A Bilevel Optimization Approach for Parameter Learning in Variational Models

In this work we consider the problem of parameter learning for variational image denoising models. The learning problem is formulated as a bilevel optimization problem, where the lower level problem is given by the variational model and the higher level problem is expressed by means of a loss function that penalizes errors between the solution of the lower level problem and the ground truth data. We consider a class of image denoising models incorporating `p-norm based analysis priors using a fixed set of linear operators. We devise semi-smooth Newton methods to solve the resulting non-smooth bilevel optimization problems and show that the optimized image denoising models can achieve state-of-the-art performance.