Fast surface interpolation using multi-resolution wavelet transform

Due to the poor convergence condition of the sparse equation system arising from the surface interpolation problem, the convergence rate for solving this problem with an iterative method is usually slow. To improve this condition, a multiresolution basis transfer scheme based on the wavelet transform is proposed. The effect of the basis transfer is to transform the original interpolation basis into two sets of bases with larger supports while the admissible solution space remains unchanged. With this transfer, a new set of nodal variables results, and an equivalent equation system with a better convergence condition can be solved. The basis transfer can be easily implemented by using a QMF (quadrature mirror filter banks) 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. As compared with other acceleration methods, this basis transfer scheme provides a more systematic approach for fast surface interpolation. The easy implementation and high flexibility of the proposed algorithm also make it applicable to various regularization problems