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.

This work is a task-oriented quantitative analysis to assess the best range of reconstruction algorithms parameters which are most suited for quantitative PET imaging of the brain. Starting from a general iterative weighted-least squares objective function, well-known methods such as the Maximum Likelihood Expectation Maximization (MLEM), the Image Space Reconstruction Algorithm (lSRA) and related techniques are obtained. A detailed analysis was done for single-frame imaging as well as a comprehensive study on the impact of post-smoothing by applying a Gaussian convolution kernel at each and every possible post-reconstruction iteration number in order to achieve the lowest mean absolute error (MAE). It has been clearly demonstrated that an appropriate choice of iteration number and post-smoothing level makes most algorithms deliver similar MAE within an interval of 5%, with a considerable reduction of the MAE in comparison to non-optimized reconstructions. Also, reconstruction method performance was influenced by the total number of counts and the activity distribution, meaning that each radiopharmaceutical is not always best reconstructed by the same method. Broadly speaking, MLEM with a point spread function (PSF), [SRA PSF with smoothed expected data as weighting factors and filtered backprojection (FBP), when applied with a suitable level of post smoothing, were the methods offering the best quantitative images and from these three methods, FBP offered the most robust performance for a broad range of post-smoothing levels. An appropriate choice of iteration number and post-smoothing level for a task-oriented analysis significantly lowered the MAE in comparison with the standard practice of using default fixed numbers of iterations and/or post-smoothing.