Imaging distribution of radioactivity within the human body: I. Theoretical considerations in optimum data processing

This paper is concerned with the application of certain techniques of statistical communication theory to determine an optimum method of data processing designed to minimize the effects of errors on the fidelity of measurement of the activity distribution. The analysis is applied to the two-dimensional case and is concerned primarily with how well ideal (theoretical) scanning systems could perform. Fidelity of imaging is measured by how well (on the average) the output image matches the activity distribution in the “best least squares fit” sense and the analysis is concerned primarily with prescribing that linear, homogeneous data processor which leads to maximum fidelity in the above sense. The analysis leads to an explicit expression for the optimum data processor (i.e., “filter”) and for the expected mean square error in terms of the autocorrelation function of the activity distribution, the collimator point, response function, and the expected total of detected photons. Application of the theory is illustrated by several numerical examples, including a comparison between optimum filters and gaussian filters.