傅里叶域与小波域的联合去模糊算法在低噪声时具有优越的恢复效果, 但是这种联合去模糊算法并不适用于含噪声的模糊图像.为了解决这一问题, 本文将先验约束分别引入傅里叶域的去模糊步骤和小波域的去噪步骤.在傅里叶域, 用矩阵形式表示目标函数.对目标函数添加平滑约束并且通过噪声水平和模糊图像高频信息计算得到平滑约束项的滤波系数.同样方式, 在小波域对小波域目标函数添加能量约束, 实现小波域目标函数的正则化过程.分析傅里叶域的噪声放大程度, 通过傅里叶域的滤波系数计算得到小波域能量约束的滤波系数.傅里叶域的平滑约束可以抑制滤波过程中噪声的产生, 小波域的能量约束可以提高小波域滤波的鲁棒性.仿真实验表明, 改进的算法相比于原始算法具有更好的鲁棒性, 可以有效提高图像的恢复质量.对于噪声标准差为0.01~0.1的模糊图像, 改进算法恢复图像峰值信噪比比原始算法恢复图像的峰值信噪比高1左右.并且改进算法对于高斯型点扩散函数误差具有鲁棒性, 当点扩散函数估计方差与实际方差相差0.4时, 改进算法的恢复效果仍优于原始算法.

Fourier and Wavelet domain based on deconvolution algorithm has a massive superiority over others when the noise level of blurred image is low. However, this kind of method will lead to a bad result when the blurred image is noisy. In this paper, to solve this problem, two constrained terms were introduced into Fourier domain filter and Wavelet domain filter correspondingly. In Fourier domain, the objective function was performed in a matric form and was added with Laplacian regularization. The parameter of this regularization term was computed from the noise power and the power of high frequencies. Similarly, the objective function in Wavelet domain was equipped with power constrain and the parameter of power constrain term was a function of the parameter of Laplacian regularization term. The Laplacian regularization term reduced the power of error caused by Fourier domain and the power constrain enhanced the anti-noise ability of Wavelet domain filter. Experiments showed that the improved algorithm led to a better results with stronger robustness. The peak signal to noise ratio of the improved algorithm was averagely 1 more than the number of initial algorithm, when the standard deviation of noise ranged from 0.01 to 0.1. And the robustness to point spread function was shown. Even when the variance of Gaussian point spread function deviated about 0.4 away from the ground truth, the peak signal to noise ratio of the improved algorithm was higher than the number of initial algorithm.