Beta 1


Title Modular Algorithms for Large Scale Total Variation Image Deblurring
Author Pedersen, Jesper (Informatics and Mathematical Modelling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Supervisor Hansen, Per Christian (Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Nielsen, Hans Bruun (Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Institution Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
Thesis level Master's thesis
Year 2005
Abstract We present the theory behind inverse problems and illustrate that regularization is needed to obtain useful solutions. The most frequently used solution techniques for solving ill posed problems are based on the use of 2 norms, which are known not to be suitable when edges are desired in the regularized solution. The thesis covers the development of an algorithm for solving ill posed problems, where edges and steep gradients are allowed. The key idea is to make use of Total Variation, thus the algorithm solves a Tikhonov based optimization problem with the Total Variation functional as penalty term. The algorithm is based on Newton s method with a line search procedure. The Total Variation functional is the essential subject for allowing edges in the solutions. We explain the theory connected with Total Variation, and we discuss how important it is to use an appropriate discretization, and propose a way of doing this. Furthermore, we discuss how to deal with the non linearity of the functional by introducing an extra set of variables. Introducing these variables we obtain an augmented system, which is globally more linear and thus easier to solve. The purpose of this is to obtain a faster convergence. The implementation of the algorithm is carried out with focus on efficiency. It is implemented in the framework of the modular Matlab toolbox MOORe Tools, which is designed for solving large scale inverse problems. This results in a modular and object oriented structure, which together with the interior use of iterative methods makes the implementation suitable for solving large scale problems. All implementation aspects are explained in detail. Finally, some experiments using the algorithm are carried out.
Imprint DK-2800 Kgs. Lyngby, Denmark
Pages 122
Keywords Total Variation; Tikhonov; ill posed problems; regularization; steep gradients; MOORe Tools; large scale inversion; iterative methods; object oriented implementation; non linear optimization; Newton's method; augmented system
Fulltext
Original PDF imm3849.pdf (1.61 MB)
Admin Creation date: 2006-06-22    Update date: 2012-12-17    Source: dtu    ID: 185865    Original MXD