This thesis describes a method of transforming a deconvolution problem into an equivalent convolution problem. A short discussion of the theory behind convolution and deconvolution is included, along with a survey of techniques now being used. A new method using a synthesized compensator is proposed and mathematically developed. Finally, the results of applying this method to several real and analytical signals are given.

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Thèse en cotutelle : Université Laval, Québec, Canada et Université Félix-Houphouët-Boigny, Abidjan, Côte d'ivoire

Thesis (Ph. D.)--University of Wisconsin--Madison, 1960. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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The adaptation of a general purpose laboratory minicomputer for nuclear medicine imaging is described. Electronic interfaces have been designed and constructed to link nucleonic equipment to a PDP 12 computer. A computer television display system has been developed to facilitate interactive processing of scintigraphic data. The main features of the television system are that it is relatively inexpensive and reliable. A domestic quality receiver has been adapted for use as a colour monitor. Any instrument that records data will produce a distorted or degraded version of the input signal. Generally, imaging equipment will produce a blurred image of the object, and in the case of scintigraphic imaging the blurs may be comparable to the size of the physiological structures being investigated. The process of refocussing the recorded data is called, in mathematical terms, deconvolution. In this study Fourier transform techniques have been developed as methods of implementing deconvolution. It is shown that the restoration of images in the presence of noise is likely to be a mathematically unstable process. Four methods of accommodating the problems associated with noise are described. Each method has built in optimisation of one form or another so that mathematically stable algorithms are used to implement deconvolution. This means that all the parameters used by the computer programs are determined automatically so that the computer operator is not required to select any parameters manually. A brief description of two dimensional digital filtering is given to enable comparison between filtering and deconvolution of scintigrams. A two dimensional lowpass filter is developed which automatically defines the passband frequency response appropriate to a particular scintigram. Finally, all the signal processing methods are tested on both simulated and clinical data. Results show that deconvolution offers advantages over digital filtering particularly for scintigrams obtained from morphic structures. Some of the problems of deconvolving certain types of scintigram are discussed.