This paper proposes a boundary operation technique of 2-D nonseparable linear-phase paraunitary filter banks (NS-LPPUFBs) for size limitation. The proposed technique is based on a lattice structure consisting of the 2-D separable block discrete cosine transform and nonseparable support-extension processes. The bases are allowed to be anisotropic with the fixed critically subsampling, overlapping, orthogonal, symmetric, real-valued, and compact-support properties. First, the blockwise implementation is developed so that the basis images can be locally controlled. The local control of basis images is shown to maintain orthogonality. This property leads a basis termination (BT) technique as a boundary operation. The technique overcomes the drawback of NS-LPPUFBs that the popular symmetric extension method is invalid. Through some experimental results of diagonal texture coding, the significance of the BT is verified.
In this paper, theoretical properties of deinterlacer banks are analyzed. Deinterlacer banks are novel filter banks in the sense that a progressive video sequence is separated into two progressive video sequences of a half frame rate and, furthermore, interlaced sequences are produced as intermediate data. Unlike the conventional filter banks, our deinterlacer banks are constructed in a way unique to multidimensional systems by using invertible deinterlacers, which the authors have proposed before. The system is a kind of shift-varying filter banks and it was impossible to derive the optimal bit-allocation control without any equivalent parallel filter banks. This paper derives an equivalent polyphase matrix representation of the whole system and its equivalent parallel structure, and then shows the optimal rate allocation for the deinterlacer banks. Some experimental results justify the effectiveness of the optimal rate allocation through our theoretical analysis.
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