DECONVOLUTION USING ORTHOGONAL POLYNOMIALS IN NUCLEAR-MEDICINE - A METHOD FOR FORMING QUANTITATIVE FUNCTIONAL IMAGES FROM KINETIC-STUDIES

Dynamic scintigraphy by means of gamma camera or positron emission tomography (PET) imaging is a tool in nuclear medicine to quantitate physiological and abnormal function in specific organs. But biological processes, not necessarily imaged with the organ, impose fundamental limitations on the power of quantitation. This problem can be formulated as the solution of a convolution-type integral equation, called temporal deconvolution. Solving this equation is difficult due to inevitable noise in the image data. A new deconvolution technique was put forward which utilizes orthogonal polynomials (DOP) and handles inevitable noise in such a way that pixel time activity curves can be deconvolved. This solves the issue of quantitative analysis of serial scintigraphic data in a manner that preserves the high spatial resolution inherent in raw data. In this article a complete mathematical description of the new deconvolution technique is presented. The DOP method is designed for use with an array processor, and results in a set of linear response function (LRF) images. It is also described how to calibrate the measuring devices, and correct for distorted input functions in order to obtain the LRF images in absolute units. A simulation study compares the DOP method with the Fourier transform and the discrete deconvolution algorithm both without and with various noise levels. We also simulated the impact of undesired blood activity simultaneously measured with the organ-target activity on the convergence of the DOP algorithm. © 1990 IEEE