A Maximum Likelihood Approach to Transmission Image Reconstruction from Projections

The stochastic nature of the projections used in transmission image reconstruction has received little attention to date. This paper utilizes the joint probability density function of the projections to derive the reconstruction scheme which is optimum in the maximum likelihood sense. Two regimes are examined: that where there is significant probability of a zero count projection, and that where the zero count event may be safely ignored. The former regime leads to a complicated algorithm whose performance is data dependent. The latter regime leads to a simpler algorithm. Its performance, in terms of its bias and variance, has been calculated. It is shown that, for an average number of counts detected in excess of approximately 100 per projection, the image is essentially unbiased, and for counts in excess of approximately 2500 per projection, the image approximately attains the minimum variance of any reconstruction scheme using the same measurements.