Scanning singular-value-decomposition method for restoration of images with space-variant blur
David A. Fish, Jan Grochmalicki, Edward R. Pike · Journal of the Optical Society of America A · 1996
We present a method that can efficiently restore large images, blurred possibly nonuniformly and contaminated with noise, by use of a scanning singular-value-decomposition (SVD) method. Such an approach bypasses the prohibitive storage and speed limitations of the SVD method, thus, to our knowledge for the first time, making possible the restoration of reasonably sized images. We make use of the linear and local nature of the point spread function (PSF) to scan the image and restore it in the same raster without incurring blocking effects that are due to the overlap in neighboring reconstruction areas. The increase in speed compared with the conventional SVD approach can be many orders of magnitude, depending on the ratio of the point-spread blur to the image size. For example, if the linear extent of the PSF is one-eighth that of the image, a speed-up factor greater than 106 is achieved. A similar but less accurate solution to the problem of spatially variant blur by use of scanning Fourier transforms, which allows an even faster solution, is also described.