Iterative Optimization in Inverse Problems

128 Iterative Optimization in Inverse Problems

9.2 Overview

We are concerned here with iterative methods for solving, at least ap-

proximately, the system of I linear equations in J unknowns symbolized

by Ax = b. In the applications of interest to us, such as medical imaging,

both I and J are quite large, making the use of iterative methods the only

feasible approach. It is also typical of such applications that the matrix

A is sparse, that is, has relatively few non-zero entries. Therefore, itera-

tive methods that exploit this sparseness to accelerate convergence are of

special interest to us.

Cimmino’s method [98] is a simultaneous method, in which ...