DocumentCode :
62325
Title :
Bayesian Estimation for Continuous-Time Sparse Stochastic Processes
Author :
Amini, Amin ; Kamilov, Ulugbek S. ; Bostan, Emrah ; Unser, Michael
Author_Institution :
Biomed. Imaging Group (BIG), Ecole Polytech. Fed. de Lausanne (EPFL), Lausanne, Switzerland
Volume :
61
Issue :
4
fYear :
2013
fDate :
Feb.15, 2013
Firstpage :
907
Lastpage :
920
Abstract :
We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By relying on tools from the theory of splines, we derive the joint a priori distribution of the samples and show how this probability density function can be factorized. The factorization enables us to tractably implement the maximum a posteriori and minimum mean-square error (MMSE) criteria as two statistical approaches for estimating the unknowns. We compare the derived statistical methods with well-known techniques for the recovery of sparse signals, such as the 1 norm and Log (1-0 relaxation) regularization methods. The simulation results show that, under certain conditions, the performance of the regularization techniques can be very close to that of the MMSE estimator.
Keywords :
Bayes methods; compressed sensing; estimation theory; interpolation; least mean squares methods; matrix decomposition; signal denoising; signal sampling; splines (mathematics); stochastic processes; Bayesian estimation; MMSE criteria; MMSE estimator; a priori distribution; continuous-time sparse stochastic processes; factorization; interpolation problem; minimum mean-square error criteria; noiseless samples; noisy samples; probability density function; regularization methods; regularization techniques; signal denoising; sparse signals; spline theory; statistical methods; Estimation; Joints; Noise measurement; Probability density function; Random variables; Stochastic processes; Technological innovation; Denoising; Lévy process; MAP; MMSE; interpolation; sparse process; statistical learning;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/TSP.2012.2226446
Filename :
6339101
Link To Document :
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