Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

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 l(1) norm and Log (l(1)-l(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.


Published in:
Ieee Transactions On Signal Processing, 61, 4, 907-920
Year:
2013
Publisher:
Piscataway, Ieee-Inst Electrical Electronics Engineers Inc
ISSN:
1053-587X
Keywords:
Laboratories:




 Record created 2013-03-28, last modified 2018-03-17

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