Comparing maximum likelihood estimation and constrained Tikhonov-Miller restoration

The authors have compared the performance of the EM-MLE and ICTM restorations applied to confocal images. Both methods greatly reduce diffraction-induced distortions of confocal images. Due to their nonlinearity, both are able (partially) to restore data of missing frequencies. From the authors' experiments, it is clear that for their test objects, the EM-MLE algorithm performs much better than ICTM. The EM-MLE algorithm produces better results under all the conditions the authors tested, and with respect to all 3 performance measures (I-Divergence, MSE, GDT) the authors used. Only for high SNR conditions, the MSE performance of ICTM approaches the EM-MLE results. It must be noted that this conclusion is only valid for the type of objects the authors used in their experiments (sparse objects); it may well be that for more dense objects, the situation is different. The poor ICTM performance shows that its functional is not well suited for images distorted with Poisson noise. The authors did not find artifacts such as ringing in the results of either algorithm. The restoration results on the cylindrical objects show, however, that the EM-MLE algorithm has a tendency to reconstruct an image that is sharper and smaller than the original object. This aspect of EM-MLE should be investigated thoroughly. Greander's method of Sieves (1991) seems promising for regularizing the EM-MLE algorithm. Finally, to reduce the computational burden of ICTM and EM-MLE, methods to speed up these algorithms should be investigated more fully.