A general framework for whiteness-based parameters selection in variational models
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In this work, we extend the residual whiteness principle (RWP), originally proposed for the estimation of the regularization parameter in variational models for additive white noise corruption, to more general scenarios. More specifically, we address the problem of estimating a certain number of parameters for imaging inverse problems subject to non-white but whitenable noise corruptions. The proposed principle is thus referred to as Generalized Whiteness Principle (GWP), that is formulated as a bilevel optimization problem. To circumvent the non-smoothness of the variational models typically employed in imaging problems - the non-smoothness representing a bottleneck in the bilevel set-up - we propose to adopt a derivative free minimization algorithm for the solution of the GWP bilevel problem. We refer to this novel solution paradigm as Bilevel Derivative Free (BDF) approach. Numerical tests highlight the robustness of the GWP and the significant advantages, in terms of computational cost, of the BDF framework.