基于Hessian核范数正则化的快速图像复原算法

利用Hessian核范数进行图像复原是目前较好的高阶正则化方法,但是由于Hessian核范数正则项的高度非线性和不可微性,图像去模糊和去噪过程耦合度高,求解算法的复杂度高.本文利用变量分裂设计了一种具有闭解形式的交替迭代最小化快速图像复原算法,将图像去模糊、去噪分步进行,并给出算法的收敛性证明.实验结果表明,本文方法不仅在峰值信噪比方面优于原有的基于Hessian核范数图像复原的主优化(Majorization-Minimization,MM)方法,而且大大降低了算法的迭代次数和运行时间.

A Fast Algorithm for Image Restoration Based on Hessian Nuclear Norm Regularization

Recently, the Hessian Nuclear norm regularization method has been a preferable higher order regularization scheme for image restoration, but with the Hessian Nuclear norm regularization term been highly non-linear and non-differentiable, image deblurring and denoising processes are highly coupled so that their minimization algorithms are with highly computational complexity.In this paper, we employ variable splitting to design a fast alternating iterative minimization algorithm with closed-form solutions for image restoration, in which we separate image restoration into image deblurring and denoising.Furthermore, we show the convergence of our proposed algorithm.Finally, experimental results demonstrate the effectiveness of the proposed method which consists in not only giving the improved performance in terms of peak signal to noise ratio (PSNR), but also exhibiting a much faster convergence rate than the previous majorization-minimization (MM) method for Hessian Nuclear norm regularization based image restoration.