Statistical pixelwise inference models for planar data analysis: an application to gamma-camera uniformity monitoring

Abstract

In this paper two tests based on statistical models are presented and used to assess, quantify and provide positional information of the existence of bias and/or variations between planar images acquired at different times but under similar conditions. In the first test a linear regression model is fitted to the data in a pixelwise fashion, using three mathematical operators. In the second test a comparison using z-scoring is used based on the assumption that Poisson statistics are valid. For both tests the underlying assumptions are as simple and few as possible. The results are presented as parametric maps of either the three operators or the z-score. The z-score maps can then be thresholded to show the parts of the images which demonstrate change. Three different thresholding methods (naïve, adaptive and multiple) are presented: together they cover almost all the needs for separating the signal from the background in the z-score maps. Where the expected size of the signal is known or can be estimated, a spatial correction technique (referred to as the reef correction) can be applied. These tests were applied to flood images used for the quality control of gamma camera uniformity. Simulated data were used to check the validity of the methods. Real data were acquired from four different cameras from two different institutions using a variety of acquisition parameters. The regression model found the bias in all five simulated cases and it also found patterns of unstable regions in real data where visual inspection of the flood images did not show any problems. In comparison the z-map revealed the differences in the simulated images from as low as 1.8 standard deviations from the mean, corresponding to a differential uniformity of 2.2% over the central field of view. In all cases studied, the reef correction increased significantly the sensitivity of the method and in most cases the specificity as well. The two proposed tests can be used either separately or in combination and are capable of showing trends and/or the magnitude of difference between images acquired under similar conditions with high positional and statistical precision. In addition to gamma camera quality control, they could be applied to any pair (or set) of registered planar images to detect subtle changes, e.g. a set of scintigrams or conventional radiographs of a patient before, during and after treatment.