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We propose an adaptive regularization scheme in a variational framework wherea convex composite energy functional is optimized. We consider a number ofimaging problems including denoising, segmentation and motion estimation, whichare considered as optimal solutions of the energy functionals that mainlyconsist of data fidelity, regularization and a control parameter for theirtrade-off. We presents an algorithm to determine the relative weight betweendata fidelity and regularization based on the residual that measures how wellthe observation fits the model. Our adaptive regularization scheme is designedto locally control the regularization at each pixel based on the assumptionthat the diversity of the residual of a given imaging model spatially varies.The energy optimization is presented in the alternating direction method ofmultipliers (ADMM) framework where the adaptive regularization is iterativelyapplied along with mathematical analysis of the proposed algorithm. Wedemonstrate the robustness and effectiveness of our adaptive regularizationthrough experimental results presenting that the qualitative and quantitativeevaluation results of each imaging task are superior to the results with aconstant regularization scheme. The desired properties, robustness andeffectiveness, of the regularization parameter selection in a variationalframework for imaging problems are achieved by merely replacing the staticregularization parameter with our adaptive one.

Adaptive Regularization in Convex Composite Optimization for Variational Imaging Problems