A new approach to the design of multidimensional nonseparable two-channel orthonormal filterbanks and wavelets

We propose a novel approach to the design of multidimensional nonseparable two-channel orthonormal filterbanks and wavelets, which has been a challenging problem. We perform spectral factorization of the multidimensional product filter by jointly optimizing the product filter and the associated low-pass filter using an iterative algorithm. Our example shows that the resulting filterbanks have negligible reconstruction error and hence can be treated as orthonormal filterbanks and wavelets in practice.