Regularization Methods for Positron Emission Tomography

University Of Montana, Missoula MT

Investigators

Abstract

It has been well-established in the positron emission tomography (PET) literature that statistical imaging algorithms for tracer density reconstruction are superior to fully analytic methods, such as filtered back projection. However, statistical imaging methods require some form of regularization, which is usually implemented in one of two ways: via the truncation of an iterative method applied to the maximum likelihood estimation problem, or by solving a penalized maximum likelihood (PML) problem. The investigator's focus in this proposal is on the later approach. PML methods are attractive because they allow for the incorporation of prior information via the choice of the regularization function. One of the investigator's main objectives in this proposal is the development of edge-preserving regularization functions for PET stemming from discretized diffusion operators. Edge-preservation in PET is important due to the fact that tracer densities change abruptly at tissue boundaries. However, a main issue with the PML approach is the need for methods for choosing the regularization parameter. A second main objective of this proposal is the development of regularization parameter choice methods for PET. Finally, a statistical analysis of the resulting reconstructions is a goal of the work. Most Americans are familiar with the terms 'X-ray', 'CAT scan', and 'MRI'. Indeed, the use of machines to view the interior of the human body is so commonplace in this day-and-age that the challenging mathematics and computation behind their use is largely unknown and unappreciated. In this proposal, the investigator seeks to improve upon existing computational methods for the medical imaging modality known as positron emission tomography (PET). In PET, which is often used in cancer diagnostics, the patient ingests a substance called a tracer that concentrates in various regions throughout the body. The tracer then radioactively decays, resulting in the emission of photons (i.e. light) outside of the body. The PET machine counts the emitted photons and then reconstructs the amount of tracer at each location within the patient. In this proposal, the investigator focuses on the development of computational methods for PET that yield higher resolution reconstructions than current approaches.