Separation of superimposed images with subpixel shift.

The problem of the separation of superimposed images is considered in the particular case of a steady background and a foreground that is composed of different patterns separated in space, each with a compact support. Each pattern of the foreground may move in time independently. A single pair of these superimposed images is assumed to be available, and the displacement amplitude is typically smaller than the pixel size. Further, assuming that the background is smoothly varying in space, an original algorithm is proposed. To illustrate the performance of the method, a real test case of X-ray tomographic radiographs with moving patterns due to dust particles or surface scratches of optical elements along the beam is considered. Finally an automatic and simple treatment is proposed to erase the effects of such features.