Dual domain interactive image restoration: basic algorithm

This paper describes a new fast, iterative algorithm for interactive image noise removal. Given the locations of noisy pixels and a prototype image, the noisy pixels are to be restored in a natural way. Most existing image noise removal algorithms use either frequency domain information (e.g. low pass filtering) or spatial domain information (e.g median filtering or stochastic texture generation). However, for good noise removal, both spatial and frequency information must be used. The existing algorithms that do combine the two domains (e.g. Gerchberg-Papoulis and related algorithms) place the limitation that the image be band-limited and the band limits be known. Also, some of these may not work well when the noisy pixels are contiguous and numerous. Our algorithm combines the spatial and frequency domain information by using projection onto convex sets (POCS). But unlike previous methods it does not need to know image band limits and does not require the image to be band-limited. Results given here show noise removal from images with texture and prominent lines. The detailed textures as well as the pixels representing prominent lines are created by our algorithm for the noise pixels. The algorithm is fast, the cost being a few iterations (usually under 10), each requiring an FFT, IFFT and copying of a small neighborhood of the noise