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Improvement in quantitative data analyses by numerical deconvolution techniques.

Frequently, the data collected in scientific and clinical studies are distorted by the experimental technique or measuring apparatus. The lack of resolution and contrast in nuclear images is a good example of how the distribution of radiotracer within a patient is degraded by the imperfect response of the intrinsic detector and collimator and by in vivo Compton scattering. A second example is that which occurs in first-transit flow studies, where the output time-activity distribution from an organ is altered by an imperfect, finite-width bolus at its input. The manner in which distortions enter these and many other important measurement problems is through a process called convolution. The output function of a convolution is the result of a linear superposition of shifted products of the input function and system response function. In one dimension with time as the abscissa, the convolution integral is written: