A major challenge in thoracic PET imaging is respiratory motion, which degrades image quality to the extent that it can affect subsequent diagnosis and patient management. This paper presents an approach to overcoming this problem using a deformable registration algorithm for respiratory gated PET images. Registration is based entirely on PET images without increasing the radiation burden. A Markov random field regularizer is introduced to the registration, which penalizes noisy deformation fields. Experimental results on both simulated and real data show that regularized registration effectively suppresses the noise in images, yielding satisfactory deformation fields. In addition, motion correction using the registration algorithm significantly improves the quality of PET images.