2-D non-separable GenLOT with trend vanishing moments

A novel design method of 2-D non-separable linear-phase paraunitary filter banks (LPPUFBs) is proposed. The trend vanishing moment (TVM) condition is newly derived for the lattice structure. The TVM condition can be regarded as a natural extension of 1-D VM to 2-D one and alternative of the conventional directional vanishing moments(DVMs). The structure is based on the 2-D DCT and can be regarded as an extension of GenLOT to the 2-D non-separable case. Because of the non-separability, the bases are allowed to be anisotropic and directional in addition to the fixed-subsampling, overlapping, orthogonal, real-valued, symmetric and compact-support property. As a previous work, the authors have shown that the block-wise implementation is appealing for the image processing application since the technique serves boundary operation for size-limitation, seamless basis alteration and compatibility with the block DCT. This work further contributes to yield the TVM condition so that piece-wise smooth images with smooth contours are compactly approximated. The condition is imposed directly on the design parameters and, therefore, the desirable properties of the lattice structure are maintained. From an experimental result of coding, it is shown that the TVM condition gives smooth reconstruction of a diagonal texture image.