ABSTRACT

Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation. It incorporates recent work that has not appeared in other books and draws on the author's considerable research in the field, including his recently developed class of SUMMA algorithms

chapter 1|24 pages

Background

chapter 2|10 pages

Sequential Optimization

chapter 4|18 pages

Proximal Minimization

chapter 5|10 pages

The Forward-Backward Splitting Algorithm

chapter 6|16 pages

Operators

chapter 7|12 pages

Averaged and Paracontractive Operators

chapter 8|20 pages

Convex Feasibility and Related Problems

chapter 9|24 pages

Eigenvalue Bounds

chapter 10|12 pages

Jacobi and Gauss-Seidel Methods

chapter 11|14 pages

The SMART and EMML Algorithms

chapter 12|10 pages

Alternating Minimization

chapter 13|18 pages

The EM Algorithm

chapter 14|12 pages

Geometric Programming and the MART

chapter 16|6 pages

Set-Valued Functions in Optimization

chapter 17|12 pages

Fenchel Duality

chapter 18|10 pages

Compressed Sensing