Abstract: Non-Local Means （NLM） algorithm has good characteristic for removing noise and preserving image details. But the algorithm is time consuming and the accuracy decreases significantly with the increase of noise. Fast Non-Local Means （FNLM） algorithm speeds up operation and reduces time cost, but the performance of denoising has not improved when noise increased. Aiming at the problem, this paper proposes a novel non-local means denoising method. A new exponential-Turky kernel function is put forward by combining Turky function and exponential function, which subsitutes the original exponential kernel function in both NLM algorithm and FNLM algorithm. Furthermore, both the Structure Similarity （SSIM） and Euclidean distance are introduced to measure the similarity between image neighborhood, which make the selection of weight more reasonable, and eliminate the interference of the neighborhood with dissimmilar structure in the image, as a result, the performance of denoising is approved. The experiments carried out with images in database by adding different level of Gaussian noise, the results demonstrate that the proposed method improves denoising capacity greatly, especially for image with large noise. Additionly, the efficiency of proposed method is enhanced obviously against NLM algorithm, and the time complexity is equal to FNLM algorithm and time consumption is close to FNLM algorithm too.

Key words: image denoising, non-local means, integral images, Turky function, structure similarity

摘要： 非局部均值滤波算法（Non-Local Means，NLM）有良好的去噪效果，且能保持图像细节。但其复杂度过高引起效率低下，在噪声增大时去噪精度明显下降。快速非局部均值滤波（Fast Non-Local Means，FNLM）虽然提高了算法的效率，但去噪效果没有明显改善，在噪声增大时去噪效果仍不理想。针对该问题，提出一种新的非局部均值滤波算法，算法将Turky型函数与指数型相结合，提出一种新的指数-Turky型权值核函数，替代原NLM算法和FNLM算法中的指数型核函数，同时综合了结构相似性（Structural Similarity，SSIM）和欧氏距离来衡量图像邻域间的相似性，从而使得权值的选取更加合理，有效排除图像中不相似邻域的干扰，提高了算法的去噪性能。通过对添加不同噪声水平的高斯噪声图像进行实验，结果表明提出的算法在去噪性能上与NLM和FNLM相比有较大提高，尤其对于噪声较大的图像效果更为显著，在去噪效率上与NLM相比有明显提高，与FNLM算法的时间复杂度相当，时耗接近略有降低。

关键词: 图像去噪, 非局部均值滤波, 积分图, Turky函数, 结构相似性