基于移位反射边界条件的图像复原

在信号和图像处理中,期望将原始场景从观测到的降质数据中恢复出来.在数学上,这个过程就转化成为求解一个系数矩阵为模糊矩阵的线性系统.该模糊矩阵是由刻画模糊的点扩散函数和假设原始图像外部数据的边界条件所决定的.为了更好地保留边界连续性以及减少复原图像中的振铃效应,本文提出移位反射边界条件,并在不依赖于点扩散函数对称性的情形下,给出了对该边界条件下的模糊矩阵的Kronecker积逼近和相应的SVD型正则化算法.实验结果表明,基于移位反射边界条件的SVD型正则化算法效果很好.

Image restoration with shifting reflective boundary conditions

In signal and image processing,we want to recover a faithful representation of an original scene from blurred,noisy image data.This process can be transformed mathematically into solving a linear system with a blurring matrix.Particularly,the blurring matrix is determined from not only a point spread function(PSF),which defines how each pixel is blurred,but also boundary conditions(BCs),which specify our assumptions on the data outside the domain of consideration.In this paper,we first propose shifting reflective BCs which preserve the continuity at the boundaries and,therefore,reduce ringing effects in the restored image.A Kronecker product approximation of the corresponding blurring matrix is then provided,regardless of symmetry requirement of the PSF.Finally,we demonstrate the efficiency of our approximation in an SVD-based regularization method by several numerical examples.