Abstract: For noise reduction in a two-dimensional image it is sampled according to a regular array of window sampling positions. The image function is then subjected to multiplication by a window function and conversion to a weighted sum of polynomials according to ascending order. If the next-m-lowest order coefficient signals a sufficient intensity variation in the window, all coefficients are used for subsequent inverse polynomial transform. Otherwise, predominantly only the lowest order coefficient is used therefore. In a cascaded organization, the lowest order coefficient is viewed as itself representing the image information and likewise processed in a forward-inverse polynomial transform organization with respect to an upscaled-size window. The result is then used in a next lower cascade level in lieu of the unprocessed lowest order coefficient itself.