Boundary operation of 2-D non-separable oversampled lapped transforms

This paper proposes a boundary operation technique of 2-D non-separable oversampled lapped transforms (NSOLT). The proposed technique is based on a lattice structure consisting of the 2-D separable block discrete cosine transform (DCT) and non-separable redundant support-extension processes. The atoms are allowed to be anisotropic with the oversampled, overlapping, symmetric, real-valued, and compact-support property. First, the blockwise implementation is developed so that the atoms can be locally controlled. The local control of atoms is shown to maintain perfect reconstruction. This property leads an atom termination (AT) technique as a boundary operation. The technique overcomes the drawback of NSOLT that the popular symmetric extension method is invalid. Through some experimental results, the significance of AT is verified.