Journal ArticleDOI
Bayesian Compressive Sensing Using Laplace Priors
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TLDR
This paper model the components of the compressive sensing (CS) problem, i.e., the signal acquisition process, the unknown signal coefficients and the model parameters for the signal and noise using the Bayesian framework and develops a constructive (greedy) algorithm designed for fast reconstruction useful in practical settings.Abstract:
In this paper, we model the components of the compressive sensing (CS) problem, i.e., the signal acquisition process, the unknown signal coefficients and the model parameters for the signal and noise using the Bayesian framework. We utilize a hierarchical form of the Laplace prior to model the sparsity of the unknown signal. We describe the relationship among a number of sparsity priors proposed in the literature, and show the advantages of the proposed model including its high degree of sparsity. Moreover, we show that some of the existing models are special cases of the proposed model. Using our model, we develop a constructive (greedy) algorithm designed for fast reconstruction useful in practical settings. Unlike most existing CS reconstruction methods, the proposed algorithm is fully automated, i.e., the unknown signal coefficients and all necessary parameters are estimated solely from the observation, and, therefore, no user-intervention is needed. Additionally, the proposed algorithm provides estimates of the uncertainty of the reconstructions. We provide experimental results with synthetic 1-D signals and images, and compare with the state-of-the-art CS reconstruction algorithms demonstrating the superior performance of the proposed approach.read more
Citations
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Journal ArticleDOI
MIMO Radar Super-Resolution Imaging Based on Reconstruction of the Measurement Matrix of Compressed Sensing
TL;DR: In this paper , the authors proposed a sparse recovery method of multiple-input and multiple-output (MIMO) radar compressed sensing (CS) imaging algorithms, which leverages the prior structure of the measurement matrix to judge targets' locations and estimate the sparsity level in the grid roughly and finally inhabits the emergence of false targets in the imaging figure.
Proceedings ArticleDOI
A fast iterative Bayesian inference algorithm for sparse channel estimation
TL;DR: In this paper, a hierarchical representation of the Bessel K probability density function is used to estimate the prior distribution of multipath components' gains with a hierarchical Bayesian inference method, and the resulting estimator outperforms other state-of-the-art Bayesian and non-Bayesian estimators.
Posted Content
SubTSBR to tackle high noise and outliers for data-driven discovery of differential equations
Sheng Zhang,Guang Lin +1 more
TL;DR: A novel algorithm subsampling-based threshold sparse Bayesian regression (SubTSBR) to tackle high noise and outliers and the merits of discovering differential equations from data are discussed.
Journal ArticleDOI
Uncertainty Quantification of Random Fields Based on Spatially Sparse Data by Synthesizing Bayesian Compressive Sensing and Stochastic Harmonic Function
TL;DR: The proposed BCS-SHF approach is employed to quantify the uncertainty of the random field of concrete strength, and then further applied to the stochastic response analysis of a reinforced concrete shear wall model under cyclic loading, revealing that the spatial variation will greatly affect the failure modes of the shear walls.
Proceedings ArticleDOI
Spatial rainfall mapping from path-averaged rainfall measurements exploiting sparsity
TL;DR: A proper selection of the representation basis and the priors that directly relate to the spatial properties of the rainfall guarantee an efficient reconstruction with a low compression rate (fewer measurements).
References
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Pattern Recognition and Machine Learning
TL;DR: Probability Distributions, linear models for Regression, Linear Models for Classification, Neural Networks, Graphical Models, Mixture Models and EM, Sampling Methods, Continuous Latent Variables, Sequential Data are studied.
Journal ArticleDOI
Pattern Recognition and Machine Learning
TL;DR: This book covers a broad range of topics for regular factorial designs and presents all of the material in very mathematical fashion and will surely become an invaluable resource for researchers and graduate students doing research in the design of factorial experiments.
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Compressed sensing
TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
Journal ArticleDOI
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
TL;DR: In this paper, the authors considered the model problem of reconstructing an object from incomplete frequency samples and showed that with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the lscr/sub 1/ minimization problem.
Journal ArticleDOI
Atomic Decomposition by Basis Pursuit
TL;DR: Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.