Browsing by Author "YAOU, MH"

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FAST SURFACE INTERPOLATION USING MULTIRESOLUTION WAVELET TRANSFORM
(1993)
YAOU, MH
;
CHANG, WT
;
傳播研究所
;
Institute of Communication Studies
FAST SURFACE INTERPOLATION USING MULTIRESOLUTION WAVELET TRANSFORM
(1994-07-01)
YAOU, MH
;
CHANG, WT
;
電信工程研究所
;
Institute of Communications Engineering
Discrete formulation of the surface interpolation problem usually leads to a large sparse linear equation system. Due to the poor convergence condition of the equation system, the convergence rate of solving this problem with iterative method is very slow. To improve this condition, a multiresolution basis transfer scheme based on the wavelet transform is proposed. By applying the wavelet transform, the original interpolation basis is transformed into two sets of bases with larger supports while the admissible solution space remains unchanged. With this basis transfer, a new set of nodal variables results and an equivalent equation system with better convergence condition can be solved. The basis transfer can be easily implemented by using an QMF matrix pair associated with the chosen interpolation basis. The consequence of the basis transfer scheme can be regarded as a preconditioner to the subsequent iterative computation method. The effect of the transfer is that the interpolated surface is decomposed into its low-frequency and high-frequency portions in the frequency domain. It has been indicated that the convergence rate of the interpolated surface is dominated by the low-frequency portion. With this frequency domain decomposition, the low-frequency portion of the interpolated surface can be emphasized. As compared with other acceleration methods, this basis transfer scheme provides a more systematical approach for fast surface interpolation. The easy implementation and high flexibility of the proposed algorithm also make it applicable to various regularization problems.
M-ARY WAVELET TRANSFORM AND FORMULATION FOR PERFECT RECONSTRUCTION IN M-BAND FILTER BANK
(1994-12-01)
YAOU, MH
;
CHANG, WT
;
交大名義發表
;
傳播研究所
;
National Chiao Tung University
The binary wavelet transform is generalized and extended to the M-ary biorthonormal case. The computational equivalence between the discrete wavelet analysis and the M-band multirate signal filtering is indicated. The equivalence allows the perfect reconstruction requirement in a filter bank to be investigated from the vector space decomposition/reconstruction in wavelet analysis. From the construction of the biorthonormal wavelet bases, the necessary and sufficient condition for the filters in a perfect reconstruction filter bank is formulated. Under this formulation, an additional optimization procedure is then used to model the frequency domain requirement in filter bank design.
WAVELET TRANSFORM IN SCATTERING DATA INTERPOLATION
(1993-10-14)
YAOU, MH
;
CHANG, WT
;
傳播研究所
;
Institute of Communication Studies
A fast algorithm for scattering data interpolation is presented. Based on the multiresolution wavelet transform, a preconditioning scheme is proposed to expedite the slow computation speed in the interpolation problem. By applying the wavelet transform before and after any conventional iterative solving method, fast data interpolation can be easily achieved.