NEW METHODS OF NONLINEAR DIGITAL IMAGE RESTORATION

Abstract

In this dissertation we develop four new methods for image restoration. The common feature of all these methods is that the object estimates have a nonlinear dependence on the image data and that iterative methods of solution are needed. The restoration algorithms have been compared with some previously developed methods by means of computer simulations. The problem of restoring noisy images where the spread function is known is treated in two ways. First, this restoration problem is regarded as a constrained least squares optimization problem. Different methods of enforcing smoothness on the restoration are considered. It is shown that the use of an arc length penalty function permits better restoration of edges than can be obtained by pure quadratic penalty functions. We also treat some methods for enforcing upper and lower bounds on the restoration. The second approach taken on the known spread function restoration problem is statistical. Here we consider the image forming system as a communication channel in which the unknown object to be estimated is one member from a random ensemble. We propose a new approach to restoration based on maximum entropy methods. This new approach allows one to easily synthesize estimators to comply with various prior constraints the image restorer wishes to impose. We show how this new maximum entropy synthesis procedure relates to previous uses of maximum entropy principles for the restoration problem. The problem of restoring atmospherically degraded images is treated in Chapter 4. Here, in addition to random noise in the image, we are faced with a randomly changing spread function. We formulated two algorithms for restoration that have better noise immunity than any previously proposed methods. Both proposed methods are based on processing a series of short exposure speckle images. The first method is an ad hoc successive least squares estimation procedure which uses the second order moments of the image and the spread function discrete Fourier transforms (DFT). The second method, which performs even better than the first, is a maximum likelihood estimation algorithm to find the object's DFT. The maximum likelihood algorithm uses both the first and second moments of the transfer function and the image's DFT.