基于多正则化约束的图像去运动模糊

针对图像去运动模糊问题的病态性，已有的方法通常引入对图像的正则化约束从而缩小解空间范围使其良态化，但单一的正则化约束并不能很好地估计点扩散函数和复原原始图像。基于此，本文提出一种基于多正则化约束的图像去运动模糊方法。首先,根据图像梯度符合重尾分布的特性，采用归一化的超拉普拉斯先验项作为对图像先验约束的正则项。其次，分析描述图像运动模糊的点扩散函数的内在特性包括稀疏性和连续光滑性；同时,采用点扩散函数自身的L₁范数保证其稀疏性并作为其中一项点扩散函数先验约束的正则项，采用Tikhonov正则化约束保证其连续平滑性并作为另一项点扩散函数先验约束的正则项，避免估计的点扩散函数中存在孤立的点。由于所建立的正则项虽然不可微但其是非严格凸函数，故引入辅助变量采用分裂法和交替求解法对所建能量方程进行求解，并利用小波软阈值公式求解辅助变量。本文方法对合成的运动模糊图像和实际相机抖动造成的自然模糊图像均进行实验，实验结果验证了该模型和求解算法的有效性和快速性。实验结果表明，本文方法提高了点扩散函数估计准确度，同时提高了复原图像质量，具有较好的复原效果。

Image Motion Deblurring with Multi-regularization Constraints

In order to overcome the ill-posedness of image motion deblurring,the existing algorithms usually introduce regularization constraints to narrow the solution space.However,a single regularization constraint may not be helpful to estimate the point spread function and restore the original image.In this paper,the method based on multi-regularization constraints was introduced for image motion deblurring.Firstly,the normalized Hyper-Laplacian prior on the heavy-tailed distribution of the image gradient was adopted as one regularization term of the proposed algorithm.Secondly,the L₁-norm of point spread function was adopted as one regularized term to constrain the sparseness of point spread function and Tikhonov regularization was used to ensure the sparseness of point spread function as a regularization term to avoid isolated points in point spread function.Thirdly,since the regularization terms are not differentiable and strictly convex function,the auxiliary variables and splitting method were introduced to solve the constructed energy equation.Meanwhile,the introduced auxiliary variables can be solved by soft-thresholding equation.Lastly,the synthesized and real motion blurry images were used to verify the validity and efficiency of the proposed algorithm.The experiments demonstrated that it improved the accuracy of point spread function estimation and the quality of restored images.