Dualization and Automatic Distributed Parameter Selection of Total Generalized Variation via Bilevel Optimization

Total Generalized Variation (TGV) regularization in image reconstruction relies on an infimal convolution type combination of generalized first- and second-order derivatives. This helps to avoid the staircasing effect (TV) regularization, while still preserving sharp contrasts images. The associated crucially hinges two parameters whose proper adjustment represents a challenging task. In this work, bilevel optimization framework with suitable statistics-based upper level objective is proposed order automatically select these parameters. allows for spatially varying parameters, thus enabling better recovery high-detail areas. A rigorous dualization established, numerical solution, Newton method solution lower problem, i.e. TGV algorithm are introduced. Denoising tests confirm that selected distributed lead general improved reconstructions when compared results scalar