A TGV Based Image Reconstruction Model: Numerics

Martin Holler* and Kristian Bredies

The problem of reconstructing multichannel images from inexact or incomplete data is considered. The main motivation is the improved decompression of transform-coded images, such as JPEG or JPEG 2000 compressed files. To this aim, a minimization problem has to be solved. \newline In function space setting, existence of a solution and optimality conditions have been obtained in a general form including the desired applications. \newline Numerically, the sum of two non-smooth functionals has to be minimized. Based on the general framework of a primal-dual algorithm by \emph{Chambolle and Pock}, we present numerical solution schemes for the application to JPEG and JPEG 2000 decompression. \newline An important difference between these two applications is that, in contrast to JPEG compression, JPEG 2000 compression is based on a non-orthogonal basis transform. This has to be taken into account for the formulation of a solution scheme and requires additional considerations. Finally, also a suitable stopping criterion is presented for both settings.

Mathematics Subject Classification: 94A08 49K30 49M29

Keywords: JPEG Decompression; Total Generalized Variation Regularization; Primal-Dual Algorithm;

Minisymposion: Computational Methods for Inverse Problems/Control Problems in Banach Spaces