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Consistent Discretization of Linear Inverse Problems Using Sparse Stochastic Processes

E. Bostan, U.S. Kamilov, M. Nilchian, M. Unser

Signal Processing with Adaptive Sparse Structured Representations (SPARS'13), Lausanne VD, Swiss Confederation, July 8-11, 2013.



We introduce a novel discretization paradigm and specify MAP estimators for linear inverse problems by using the theory of continuous-domain sparse stochastic processes. We characterize the complete class of admissible priors for the discretized version of the signal and show that the said class is restricted to the family of infinitely divisible distributions. We also explain the connections between our estimators and the existing deterministic methods such as Tikhonov and ℓp-type (with p ∈ (0, 1]) regularizations.


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