This book 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. Related to sequential unconstrained minimization methods, the SUMMA class includes a wide range of iterative algorithms well known to researchers in various areas, such as statistics and image processing.

Background. Sequential Optimization. Barrier-Function and Penalty-Function Methods. Proximal Minimization. The Forward-Backward Splitting Algorithm. Operators. Averaged and Paracontractive Operators. Convex Feasibility and Related Problems. Eigenvalue Bounds. Jacobi and Gauss-Seidel Methods. The SMART and EMML Algorithms. Alternating Minimization. The EM Algorithm. Geometric Programming and the MART. Variational Inequality Problems and Algorithms. Set-Valued Functions in Optimization. Fenchel Duality. Compressed Sensing. Appendix. Bibliography. Index.