Ill-posed sets of linear equations typically arise when discretizing certain types of integral transforms. A well known example is image reconstruction, which can be modeled using the Radon transform. After expanding the solution into a finite series of basis functions a large, sparse and ill-conditioned linear system occurs. We consider the solution of such systems. In particular we study a new class of iteration methods named DROP (for Diagonal Relaxed Orthogonal Projections) constructed for solving both linear equations and linear inequalities. This class can also be viewed, when applied to linear equations, as a generalized Landweber iteration. The method is compared with other iteration methods using test data from a medical application and from electron microscopy…
Contents
1 Introduction
1 Semi-convergence behavior of Landweber-type iteration
2 Projection algorithms
2.1 Iterative algorithms
3 Stopping rules
2 Summary of papers
References
Appended manuscripts
I On Diagonally Relaxed Orthogonal Projection Methods
II Stopping Rules for Landweber-type Iteration
III Some Properties of ART-type Reconstruction Algorithms
IV Some Block-Iterative Methods used in Image Reconstruction
V Semi-Convergence and Choice of Relaxation Parameters in Landweber-type Algorithms
Author: Nikazad, Touraj
Source: Linköping University
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