PDE-based Image Restoration and Segmentation and Their Applications to Medical Imagery

Mississippi State University, Mississippi State MS

Investigators

Abstract

The investigator and his colleagues develop novel diffusion-like PDE models and computational methods for image restoration and segmentation of medical imagery acquired from ultrasound, magnetic resonance (MR), computed tomography (CT), positron emission tomography (PET), and single photon emission computed tomography (SPECT) scanners. For restoration, the project investigates various PDE models and related numerical procedures that can effectively preserve and restore important image features, not only fine structures but also slow transitions, for various medical images in 2D and 3D. Given basic models derived from variational approaches, non-variational variants will be developed in order to optimize their performances in image restoration, by integrating noise characteristics and by incorporating appropriate diffusion modulators and dynamic constraint terms. Conventional level set formulations of the Mumford-Shah functional in segmentation work well for essentially binary images; however, they may fail to detect desired edges for general images, due to ambiguity in the computation of the complementary function (the piecewise cartoon image) and the ability to detect smooth boundaries. In order to overcome the difficulty, the project will develop various mathematical and numerical techniques. The innovative models and computational algorithms will broadly impact various other fields, while enhanced knowledge on medical images will institute advancements on medical scanner design. The project develops state-of-the-art algorithms in image restoration and segmentation for medical imagery in both planar and volumetric formats. Although there have been remarkable advancements in medical scanner design, medical images can easily incorporate certain noise and various artifacts. It is extremely important to suppress such artifacts for an accurate medical diagnosis. On the other hand, in various modern medical diagnoses and operations, computer algorithms are being utilized to detect-and-measure body parts automatically; however, these algorithms are yet to be improved for more accurate feature detection. The investigator and his colleagues study various mathematical and computational algorithms in order to enhance the image quality and segment important image features effectively. Besides, the project will advance imaging techniques for the reduction of radiation exposure to the patient at X-ray computed tomography (CT). Here the goal is to keep patient radiation exposures from CT as low as possible while achieving the required image quality and medical benefit. The planned research will have an important impact on improved understanding of the current mathematical image processing techniques, advance knowledge on medical images, and institute advancements on medical scanner design. The research project will support a graduate student and accelerate activities in a research group at Mississippi State University, called the IMage Processing And Computational Techniques (IMPACT) which is organized by the investigator. All developed software will be freely shared with the community.