Modeling the performance of image restoration from motion blur.

When dealing with motion blur there is an inevitable trade-off between the amount of blur and the amount of noise in the acquired images. The effectiveness of any restoration algorithm typically depends on these amounts, and it is difficult to find their best balance in order to ease the restoration task. To face this problem, we provide a methodology for deriving a statistical model of the restoration performance of a given deblurring algorithm in case of arbitrary motion. Each restoration-error model allows us to investigate how the restoration performance of the corresponding algorithm varies as the blur due to motion develops. 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 uniform (rectilinear) motion, and, for each of these, identify the specific exposure time that maximizes the image quality after deblurring.