Adaptive multidimensional perfect reconstruction filter banks using McClellan transformations

A technique for the design of 2D nonseparable perfect reconstruction filter banks is developed where the isopotentials of the frequency response can be optimized and adapted to local signal statistics. By employing existing odd-length symmetric perfect reconstruction filterbanks as the 1D normal filters for a 2D filter parameterized by the McClellan transformation, conditions under which the resulting 2D filter bank retains the perfect reconstruction property are derived. A two-parameter transformation function is developed whose optimization involves a simple constrained least-squares problem in which the feasible set lies on a circle. The results have practical applications in many areas of image and video processing where multirate filterbanks are used