基于L_p稀疏正则的图像去模糊方法研究

Research on Blind Image Deblurring Based on L_p Regularization Method

在图像去模糊问题中,图像的模糊核估计是重中之重.通常图像的梯度服从重尾分布这一先验被广泛的运用于图像的模糊核估计中,然而受限于非凸优化的数值求解方法,人们往往采用图像梯度的L1范数或者L2范数来近似,从而构造出计算较为简单的凸优化能量函数来估计模糊核.为此,本文提出一种基于Lp稀疏正则的非凸优化的模糊核估计方法,该方法以服从超拉普拉斯分布的图像梯度的Lp范数为稀疏先验项,有效的提高了先验知识的准确性的同时增强图像的强边缘,抑制了细小边缘对模糊核估计的影响.在对Lp范数的数值求解问题中,本文采用GISA(generalized iterated shrinkage algorithm)可以简单且有效的求得任意p值下的最优解.实验表明与传统方法相比,本文方法有效地提升图像的质量,去模糊后的图像更加清晰.

Kernel estimation is the core problem of blind image deblurring. Usually, image gradient obeying heavy-tailed distribution as a priori knowledge is widely used in kernel estimation. Unfortunately, it is difficult solved as a non-convex optimization. Typically, the heavy-tailed distribution can be well modeled by a hyper-Laplacian distribution. In this paper, a kernel estimation method for Lp sparse regularization is proposed. Under the MAP framework, the Lp regularization of image gradient obeys the hyper-Laplacian distribution, which can improve the accuracy of kernel estimation. At the final non-convex optimization, the generalized iterated shrinkage algorithm is extended for Lp minimization with any p value. Compared with the traditional method, the new method can effectively improve the image quality, and the deblurred image is clearer.