a nonparametric dictionary learning prior for representing an image patch as a sparse combination of dictionary elements. The size of the dictionary and the patch-specific sparsity pattern are inferred from the data, in addition to other dictionary learning variables. Dictionary learning is performed directly on the compressed image, and so is tailored to the MRI being considered. In addition, we investigate a total variation penalty term in combination with the dictionary learning model, and show how the denoising property of dictionary learning removes dependence on regularization parameters in the noisy setting. We derive a stochastic optimization algorithm based on Markov Chain Monte Carlo (MCMC) for the Bayesian model, and use the alternating direction method of multipliers (ADMM) for efficiently performing total variation minimization. We present empirical results on several MRI, which show that the proposed regularization framework can improve reconstruction accuracy over other methods.

Cited by 0Open access

Bayesian compressed sensing with new sparsity-inducing prior

Zai Yang, Lihua Xie, Cishen Zhang · arXiv (Cornell University) · 2012

Sparse Bayesian learning (SBL) is a popular approach to sparse signal recovery in compressed sensing (CS). In SBL, the signal sparsity information is exploited by assuming a sparsity-inducing prior for the signal that is then estimated using Bayesian inference. In this paper, a new sparsity-inducing prior is introduced and efficient algorithms are developed for signal recovery. The main algorithm is shown to produce a sparser solution than existing SBL methods while preserving their desirable properties. Numerical simulations with one-dimensional synthetic signals and two-dimensional images verify our analysis and show that for sparse signals the proposed algorithm outperforms its SBL peers in both the signal recovery accuracy and computational speed. Its improved performance is also demonstrated in comparison with other state-of-the-art methods in CS.

Cited by 9Open access

Bayesian signal reconstruction for 1-bit compressed sensing

Yingying Xu, Yoshiyuki Kabashima, Lenka Zdeborová · Journal of Statistical Mechanics Theory and Experiment · 2014

The 1-bit compressed sensing framework enables the recovery of a sparse vector x from the sign information of each entry of its linear transformation. Discarding the amplitude information can significantly reduce the amount of data, which is highly beneficial in practical applications. In this paper, we present a Bayesian approach to signal reconstruction for 1-bit compressed sensing, and analyze its typical performance using statistical mechanics. Utilizing the replica method, we show that the Bayesian approach enables better reconstruction than the L1-norm minimization approach, asymptotically saturating the performance obtained when the non-zero entries positions of the signal are known. We also test a message passing algorithm for signal reconstruction on the basis of belief propagation. The results of numerical experiments are consistent with those of the theoretical analysis.

Cited by 19Open access

Bayesian approximate message passing for distributed compressed sensing

Hannák, Gábor · reposiTUm (TU Wien) · 2020

In recent years, the low-dimensional representation of high-dimensional signals has been recognized as an essential concept in modern signal processing. An important family of problems is subsumed under the term compressed sensing (CS). CS copes with the reconstruction or estimation of a high-dimensional vector from a (noisy) underdetermined system of linear equations, assuming that the measured vector has only a relatively low number of nonzero components. Under mild conditions on the dimensions and the structure of the system matrix (measurement matrix), reconstruction or robust estimation is feasible. However, due to the high dimension of the problem and the nonlinear (sparsity) constraint, standard methods fail. Approximate message passing (AMP), an approximate and highly simplified version of loopy belief propagation, has proven to cope efficiently with high-dimensional sparse problems. Its simplicity and fast convergence make it a preferred choice for recovery. Its Bayesian version, Bayesian approximate message passing (BAMP), which is an approximate minimum mean squared error (MMSE) estimator, is a versatile algorithm that can incorporate prior knowledge about the measured vector in the form of a prior probability density function (pdf) of its components. When there is a set of measured vectors which are not completely independent, but jointly sparse (i.e., their sets of nonzero components are identical), joint recovery proves advantageous. More specifically, when a multivariate prior for the vector components of the jointly measured vectors is available, BAMP can be extended to its vector version, the vector Bayesian approximate message passing (V-BAMP). V-BAMP is an approximate MMSE estimator for the whole set of jointly measured vectors, and its analysis methods can be derived from the scalar BAMP. Specifically, the state evolution (SE) equations provide an analytical prediction for the residual mean squared error (MSE) of the vector estimates. Understanding the dynamics of SE in terms of fixed points as a function of the signal prior, the noise parameters, and the sampling rate is of crucial importance because it uncovers the expected behavior of V-BAMP. In this work it is shown that arbitrary signal and noise correlations can be eliminated in the joint measurement case. That is, every measurement instance can be transformed into an equivalent measurement in which both the signal and the noise are uncorrelated. Furthermore, it is proven that for the widely employed Bernoulli-Gauss (BG) signal prior this property is preserved through the V-BAMP iterations. It follows that the V-BAMP is equivariant with respect to such transformations, and that the latter has to be done only once before starting V-BAMP. The inverse transform can be done at any iteration, and neither the convergence nor the MSE performance are affected. The SE equations are extended to the multivariate case and extensive simulations show the effect of having multiple measurement vectors and the effect of having correlation on the recovery. Recently, based on the analogy between the statistical physics of large disordered systems and loopy belief propagation, the replica method was used to derive the MMSE of the Bayesian estimator of the CS measurement, given its parameters, and BG signal prior with standard Gaussian nonzero signal components and uniform uncorrelated Gaussian noise. In this work the replica analysis is extended to the case with arbitrary (nonuniform) uncorrelated Gaussian noise. Together with the joint decorrelation transform and the equivariance property of V-BAMP, the replica analysis turns out to predict the dynamics of V-BAMP for any BG measurement instance with Gaussian noise. Simulations confirm the analogy between the SE analysis and the replica analysis, and demonstrate the effect of signal correlation from multiple aspects.

Cited by 0Open access

Bayesian sequential compressed sensing in sparse dynamical systems

Christophe Andrieu, Robert Piechocki · 2010

Abstract—While the theory of compressed sensing provides means to reliably and efficiently acquire a sparse high-dimensional signal from a small number of its linear projections, sensing of dynamically changing sparse signals is still not well understood. We pursue a Bayesian approach to the problem of se-quential compressed sensing and develop methods to recursively estimate the full posterior distribution of the signal. I.

Cited by 0

Field of experts: Optimal structured Bayesian compressed sensing

Xinjie Lan, Kenneth E. Barner · 2017

Exploiting signal structure can improve Compressed Sensing reconstruction performance. In this paper, we propose an optimal structured Bayesian Compressed Sensing (BCS) reconstruction framework. Constructed to capture signal structure precisely, this framework employs Field of Experts (FoE) to fuse Hidden Markov Random Fields with Gaussian Scale Mixtures as prior distributions. This approach optimizes the parameters of FoE by minimizing KL-divergence via Contrastive Divergence learning method. An analytical posterior inference via auxiliary-variable Gibbs sampler is then constituted to reconstruct the signal. Simulations show that this proposed method, named Optimal Structured BCS based on FoE (OS-BCS-FoE), outperforms previous CS recovery methods used for image restoration applications.

Cited by 6

Medical image reconstruction based on Bayesian compressed sensing

Yuhong Li, Defeng Wang, Lok Ming Lui et al. · 2011

A medical image reconstruction method based on sparse Bayesian compressed sensing is presented, and the method employs a hierarchical model of the Laplace prior to model the sparse wavelet coefficients and unknown images. The experiments are designed to compare the Bayesian Compressed Sensing (BCS) method with the Basis Pursuit (BP) algorithm and the Orthogonal Matching Pursuit (OMP) algorithm. The results imply that the presented algorithm exceeds the greedy algorithm and the linear programming such as BP and OMP etc.

Cited by 1