Quaternionic approach to the one-regular eight-band linear phase paraunitary filter banks

Besides perfect reconstruction and linear phase, regularity is a desirable essential property of filter banks for image coding as it is associated with the smoothness of the related wavelet basis. This paper shows how to constrain quaternionic factorizations of eight-band linear phase paraunitary filter banks to have the first regularity structurally imposed. The result is not very general but some facts make it notable. Firstly, these systems are a direct extension of the standard eight-point discrete cosine transform (DCT) and this facilitates practical applications. Secondly, the first regularity eliminates the DC leakage which cause visually annoying checkerboard artifact. Finally, our solution offers clear advantages over the known ones as the regularity conditions are formulated directly in terms of quaternionic lattice coefficients. Namely, both regularity and losslessness can be easily preserved regardless of coefficient quantization unavoidable in finite-precision implementations.