A continuation method for emission tomography

The authors offer a framework, deterministic annealing (DA), in which two important technical problems are addressed. One of these problems is associated with the minimization of objective functions composed of both binary and continuous variables. The second concerns local minima. The DA method offers a principled and efficient means of handling the problems associated with mixed continuous and binary variable objectives. The application of the DA method results in a sequence of objective functions (defined only on the continuous variables) whose sequence of solutions approaches that of the original mixed variable objective function. The sequence is indexed by a control parameter (β). At each β, a standard descent optimization algorithm is used to find a solution that is then used as an initial condition for the next setting of β. The energy functions at low β are smooth approximations of the energy functions at higher β. Consequently, it is easier to minimize the energy functions at low β and then track the minimum through the variation of β