高效的图像超分辨率重建参数估计算法

Efficient Parameter Estimation Algorithm for Super-resolution Image

估计正则化参数的有效方法是计算L-曲线的最大曲率,然而在超分辨率图像重建中,计算L-曲线的曲率代价十分昂贵.提出一种基于截断Arnoldi过程的图像超分辨率重建正则化参数估计算法.该方法将超分辨率重建中的系统矩阵进行截断Arnoldi过程的分解,得出简化的Hessenberg矩阵.借助Galerkin方程可将超分辨率重建方程组转化为与Hessenberg矩阵相关的简化方程组,通过Given旋转变换来快速求该方程组的解.给出了计算L曲率的计算公式.该方法能高效得到正则化参数.

The valid method of regularized parameter estimation is to compute the maximum curvature of L-curve. However, the com- putation is quite costly for the estimation of the unknown parameter in a super-resolution image reconstruction. The paper proposes an efficient approximate method based on the truncate Arnoldi process. The method can factorize the system matrix in the super-resolu- tion reconstruction into a Hessenberg matrix by the partial Arnoldi process. The linear equations in the super-resolution reconstruction are translated into simple ones associated with Hessenberg matrix through the Galerkin equations. Then the equations can quickly be solved by the Given rotation translations. The formula of L-curve curvature is presented. The computational complexity of the L-cur- vature can be reduced through partial factorization of Arnoldi process. The theory analytics and experiments demonstrate that the method can be valid.