Abstract: 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.