Evaluation of Scanning Procedures on Terms of Information Theory

While a number of efforts have been made to analyse scanning procedures in terms of information theory, the formulation of scanning resolution using modulation transfer has enlarged the scope and flexibility of the subject and provided additional avenues of approach. It becomes possible to compute the amount of information which can be transmitted in any space frequency component of the image in the presence of the statistical fluctuation of radioactive decay. Manipulation of scanning data by background subtraction, contrast enhancement, data blending, spatial filtering, et cetera, either reduces the information density in the scan or leaves it unchanged, but never increases it, and under conditions where viewing and read-out parameters are not controlling factors, the information density appears to be a basic limitation on the attainable scanning image quality. The basic formulation assumes an information cell in the image as one square wave length of the space frequency component concerned. The received message is defined as the difference between the counts collected in the high half of the cell: 0 to π and in the low half: π to 2π. The transmitted message, unperturbed by statistical fluctuation (noise) is the same difference expressed as a true mean count. Shannon's expression for the transmission of information in the presence of noise may then be applied: I = (H(y) - HX(y)); that is, the transmitted information is equal to the entropy of y, the received message, minus the entropy of y, when x, the transmitted message, is known. This leads to a simple expression in mean count density, system modulation transfer function, and space frequency which is closely related to the statistical figure of merit proposed by Dewey and Sinclair, and by Beck. The response to a sine wave test pattern with constant average count density and unit modulation provides an instrumental performance criterion in which actual scans and computed information densities correlate in a meaningful way, and system optimization in terms of information density determines uniquely the space frequency, collimator radius of view, and mean count density. The extension of this method of analysis to real objects appears reasonable and possible. (author)