General restoration filter for vibrated-image restoration

Mechanical vibrations are often the principal cause of image degradation. Low temporal-frequency mechanical vibrations involve random image degradation that depends on the instant of exposure. Exact restoration requires the calculation of a specific filter unique to each vibrated image. To calculate the restoration filter for each image, one needs the specific optical transfer function unique to the motion in the image. Therefore the instant of exposure and the motion function have to be measured or estimated by some other means. We develop a restoration filter for individual images blurred randomly by low-frequency mechanical vibrations. The filter is independent of the instant of exposure. The filter is designed to give its best performance averaged over a complete ensemble of vibrated images. Although when applying the new filter to any vibrated image the restoration achieved is slightly poorer than that achieved with an exact filter unique to the specific motion function, the new filter has the advantage of simplicity.