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M.H. Yaou, W.T. Chang, "Fast Surface Interpolation using Multiresolution Wavelet Transform," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 7, pp. 673688, July, 1994.  
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@article{ 10.1109/34.297948, author = {M.H. Yaou and W.T. Chang}, title = {Fast Surface Interpolation using Multiresolution Wavelet Transform}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {16}, number = {7}, issn = {01628828}, year = {1994}, pages = {673688}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.297948}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Fast Surface Interpolation using Multiresolution Wavelet Transform IS  7 SN  01628828 SP673 EP688 EPD  673688 A1  M.H. Yaou, A1  W.T. Chang, PY  1994 KW  interpolation; convergence of numerical methods; wavelet transforms; signal processing; surface interpolation; multiresolution wavelet transform; large sparse linear equation system; convergence; multiresolution basis transfer scheme; interpolation basis; QMF matrix pair; preconditioner; frequency domain VL  16 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
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 lowfrequency and highfrequency portions in the frequency domain. It has been indicated that the convergence rate of the interpolated surface is dominated by the lowfrequency portion. With this frequency domain decomposition, the lowfrequency 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.
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