The feasibility of images reconstructed with the methods of sieves

The concept of sieves has been applied with the maximum likelihood estimator (MLE) to image reconstruction in emission tomography. While it makes it possible to recover smooth images consistent with the data, the degree of smoothness provided by it is arbitrary. It is shown that the concept of feasibility is able to resolve this arbitrariness. By varying the values of parameters determining the degree of smoothness, one can generate images on both sides of the feasibility region, as well as within the region. Feasible images recovered by using different sieve parameters are compared with feasible results of other procedures. One- and two-dimensional examples using both simulated and real data sets are considered