Abstract: For the requirement of fast restoration of the turbulence-degraded image with complex background in space flight craft imaging system，the theory of 2-D convolution，and construct a shift operator are studied.A fast restoration algorithm for the two neighboring frames of turbulence-degraded images based on the theory of 2-D convolution and shift operator is proposed，which incorporating the minimization of the second-order weighted differences in the process of the restoration for the turbulence-degraded images.Some second-order weighted difference items are defined，and a fast method to construct the matrix of the weighted second-order operator is derived.The values of the point spread function can be solved by converting their non-linear estimation into fast solution of linear equations based on lagged iterative technique，and it provides a quickly and effect method for the restoration for the turbulence-degraded image with complex background.The experiment results show that，the proposed algorithm is effective，stable and fast for the restoration of turbulence-degraded image in real situation.

Key words: turbulence-degraded image, image restoration, shift operator, second-order weighted difference

摘要： 针对航天飞行器成像系统大气湍流扰动条件下退化图像的快速复原需求，对二维卷积理论进行了探讨，构造了移位算子。提出了基于二维卷积理论和移位算子的复杂背景图像大气湍流退化图像的相邻帧快速复原算法，该算法主要将基于二阶的加权差分极小作为空间相关性约束应用在湍流退化图像的复原校正过程中，自定义几个二阶加权差分项，推导了二阶加权差分算子矩阵快速构造的理论方法。在此基础上，将点扩展函数的非线性估计转化为基于递归迭代的线性方程快速求解，为大气湍流干扰所引起的退化图像的复原校正提供了一种快速的有效方法。实际场景大气湍流退化图像的复原校正实验结果表明，该方法对湍流退化图像的复原效果好，且算法稳定，速度较快。

关键词: 湍流退化图像, 图像恢复, 移位算子, 二阶加权差分