Positron emission tomography (PET) imaging is used to track biochemical processes in the human body. PET image quality is limited by noise and several methods have been implemented to improve the quality. Kernel-based image reconstruction is among the methods implemented to increase PET image quality and commonly uses a Gaussian kernel. Unfortunately, the Gaussian kernel tends to smooth details in the reconstructed image. To reduce noise without losing contrast details, a different kernel is needed. This work gives an overview of Gaussian kernel PET image reconstruction and focuses on finding substitutes for the Gaussian kernel that tackles its shortcomings. A wavelet kernel can be more efficient than the Gaussian kernel in reducing noise while keeping contrast details by better separating signal from noise and thus it does not over smooth peak values in the final reconstructed images. In this thesis, a wavelet kernel was first applied on prior information derived from dynamic PET series, and its usefulness has been evaluated using simulated brain data, physical phantom data and patient data. Reconstruction results are presented and discussed in detail comparing the wavelet kernel method with the Gaussian kernel method. In the next step, using magnetic resonance (MR) information as prior information for kernel-based PET image reconstruction, the wavelet method is improved and extended by proposing a multi-scale wavelet kernel. This method identifies the directionality in the MR image and includes that information for kernel construction as well. Methods developed in this thesis allow for higher SNR in the reconstructed PET image while preserving contrast. They also produce reconstructed PET images with higher visual quality compared to Gaussian kernel methods.