A TGV-Based Framework for Variational Image Decompression, Zooming, and Reconstruction. Part II: Numerics

The present work is the second of two papers on a variational model for image reconstruction whose specific features are twofold: First, data fidelity is realized by interval constraints on the coefficients of a Riesz basis representation, and second, total generalized variation (TGV) of arbitrary order is employed as image prior. While Part I provides a comprehensive analysis of the model in a general function space setting as well as discusses applications such as artifact-free JPEG, JPEG 2000 decompression, and variational zooming, Part II deals with the discretized setting and presents globally convergent algorithms for these applications. In the case of JPEG and JPEG 2000 decompression, highly improved color image reconstructions are obtained from the encoded files. The numerical results are supplemented by duality based stopping criteria, a parallelized implementation, and a comparison of results obtained with TV and second and third order TGV regularization.