State-space blur model for high-speed forward-moving imaging system and its recursive restoration

When an imaging system is approaching the object at a high speed, because of the existence of integration time, the images obtained are always blurred radially. Since the degradation process is space variant, this kind of blur is difficult to handle, traditional frequency domain techniques can't be applied here. Obviously, the radially blurred image obtained is rotation symmetrical, so the usual uniformly sampled image can be resampled with fan-shaped grids, and the gray level of these new sampling points build up a new image matrix. The new image matrix's columns and rows are never the edges of the image, but the image's radius and angle. So, the original two-dimensional problem is simplified. Even after the resampling, the blur is still space variant, and the PSF (point spread function) will change along the radius direction. So the authors come up with a state-space method, a state-space blur model is constructed, which handles the problem recursively. To restore the degraded image simply means to find the inverse of the degradation system and computer simulation result shows the restoration algorithm restored the radially blurred image approvingly.