THE USE OF FINITE IMPULSE RESPONSE KERNELS FOR IMAGE RESTORATION.

Abstract

This dissertation examines the suitability of Display-Processor (DP) image computers for image enhancement and restoration tasks. Because the major architectural feature of the DP devices is their ability to rapidly evaluate finite impulse response (FIR) convolutions, much of the study focusses on the use of spatial-domain FIR convolutions to approximate Fourier-domain filtering. When the enhancement task requires the evaluation of only a single convolution, it is important that the FIR kernel used to implement the convolution is designed so that the resulting output is a good approximation of the desired output. A Minimum-Mean-Squared-Error design criterion is introduced for the purpose of FIR kernel design and its usefulness is demonstrated by showing some results of its use. If the restoration or enhancement task requires multiple convolutions in an iterative algorithm, it is important to understand how the truncation of the kernel to a finite region of support will affect the convergence properties of an algorithm and the output of the iterative sequence. These questions are examined for a limited class of nonlinear restoration algorithms. Because FIR convolutions are most efficiently performed on computing machines that have limited precision and are usually limited to performing fixed-point arithmetic, the dissertation also examines the effects of roundoff error on output images that have been computed using fixed point math. The number of bits that are needed to represent the data during a computation is algorithm dependent, but for a limited class of algorithms, it is shown that 12 bits are sufficient. Finally, those architectural features in a DP that are necessary for useful enhancement and restoration operations are identified.