For about the last forty years, Positron Emission Tomography (PET) has been used to assess biochemical processes in the human body. Using data obtained from PET scanners, reconstruction algorithms generate images that contain important information about the functionality of an organ or region of interest. This research involves the development of fast, robust reconstruction algorithms that provide accurate PET images. With more accurate images, physicians and researchers will be able to better understand the functionality of vital organs; and subtle differences between healthy and unhealthy tissue would become more distinguishable. The knowledge gained through the research will be shared with both undergraduate and graduate students. In particular, undergraduate students from under-represented groups will be mentored through summer research programs and senior projects. To reconstruct PET images, the investigator is undertaking a two part strategy. First, Poisson noise in the data is reduced using a modified wavelet denoising method. Specifically, a variance stabilizing transformation, known as Anscombe's transformation, is applied to the data to convert the Poisson noise to Gaussian noise with mean zero and variance one. The transformed data is then further processed using a well-known wavelet denoising method due to Donoho and Johnstone. Once the Poisson noise has been reduced, the desired images are reconstructed using set theoretic estimation methods. An advantage of using a set theoretic formulation is that it is flexible enough to incorporate all available a priori information and to address the uncertainty in the transmission data used to correct errors due to attenuation. The resulting algorithms will be tested using real phantom and subject data from PET centers at the Massachusetts General Hospital in Boston, MA and Emory Hospital in Atlanta, GA.
