In this paper, we propose a new class of two dimensional (2D) M-channel (M-ch) non-separable filter banks (FBs) based on cosine modulated filter banks (CMFBs) via a new diagonally modulation scheme. Until now, many researchers have proposed 2D non-separable CMFBs. Nevertheless, efficient direction-selective CMFBs have not been yet. Thanks to our new modulations with diagonal shifts, proposed CMFBs have several frequency supports including direction-selective ones which cannot be realized by conventional ones. In a simulation, we show design examples of proposed CMFBs and their various directional frequency supports.

In this paper, a design method of two-dimensional (2-D) orthogonal symmetric wavelets is proposed by using a lattice structure for multi-dimensional (M-D) linear-phase paraunitary filter banks (LPPUFB), which the authors have proposed as a previous work and then modified by Lu Gan et al. The derivation process for the constraints on the second-order vanishing moments is shown and some design examples obtained through optimization with the constraints are exemplified. In order to verify the significance of the constraints, some experimental results are shown for Lena and Barbara image.