Constrained optimisation and its application to scintigraphy

Any instrument that records data will produce a distorted or degraded version of the input signal. For example, 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 refocusing is called, in mathematical terms, deconvolution. In scintigraphy most workers have implemented deconvolution based on Wiener filtering. The shortcomings of the Wiener method when applied to scintigraphy are identified and an alternative approach to deconvolution using constrained optimisation is presented. The mathematical derivation of the new restoring filter is given in terms of the discrete Fourier transform. The practical implementation of the method on a digital computer is described and, as an example, the result of deconvolving a brain scan is presented.