Confidence Interval Constraint-Based Regularization Framework for PET Quantization

In this paper, a new generic regularized reconstruction framework based on confidence interval constraints for tomographic reconstruction is presented. As opposed to usual state-of-the-art regularization methods that try to minimize a cost function expressed as the sum of a data-fitting term and a regularization term weighted by a scalar parameter, the proposed algorithm is a two-step process. The first step concentrates on finding a set of images that rely on the direct estimation of confidence intervals for each reconstructed value. Then, the second step uses confidence intervals as a constraint to choose the most appropriate candidate according to a regularization criterion. Two different constraints are proposed in this paper. The first one has the main advantage of strictly ensuring that the regularized solution will respect the interval-valued data-fitting constraint, thus preventing over-smoothing of the solution while offering interesting properties in terms of spatial and statistical bias/variance trade-off. Another regularization proposition based on the design of a smoother constraint also with appealing properties is proposed as an alternative. The competitiveness of the proposed framework is illustrated in comparison to other regularization schemes using analytical and GATE-based simulation and real PET acquisition.