The subject matter of the article is the improvement in the accuracy of multimodal image registration between PET and MRI images in the medical field. The focus of the article pertains to the importance of these images in diagnosis, interpretation, and surgical intervention. This study increased the accuracy of PET/MRI multimodal image registration achieved through a new approach based on the multi-resolution image decomposition. The tasks to be solved are: The study proposes a new method, the fast and adaptive three-dimensional mode decomposition (FATEMD), to generate multi-resolution components for accurate registration. The method used: The study uses the FATEMD approach, which estimates the transformation parameters of the registration from the PET image and the residue of the second level of the MRI image that is obtained after the extraction of the first two tridimensional intrinsic mode functions (TIMFs). The following results were obtained: The proposed method of multimodal registration between PET and MRI images involves the use of the fast and adaptive three-dimensional mode decomposition (FATEMD) approach. This approach was tested on 25 pairs of images from the Vanderbilt database and was found to have improved accuracy compared to the usual method, as shown through comparative studies using measures of mutual information, normalized mutual information, and entropy correlation coefficient. Conclusion. The main objective achieved in the study was to enhance the accuracy of PET/MRI multimodal image registration through the application of the FATEMD decomposition method. This approach is novel compared to traditional methods as it involves estimating the transformation parameters from the PET image and the second level residue of the MRI image, resulting in more precise outcomes as opposed to using just the PET and MRI images alone. The integration of multiple imaging techniques, such as PET and MRI, provides healthcare professionals with a more comprehensive view of a patient's anatomy and physiology, leading to enhanced diagnosis and treatment planning.