When dealing with motion blur, there is an inevitable trade-off between the amount of blur and the amount of noise. In the light of this trade-off, we study how the restoration performance of a given image deblurring algorithm varies as the blur due to motion develops, and provide a methodology for deriving a statistical model of the restoration performance in case of arbitrary motion.
Our modeling treats the point-spread-function trajectories as random processes and, following a Monte-Carlo approach, expresses the restoration performance as the expectation of the restoration error conditioned on some motion-randomness descriptors and on the exposure time. This allows to coherently encompass various imaging scenarios, including camera shake and rectilinear motion, and, for each of these, identify the specific exposure time that maximizes the image quality after deblurring.