Maximum entropy deconvolution of low count nuclear medicine images

We address the use of the maximum entropy (ME) algorithm of Skilling and Bryan (1984) for image restoration of low count nuclear medicine scintigrams. Although such data obeys Poisson statistics we show that assigning an error of √n to a count of n events is misleading. A simple modification, σ=√(n+1.3), should result in improved restorations and also deals with the problem that arises when n=0. A still better iterative method for assigning errors in low counts is suggested and is shown to produce the exact results predicted by combining Poisson statistics and a Bayesian interpretation of the ME approach. The technique also incorporates the preservation of the total counts. The application of this method to low count scintigrams is presented and improvements in image quality are found. A comparison with using a smoothing filter is included