EXPECTATION MINIMUM (EM) - A NEW PRINCIPLE FOR THE SOLUTION OF ILL-POSED PROBLEMS IN PHOTOTHERMAL SCIENCE

The expectation-minimum (EM) principle is a new strategy for recoverin g robust solutions to the ill-posed inverse problems of photothermal s cience. The expectation-minimum principle uses the addition of well-ch aracterized random noise to a model basis to be fitted to the experime ntal response by linear minimization or projection techniques. The add ition of noise to the model basis improves the conditioning of the bas is by many orders of magnitude. Multiple projections of the data onto the basis in the presence of noise are averaged, to give the solution vector as an expectation value which reliably estimates the global min imum solution for general cases, while the conventional approaches fai l. This solution is very stable in the presence of random error on the data. The expectation-minimum principle has been demonstrated in conj unction with several projection algorithms. The nature of the solution s recovered by the expectation minimum principle is nearly independent of the minimization algorithms used and depends principally on the no ise level set in the model basis.