Generalization of the image space reconstruction algorithm

The image space reconstruction algorithm (ISRA) has been shown to be a non-negative least squares estimator, and was introduced as an alternative iterative image reconstruction method for positron emission tomography (PET) data. The implementation of ISRA is straightforward: the ratio of the backprojected measured data to that of the backprojected expected data is used to multiplicatively update the current image estimate. This work starts with a modified weighted least squares objective function to derive a more general form of the ISRA algorithm, which importantly accommodates weighting of the backprojection. Simply by changing the choice of backprojection weighting factors at a given iteration, both the well known ML-EM (maximum likelihood expectation maximization) algorithm as well as the standard ISRA, are obtained as special cases. ML-EM corresponds to using the current estimate of the expected data as the weights for backprojection, and ISRA corresponds to the case of unit weighting during backprojection. Of particular interest however, is that the framework naturally suggests the existence of many alternative reconstruction algorithms through alternative data weighting choices. By changing the weighting factors, a performance improvement over ISRA is obtained, as well as a slight performance improvement compared to ML-EM (for the task of accurate region quantification which is considered in this work). Specifically, these improvements are obtained, for example, by using a spatially-smoothed copy of the measured data as weighting factors during backprojection.