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本文从大多数图象符合指数自相关函数的假设出发,推出数字图象的数学模型,并证明其自相关阵是一个正定阵。在此基础上导出一个适合于卡尔曼滤波的动态方程。为了比较符合图象的真实情况,在滤波的过程中,本文对计算方法作了改进,采取从左到右,再从右到左的连续递推的复原顺序,在一定程度上解决了图象处理中的左边缘效应问题,并从节省计算量的角度出发,采用了稳态滤波的方式。最后在uNIVAC1100型计算机上对这些方法进行了验证。从仿真的结果来看,不论在主观质量上还是在客观质量上(功率谱)都比较好。
Starting from the assumption that most of the images meet the exponential autocorrelation function, this paper presents a mathematical model of digital images and proves that the autocorrelation matrix is a positive definite matrix. On this basis, a dynamic equation suitable for Kalman filtering is derived. In order to compare with the real situation of the image, in the process of filtering, this paper improves the calculation method, and adopts the recursion order of recursion from left to right and from right to left to some extent to solve the problem of image In the process of the left edge of the problem, and from the perspective of saving the amount of computation, using a steady-state filtering approach. Finally, these methods were verified on the uNIVAC1100 computer. From the simulation results, both in subjective quality and objective quality (power spectrum) are better.