Medical diagnosis of diseases such as stroke and Alzheimer's use a medical imaging technique called Positron Emission Tomography (PET). In addition, the process of mapping brain functions also uses a similar imaging technique. The diagnosis of any disease using such a medical imaging modality depends entirely on the quality of the images reconstructed from the raw data. An imaging modality is used to image a human organ and provides raw data for diagnostic purposes. The data has to be converted into meaningful image before the physician can use it for diagnosis. Different imaging modalities use different algorithms for converting the raw data into images, a process termed as image reconstruction. The main goal of the proposed research is to construct improved reconstructed images for better diagnosis. Two specific objectives of this research proposal are: 1) To design a wavelet using the lifting scheme that will provide improved reconstruction as compared with the traditional wavelets. The idea behind this objective is that there exist certain custom designed wavelets which when used can result in improved image reconstruction. The lifting scheme is a unique way of constructing new wavelets from existing ones and can result in wavelets suitable to the task of image reconstruction. 2) To modify the image reconstruction algorithm to perform reconstruction on sinogram data rather than the raw format being currently used. Sinogram of the raw data is achieved by rebinning the data according to the imaging angle with respect to which it was gathered.