Regularity-constrained pre- and post-filtering for block DCT-based systems

It is well known that the traditional block transform can only have at most one degree of regularity. In other words, by retaining only one subband, these transforms, including the popular discrete cosine transform (DCT), can only capture the constant signal. The ability to capture polynomials of higher orders is critical in smooth signal approximation, minimizing blocking effects. This paper presents the theory, design, and fast implementation of regularity constrained pre-/post-filters for block-based decomposition systems. We demonstrate that simple pre-/post-filtering modules added to the current block-based infrastructure can help the block transform capture not only the constant signal but the ramp signal as well. Moreover, our proposed framework can be used to generate various fast symmetric M-band wavelets with up to two degrees of regularity.