Deconvolution using orthogonal polynomials in nuclear medicine: a method for forming quantitative functional images from kinetic studies

A deconvolution technique is described 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 the current work 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. Techniques to calibrate the measuring devices and correct for distorted input functions in order to obtain the LRF images in absolute units are described. A simulation study compares the DOP method with the Fourier transform and the discrete deconvolution algorithm both with and without various noise levels. The impact on the convergence of the DOP algorithm of undesired blood activity simultaneously measured with the organ-target activity was simulated