中文摘要：

三维体数据场重建是体数据建模与分析的一个非常基础和重要的步骤，重建算法的精度直接决定了数据重采样和后续分析的准确性．文中发展了基于拟插值方法的三维体数据场重建理论，首次提出一种充分利用体数据自身信息与核函数优化相结合的预处理算法．在合理假设的前提下得到重建误差的表述式；然后充分利用三维体数据自身的信息全局优化该误差，使得重建误差在L2意义下达到最小．最后通过丰富的重建实例，显示了文中算法能有效地提高重建精度，并能够更好地保持三维体数据的高频信息．

英文摘要：

3D data field reconstruction is a fundamental and an important step for volume modeling and analysis. The precision of reconstruction affects directly the accuracy of the following process such as data resampling and analysis. Based on the quasi-interpolation theory, we develop a novel estimate of the reconstruction error which fully explores the intrinsic information embedded in the volume data and have arrived at a minimum of the reconstruction error under the L2 measurement by conducting a global optimization. Experimental results on various examples demonstrate the effectiveness of the proposed algorithm in reducing the reconstruction error and retaining the high-frequency details of the .dada field.