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
Variational Bayesian and Generalized Approximate Message Passing-Based Sparse Bayesian Learning Model for Image Reconstruction
TL;DR: In this article , a variational Bayesian (VB) and generalized approximate message passing (GAMP) model is proposed to speed up image reconstruction. But it is not suitable for large-scale image recovery.
Proceedings ArticleDOI
Two-dimension Super-resolution Range Doppler Imaging in Automotive Radar
TL;DR: In this paper , the sparsity of scattering points in space and the robustness of l 1 norm were exploited to finish the super-resolution imaging of range-Doppler (RD) map.
Journal ArticleDOI
MRI reconstruction based on Bayesian piecewise sparsity constraint and adaptive 3D transform
TL;DR: The combination of piecewise sparsity constraint and adaptive 3D transform allows one to establish a novel CS-MRI reconstruction model and the corresponding numerical algorithms are deduced under the framework of alternating direction method of multipliers (ADMM).
Unmanned aerial vehicle field sampling and antenna pattern reconstruction using Bayesian compressed sensing
Sayeh Mirzaei,Alireza Gholipour +1 more
TL;DR: A test scenario using unmanned aerial vehicles (UAV) is proposed, and it is shown that applying Bayesian CS algorithm to the samples of field intensity gathered by UAV can efficiently reconstruct the antenna pattern.
Proceedings ArticleDOI
Bayesian compressive sensing based SAR imaging for GMTI system
TL;DR: A Bayesian compressive sensing (BCS) based SAR imaging algorithm for ground moving targets indication (GMTI) system, which uses Laplace priors on the basis coefficients in a hierarchical manner is proposed.
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.