Image filtering using multiresolution representations

It is shown how multiresolution representations can be used for filter design and implementation. These representations provide a coarse frequency decomposition of the image, which forms the basis for two filtering techniques. The first method, based on image pyramids, is used for approximating the convolution of an image with a given mask. In this technique, a filter is designed using a least-squares procedure based on filters synthesized from the basic pyramid equivalent filters. The second method is an adaptive noise reduction algorithm. An optimally filtered image is synthesized from the multiresolution levels, which in this case are maintained at the original sampling density. Individual pixels of the image representation are linearly combined under a minimum mean square error criterion. This uses a local signal-to-noise ratio estimate to provide the best compromise between noise removal and resolution loss