5. Criterion minimization methods

Most inversion methods are based, explicitly or implicitly, on the minimization of a criterion. Depending on the properties of this criterion, the cost of actually calculating the solution can vary enormously: typically, by a factor of 1,000 between minimizing a quadratic criterion by inversion of a linear system and minimizing a multimodal criterion by a relaxation technique such as simulated annealing, all other things being equal. Ultimately, the choice of the "right" inversion method depends on the computational resources available. For example, in the previous comparison, it would be possible, but totally inefficient, to use the simulated annealing technique to minimize a quadratic criterion.

A non-exhaustive overview of optimization problems in the context of inverse problems in signal and image processing is offered here, along with associated algorithmic...