| The dissertation has four parts. In the first part, we restore degraded spatial patterns by using a modified version of the simulated annealing algorithm. Jumping probabilities of the annealing algorithm are incorporated without randomization. The convergence of our algorithm is proven under a practical annealing schedule. The same idea is also implemented to improve the performance of other modifications of simulated annealing. These include forcing color proportions in an image, using posterior marginals and incorporating an edge process. We also study non-linear presmoothing of the observations.; In the second part, we show how to endow a clustering routine with information derived from prior restoration of clustering data. Restoration is performed by treating clustering data as an image. The number of clusters, their locations, sizes, and shapes are incorporated into subsequent clustering by a standard technique. In this work we use possibilistic K-means clustering.; Next, we describe how the modification paradigm can be used to restore images consisting of specific features, such as cracks or clusters. In particular, the technique is applicable when the specific feature takes place with a specified prior probability.; Last, we propose three approaches to distinguish a shape of a galaxy formation. The first one treats the problem as that of restoration of special features. The other two are based on standard statistical procedures which are a likelihood ratio test and the principle component analysis. |
