改进的傅里叶域小波域联合去模糊算法

发布时间：2018-05-06 19:20

本文选题：图像复原 + 正则化　；参考：《光子学报》2017年04期

【摘要】：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0.010.1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.
[Abstract]:The joint de-blurring algorithm in Fourier domain and wavelet domain has a superior recovery effect at low noise, but this joint de-blurring algorithm is not suitable for fuzzy images with noise. In order to solve this problem a priori constraint is introduced into the steps of deblurring in Fourier domain and denoising in wavelet domain respectively. In Fourier domain, the objective function is expressed in matrix form. The smoothing constraint is added to the objective function and the filtering coefficient of the smoothing constraint is obtained by calculating the noise level and the high frequency information of the blurred image. In the same way, the energy constraint is added to the objective function in the wavelet domain to realize the regularization process of the objective function in the wavelet domain. The degree of noise amplification in Fourier domain is analyzed and the filter coefficient of energy constraint in wavelet domain is obtained by calculating the filter coefficient in Fourier domain. The smoothing constraint in Fourier domain can suppress the noise in the filtering process, and the energy constraint in wavelet domain can improve the robustness of filtering in wavelet domain. Simulation results show that the improved algorithm is more robust than the original algorithm and can effectively improve the quality of image restoration. For a fuzzy image with a noise standard deviation of 0.010.1, the improved algorithm is about 1 higher than the original algorithm in restoring the peak signal-to-noise ratio (PSNR) of the image. The improved algorithm is robust to the error of Gao Si type point diffusion function. When the estimated variance of the point diffusion function is 0.4 different from the actual variance, the improved algorithm is still better than the original algorithm.
【作者单位】：中国科学院光电研究院计算光学成像技术重点实验室;中国科学院大学;
【基金】：国家自然科学基金(No.61505219)资助~~
【分类号】：TP391.41

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