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R.L. de Queiroz and T. D. Tran, "A fast lapped transform for image coding," in Proc. IS&T/SPIE Syrup. on Electronic Imaging, Image and Video Communications and Proces,ing, 2000.

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An Adaptive Lapped Biorthogonal Transform and Its.. - Tanaka, YAMASHITA (2002)   (Correct)

....spanned by the overlapping basis functions and by the non overlapping basis functions are orthogonal. However, no work has been done on biorthogonalization of the ALT, although it has been reported that biorthogonal lapped transforms result in higher coding efficiency than orthogonal ones [14, 20, 21]. Also, in the privious work [16, 19] centers of symmetry of the long and short basis functions of the ALT are not aligned, we cannot use the symmetric extension method at the image boundaries, where special transforms should be required. Therefore, the scanning method for transform coefficients ....

....method [22, 23] at image boundaries when we transform an input image. In Section 2, we formulate a general form of a one dimensional lapped biorthogonal transform with variable length basis functions (VLLBT) In the field of filter banks, a linear phase version of the VLLBT has been introduced [21], but we provide a vector matrix form, which is easily extended to a 2 D non separable form and is not limited to linear phase. In Section 3, in order to construct non overlapping basis functions, we review the subspace Karhunen Loave transform (SKLT) 24 26] that provides the optimal ....

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R.L. de Queiroz and T. D. Tran, "A fast lapped transform for image coding," in Proc. IS&T/SPIE Syrup. on Electronic Imaging, Image and Video Communications and Proces,ing, 2000.


A Lapped Biorthogonal Transform Adapted for Local.. - Tanaka, al.   (Correct)

....subspaces spanned by the overlapping basis functions and by the non overlapping basis functions are orthogonal. However, no work has been done on biorthogonalization of the ALT, although it has been reported that biorthogonal subband systems result in higher coding efficiency than orthogonal ones [5]. In that work, furthermore, centers of symmetry of the basis functions of the ALT are different, we cannot use the symmetric extension method at the image boundaries, where special transforms should be required. At image boundaries, we must prepare special transform matrices. Therefore, the ....

....functions are symmetric or antisymmetric, then the basis function s center of symmetry are aligned. In the context of linear phase perfect reconstruction filter banks, this transform can be regarded as particular cases of the generalized lapped biorthogonal transform with variable length functions [5]. We will use the term LBT with variable length (VLLBT) to refer to the proposed transform. Substituting (6) and (7) into the LBT conditions (3) and (4) we obtain the following conditions: The long basis functions of the VLLBT are required to be biorthogonal, and the overlapping parts of the ....

R. L. de Queiroz and T. D. Tran, "A fast lapped transform for image coding," in Proc. IS&T/SPIE Symp. on Electronic Imaging, Image and Video Communications and Processing, 2000.

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