Regularization parameter selection and an efficient algorithm for total variation-regularized positron emission tomography

• Published in: Numerical algorithms Vol. 57; no. 2; pp. 255 - 271
• Main Authors: Bardsley, Johnathan M., Goldes, John
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.06.2011; Springer Nature B.V
• Subjects: Algebra; Algorithms; Computation; Computer Science; Convergence; Density; Mathematical analysis; Mathematical models; Numeric Computing; Numerical Analysis; Original Paper; Parameters; Positron emission; Radioactive tracers; Random variables; Regularization; Synthetic data; Theory of Computation; Tomography; Inverse problems; 65F22; Total variation; 65J22; 65K10; Statistical methods; Regularization parameter selection; Positron emission tomography
• ISSN: 1017-1398; 1572-9265
• DOI: 10.1007/s11075-010-9427-4

In positron emission tomography, image data corresponds to measurements of emitted photons from a radioactive tracer in the subject. Such count data is typically modeled using a Poisson random variable, leading to the use of the negative-log Poisson likelihood fit-to-data function. Regularization is needed, however, in order to guarantee reconstructions with minimal artifacts. Given that tracer densities are primarily smoothly varying, but also contain sharp jumps (or edges), total variation regularization is a natural choice. However, the resulting computational problem is quite challenging. In this paper, we present an efficient computational method for this problem. Convergence of the method has been shown for quadratic regularization functions and here convergence is shown for total variation regularization. We also present three regularization parameter choice methods for use on total variation-regularized negative-log Poisson likelihood problems. We test the computational and regularization parameter selection methods on two synthetic data sets.