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中文摘要：
为了获得质量更好的插值图像，提出了一种新的C^2。连续的支撑区间为（-2，2）的三次多结点样条插值核函数．通过增加结点带来的自由度构造了多结点样条插值公式；分析了在适当的边界条件和约束下三次多结点样条插值的逼近阶；将一维多结点样条插值算法推广到二维，建立了用于图像数据的插值公式；如果忽视图像的局部特征，通常双三次多结点样条插值图像的边缘会有模糊的现象，为此。对多结点样条插值应用逆梯度，得到了自适应多结点样条插值算法；实验所得误差图像和实验所得图像的峰值信噪比也证实了用自适应多结点样条插值算法重建的图像具有更高的质量．
英文摘要：
In order to obtain an interpolated image with a superior quality, a new C2 cubic many-knot spline interpolation kernel function with compact support （-2,2） is presented. The cubic many-knot spline interpolation formula is constructed via degrees of freedom from inserting knots. The approximation order of the interpolation with the appropriate boundary conditions and constraints is analyzed. The onedimensional many-knot splines interpolation algorithm is extended to that of two dimensions, which is applied to image processing. In general, images interpolated by the bicubic many-knot spline interpolation are blurred in the edge regions as a result of ignoring the local features of the images. In order to solve the problem of blurring in the edge regions, an adaptive interpolation method is presented based on applying an inverse gradient to the above bicubic many-knot spline interpolation formula. The experiment results are presented to show that the adaptive interpolation algorithm produces a reconstructed image with a superior quality than the conventional bicubic convolution method and the adaptive bicubic convolution method in terms of error and PSNR.
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