A bstractThis thesis focuses on denoising of positron emission tom ography (PET) data.Cardiac P E T scans generated using a rubidium-82 radiotracer are a convenient, n o ninvasive m ethod of diagnosing heart disease, b u t suffer from a high degree of noise.Denoising methods based on the wavelet transform are capable of outperform ing existing clinical m ethods due to their ability to b etter preserve detail while simul taneously suppressing noise a t multiple scales. We investigate th e applicability of recently developed wavelet denoising m ethods to cardiac P E T data. A comprehen sive set of experiments is performed, in which combinations of these techniques are applied to the different decomposition levels of wavelet coefficients. By doing so, we determine th e relevant im portance of each (and the domain in which it is applied)to the overall quality of the denoised result. W ith this inform ation, we propose P E T denoising protocols th a t substantially improve image quality (for static studies) and lead to b etter measures of myocardial perfusion (for dynam ic studies).