1. A method of reducing blocking artifacts and/or noise in an image that has been compressed by a block-based encoding process, the method comprising: for a block of image data, for different horizontal and vertical shifts, including no shift in one or both directions: selecting a block of image data according to the shift, directionally forward transforming the block by a forward horizontally selecting transform to form horizontally selected transformed data and by a forward vertically selecting transform to form vertically selected transformed data, the forward horizontally selecting transform being separable to a one-dimensional horizontal forward transform followed by a directional selection operation to select significant ones of the one-dimensionally transformed values, followed by a one-dimensional vertical forward transform, the forward vertically selecting transform being separable to a one-dimensional vertical forward transform followed by a directional selection operation to select significant ones of the one-dimensionally transformed values, followed by a one-dimensional horizontal forward transform; and inverse transforming the horizontally selected transformed data and inverse transforming the vertically selected transformed data; forming a combination of the inverse transformed horizontally selected transformed data and the inverse transformed vertically selected transformed data for the different shifts; filtering the block of image data to form a block of denoised image data; and for each pixel location in the block of image data, combining the formed combination data and the denoised image data according to one or more criteria.