边缘保持递归去噪算法及在图象处理中的应用

Edge-preserving recursive noise-removing algorithm and its applications in image processing

为了在图象处理时，既可以有效地去除噪声，又不会太多地破坏边缘，在一维卡尔曼滤波器的基础上，通过加入噪声图象边缘的结构信息，导出了一种简单的、可快速计算的边缘保持递归去噪算法。算法的主要思想是将与边缘大小和位置有关的信息从噪声图象中提取出来并将这些信息作为卡尔曼滤波器的控制输入，采用这种方法可以有效地降低图象边缘破坏的程度。对包含边缘信息和不含边缘信息的Ｘ线头影图象进行了处理，实验结果表明，加入边缘信息的卡尔曼滤波器的性能明显优于传统的卡尔曼滤波器，改进的滤波器在去除图象噪声的同时，可以有效地保持图象的边缘。

The reduction of image noise is an important problem in digital image processing. Conventional linear filters which were applied in a noisy image can reduce the noise effectively, but the edges in the image are often blurred. On the basis of 1-D Kalman filter, a simple and computationally fast recursive noise-removing algorithm is derived by providing structural information about the edges in the noisy image to the control input of Kalman filter. This algorithm can perfectly preserve the edges in the process of filtering the floisy image. The filtered images with and without edge information are presented to demonstrate that this algorithm can not only improve the performance of the filter, but also preserve the image edges effectively.