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
Automated Recovery of Compressedly Observed Sparse Signals From Smooth Background
TL;DR: A Bayesian based algorithm to recover sparse signals from compressed noisy measurements in the presence of a smooth background component is proposed and its advantage over the current state-of-the-art solutions is demonstrated.
Proceedings ArticleDOI
Sparse Recovery Assisted Doa Estimation Utilizing Sparse Bayesian Learning
Min Huang,Lei Huang +1 more
TL;DR: Numerical results show that the proposed SR-DOA algorithm is superior to the state-of-the-art methods in terms of the estimation accuracy.
Proceedings ArticleDOI
Compressive Sensing via Variational Bayesian Inference
Mohammad Shekaramiz,Todd K. Moon +1 more
TL;DR: This work considers sparse signal recovery problem from a set of compressively sensed noisy measurements using sparse Bayesian learning (SBL) modeling and variational Bayesian inference technique and derives the update rules for the latent variables and parameters of each modeling in detail.
Posted Content
Enhanced signal recovery via sparsity inducing image priors
TL;DR: This work focuses on developing novel sparse signal representation algorithms to obtain more robust systems and on the design of tractable algorithms that can recover signals under aforementioned sparse models.
Dissertation
Reconstruction of enhanced ultrasound images from compressed measurements
TL;DR: Une methode d'optimisation basee sur l'algorithme des directions alternees est ensuite proposee pour inverser le modele lineaire, en incluant deux termes de regularisation exprimant la parcimonie des images RF dans une base donnee and l'hypothese statistique gaussienne generalisee sur les fonctions de reflectivite des tissus.
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.
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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.