This paper proposes lattice structures for two-dimensional (2-D) non-separable (NS) oversampled (OS) lapped transforms. The proposed systems consist of the 2-D separable discrete cosine transform and NS support extension processes, and allow us to simply realize rational redundancy as well as the overlapping, paraunitary (PU), symmetric, real-valued and compact support property. The lattice structures have two aspects. One is an extention of OS linear-phase (LP) perfect reconstruction (PR) filter banks (FBs) to the 2-D NS case. The other is a generalization of 2-D NS LPPR FBs to the OS case. The significance is verified by showing some design examples and image restoration results with the iterative shrinkage/thresholding algorithm (ISTA).
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