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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 of Total Variation (TV) regularization, while still preserving sharp contrasts in images. The associated regularization effect crucially hinges on two parameters whose proper adjustment represents a challenging task. In this work, a bilevel optimization framework with a suitable statistics-based upper level objective is proposed in order to automatically select these parameters. The framework allows for spatially varying parameters, thus enabling better recovery in high-detail image areas. A rigorous dualization framework is established, and for the numerical solution, two Newton type methods for the solution of the lower level problem, i.e. the image reconstruction problem, and two bilevel TGV algorithms are introduced, respectively. Denoising tests confirm that automatically selected distributed regularization parameters lead in general to improved reconstructions when compared to results for scalar parameters.
Structured convex optimization on weighted graphs finds numerous applications in machine learning and computer vision. In this work, we propose a novel adaptive preconditioning strategy for proximal algorithms on this problem class. Our preconditione
Bilevel optimization has been widely applied many machine learning problems such as hyperparameter optimization, policy optimization and meta learning. Although many bilevel optimization methods more recently have been proposed to solve the bilevel o
This work is concerned with the design and effects of the synchronization gains on the synchronization problem for a class of networked distributed parameter systems. The networked systems, assumed to be described by the same evolution equation in a
Optimization in distributed networks plays a central role in almost all distributed machine learning problems. In principle, the use of distributed task allocation has reduced the computational time, allowing better response rates and higher data rel
This paper proposes a new algorithm -- the underline{S}ingle-timescale Dounderline{u}ble-momentum underline{St}ochastic underline{A}pproxunderline{i}matiounderline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel optimization problems. W