The respiratory motion leads to significant motion artifacts of the positron emission tomography （PET） image, thus influencing diagnoses and treatments in the radiation oneology. The existing approaches to correct motion artifacts involve using gating devices and/or four-dimensional （4-D） computed tomography （CT）. However, they have the disadvantages of high CT dose and high computational burden. Hence, a sinusoid vibration model is presented to simulate the respiratory motion. The motion extent and the direction are derived from the Radon transform of the cepstrum of the blurred image. Then, two typical deeonvolution algorithms, i.e. , Wiener filter （WF） and the Richardson-Lucy （RL） algorithms are used to eliminate the motion blur according to the estimated parameters and their de-blurring results are compared. Experiments on both synthetic and phantom images show good performance of the presented model for identifying vibration modeled respiration motion and reducing the motion blur. The method has advantages of safety, convenience, and economy. And it is promising to correct the motion artifacts of the non-gated PET image.
