Confidence Interval Constraint-Based Regularization Framework for PET Quantization

• Published in: IEEE transactions on medical imaging Vol. 38; no. 6; pp. 1513 - 1523
• Main Authors: Kucharczak, F., Ben Bouallegue, F., Strauss, O., Mariano-Goulart, D.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.06.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Algorithms; Alzheimer Disease - diagnostic imaging; Brain - diagnostic imaging; Competitiveness; Computational modeling; Computer simulation; Confidence Intervals; constrained regularization; Estimation; Humans; Image Processing, Computer-Assisted - methods; Image Processing, Computer-Assisted - statistics & numerical data; Image reconstruction; Interpolation; Kernel; Life Sciences; Phantoms, Imaging; Positron emission; Positron emission tomography; Positron-Emission Tomography - methods; Positron-Emission Tomography - standards; Reconstruction; Regularization; Regularization methods; Statistical analysis; Tomography; total variation; Confidence intervals; Interpolation; TV; Computational modeling; Estimation; Total variation; Constrained regularization; Positron emission tomography; Kernel; Image reconstruction
• ISSN: 0278-0062; 1558-254X
• DOI: 10.1109/TMI.2018.2886431

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.