基于波方程的运动模糊图像恢复

Motion blurred image restoration based on wave equation

为了有效去除图像中的运动模糊,提出了一种基于波方程的图像恢复方法.从光流方程出发,将运动物体的亮度用波方程描述.模糊图像是曝光时间内运动物体亮度的积分,存在大量的平行于运动方向的直线;模糊图像沿运动方向的导数等于原始图像与其移位图像的差,两者之间的距离为模糊长度.基于此,利用Radon变换和自相关函数自动估计点扩展函数,并采用Wiener滤波恢复原始图像.实验表明:该方法高信噪比(30～40 dB)下估值精确;低信噪比 (20～30 dB)下对噪声鲁棒.将该方法应用于运动模糊车牌图像,能有效恢复出车牌号码,具有很大的实用价值.

This paper presents a technique for motion blur removal in which the brightness of the moving object is described by a wave equation, with the original image brightness as its initial value. The blurred image is the integral of the brightness of the moving object during the exposure duration with many lines parallel to the motion direction. The derivative of the image along the motion direction is related to the original scene and its shifted version, displaced by the blur extent. The point spread function （PSF） is then automatically estimated using the Radon transform and the autocorrelation function. Then a Wiener filter is used to restore the image. Experiments on both synthetic and real-world motion blurred images show that the algorithm is effective and robust to noise even with the signal to noise ratio of 20～30dB and can be applied in real-world licenice plate restoration applications.