Microwave Imaging

CHAPTER SEVEN

Quantitative Stochastic Reconstruction Methods

7.1 INTRODUCTION

The current generation of computers makes it possible to utilize nonlinear global optimization procedures, which are in principle able to reach the global minimum of a given cost function. Stochastic optimization methods, which are now very common in electromagnetic imaging as well as in a great number of different inverse problems, are of particular interest.

The simulated annealing technique was one of the first stochastic minimization methods applied to electromagnetic imaging. It is an iterative method that, at each iteration, updates the current trial solution by exploiting probabilistic concepts. More recently, however, several inversion procedures founded on population-based algorithms have been proposed, since these global optimization techniques (especially the genetic algorithm) are now commonly applied in a plethora of engineering fields. Population-based algorithms can be used for imaging purposes with different implementation schemes (sometimes they assume different names depending on the choice of mechanism for generating the new solutions at the various iterative steps). Essentially, these methods start from sets of trial solutions (the populations) and iteratively evolve by applying some specific operators that are usually inspired on some biological or natural mechanisms (e.g., selection, crossover, and mutation in the genetic algorithm). During the minimization process, these algorithms ...