直线运动模糊图像复原的截断奇异值分解方法

Linear motion blurred image restoration based on TSVD

在Neumann边界条件假设下,具有对称及平移不变性的点扩散函数的图像复原问题可以转化为不适定的解卷问题,进而可以采用截断奇异值分解(TSVD)方法解卷.但是,任意方向直线运动模糊的点扩散函数不具有对称性.而直线运动模糊图像仅仅由该运动方向上的像素相互作用形成,本文用平行于该运动方向的一系列直线把模糊图像进行分割,每条直线上的运动模糊近似可看作水平直线运动模糊,而水平直线运动模糊的点扩散函数是对称的,从而利用截断奇异值分解方法,复原模糊图像,实验证明了算法的有效性.

The image restoration problem with symmetry and translational invariance of the point spread function can be transformed into ill-posed deconvolution problem under the assumption of the Neumann boundary condition, and thus can be used TSVD meth- od to solve. But the point spread function of in any direction linear motion blurred ima- ges does not have symmetry. While the linear motion blurred image caused merely by the interactions between pixels of the movement direction, in this paper a segments the blurred image with a series of straight parallel lines in the direction of motion, motion blur on each line can be considered similar to the level linear motion blur, the point spread function of the level linear motion blur is symmetry, thus it can restore the blurred image using TSVD method. Numerical experiments are given to illustrate the efficiency of our algorithm.