Partial volume effects (PVEs) are consequences of the limited spatial resolution in emission tomography. They lead to a loss of signal in tissues of size similar to the point spread function and induce activity spillover between regions. Although PVE can be corrected for by using algorithms that provide the correct radioactivity concentration in a series of regions of interest (ROIs), so far little attention has been given to the possibility of creating improved images as a result of PVE correction. Potential advantages of PVE-corrected images include the ability to accurately delineate functional volumes as well as improving tumour-to-background ratio, resulting in an associated improvement in the analysis of response to therapy studies and diagnostic examinations, respectively. The objective of our study was therefore to develop a methodology for PVE correction not only to enable the accurate recuperation of activity concentrations, but also to generate PVE-corrected images. In the multiresolution analysis that we define here, details of a high-resolution image H (MRI or CT) are extracted, transformed and integrated in a low-resolution image L (PET or SPECT). A discrete wavelet transform of both H and L images is performed by using the "à trous" algorithm, which allows the spatial frequencies (details, edges, textures) to be obtained easily at a level of resolution common to H and L. A model is then inferred to build the lacking details of L from the high-frequency details in H. The process was successfully tested on synthetic and simulated data, proving the ability to obtain accurately corrected images. Quantitative PVE correction was found to be comparable with a method considered as a reference but limited to ROI analyses. Visual improvement and quantitative correction were also obtained in two examples of clinical images, the first using a combined PET/CT scanner with a lymphoma patient and the second using a FDG brain PET and corresponding T1-weighted MRI in an epileptic patient.