Construction, Restoration, and Enhancement of 2 and 3-Dimensional Images

Abstract
The construction of an image function from the physically measured projections of some object is discussed with reference to the least squares optimum filters, originally derived to enhance the signal-to-noise ratio in communications theory. The computerized processing associated with tomography is generalized so as to include 3 distinct parts: the construction of an image from the projection information, the restoration of a blurred, noisy image, degraded by a known space-invariant impulse response, and the further enhancement of the image, e.g. by edge sharpening. In conjuction with given versions of the popular convolution algorithm, not to be confused with filtering by a 2-dimensional convolution, we consider the conditions under which a concurrent construction, restoration, and enhancement are possible. Execution speeds are compared. ** Department of Electrical Science and Engineering, School of Engineering, University of California, Los Angeles, California 90024