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arXiv · 1210.5394

Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

Arash Amini·Ulugbek S. Kamilov·Emrah Bostan·Michael Unser
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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 $\ell_1$ norm and Log ($\ell_1$-$\ell_0$ 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.

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Arash Amini, Ulugbek S. Kamilov, Emrah Bostan, Michael Unser. 2012-10-19. Bayesian Estimation for Continuous-Time Sparse Stochastic Processes. https://doi.org/10.1109/tsp.2012.2226446

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