Image Identification Using the EM-Algorithm

Abstract

In the preceding chapter we have seen that the image identification problem can be formulated as a maximum likelihood parameter estimation problem. The optimization of the associated likelihood function turned out to be not a trivial problem, because of its highly nonlinear character, in a relatively large number of unknowns. For noiseless blurred images the ML estimation problem was shown to be identical to a least-squares estimation problem, for which elegant optimization algorithms were proposed in the literature. If, however, the likelihood function for noisy data is considered, these algorithms are no longer applicable, and gradient-based optimization strategies need to be employed, using either a frequency domain expression or a recursive spatial domain relation for the likelihood function. Disadvantages of these methods are that they are computationally involving, and that convergence of the gradient-based optimization is often difficult to control due to the nonlinear properties of the likelihood function.