对因大气湍流引起的退化图像复原问题, 采用Tikhonov 正则化方法将其归结为一个适定的线性方程组的求解问题。当图像边界满足周期性条件时, 利用二维离散傅里叶变换及其逆变换即可求得复原图像。在求解方程组中, 利用L-曲线准则确定出能够平衡正则化函数和偏差函数的正则化参数, 以得到较为理想的复原结果。仿真结果表明, 当降质图像的噪声方差不是很大时, 该方法能够得到较好的复原效果。

The restoration of degenerated image caused by atmospheric turbulence can be transformed into solving a well-posed linear system by Tikhonov regularization method. When the image boundaries satisfy the periodic conditions, the restored image can be obtained by using two-dimensional discrete Fourier transform and its inverse transform. In order to get a more satisfactory recovery results, the regularization parameter that is able to balance the regularization function and discrepancy function is selected by L-curve criterion. The simulation results show that when the noise variance of the degraded image is not large, a better recovery can be received.