  Motion, e.g., due to patient movement or improper device calibration, is
inevitable in many imaging modalities such as photoacoustic tomography (PAT) by
a rotating system and can lead to undesirable motion artifacts in image
reconstructions, if ignored. In this paper, we establish a hybrid-type model
for PAT that incorporates motion in the model. We first introduce an
approximate continuous model and establish two uniqueness results for simple
parameterized motion models. Then we formulate the discrete problem of
simultaneous motion estimation and image reconstruction as a separable
nonlinear least squares problem and describe an automatic approach to detect
and eliminate motion artifacts during the reconstruction process. Numerical
examples validate our methods.
