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Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

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4 Author(s)
Amini, A. ; Biomed. Imaging Group (BIG), Ecole Polytech. Fed. de Lausanne (EPFL), Lausanne, Switzerland ; Kamilov, U.S. ; Bostan, E. ; Unser, M.

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.

Published in:

Signal Processing, IEEE Transactions on  (Volume:61 ,  Issue: 4 )