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MAP Estimators for Self-Similar Sparse Stochastic Models

E. Bostan, J. Fageot, U.S. Kamilov, M. Unser

Proceedings of the Tenth International Workshop on Sampling Theory and Applications (SampTA'13), Bremen, Federal Republic of Germany, July 1-5, 2013, pp. 197–199.

We consider the reconstruction of multi-dimensional signals from noisy samples. The problem is formulated within the framework of the theory of continuous-domain sparse stochastic processes. In particular, we study the fractional Laplacian as the whitening operator specifying the correlation structure of the model. We then derive a class of MAP estimators where the priors are confined to the family of infinitely divisible distributions. Finally, we provide simulations where the derived estimators are compared against total-variation (TV) denoising. 

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