In biological imaging of thoracic tumors using FDG-PET, blurring due to breathing motion often significantly degrades the quality of the observed image, which then obscures the tumor boundary. The effect could be detrimental in small lesions. We demonstrate a deconvolution technique that combines patient-specific motion estimates of tissue trajectories with wavelet decomposition to compensate for breathing-motion induced artifacts. The lung motion estimates were obtained using a breathing model that maps spatial trajectories in CT data as a function of tidal volume and airflow measured by spirometry. Initial results showed good improvement in the spatial resolution, especially in the direction of major lung motion (craniocaudal) on phantom data as well as on clinical data with large or small tumors.