基于凸包优化的盲源分离在图像去噪中的研究

目的针对高斯-脉冲混合噪声图像中难以有效去除大量奇异点或离群数据的问题,提出一种基于凸包优化的盲源分离方法来去除图像中的混合噪声。方法该方法把混合噪声和原图均看作未知的源信号,依据噪声图像中混合噪声与原图内容的加性关系建立盲源分离的模型,并利用凸包优化的方法构建源信号(凸包极点)的仿射包,然后通过最小化仿射包到凸包(噪声图像)上的投影误差,求解混合噪声和原图2个源信号,实现去噪混合噪声、复原原图的目的。结果实验结果发现,无论高斯-脉冲混合噪声强弱,该方法去噪复原后的峰值信噪比和平均结构相似性分别在39.9129 d B和0.9以上。结论由实验数据证实该方法可有效地从盲源分离的角度去除图像中高斯-脉冲混合噪声、复原原始图像。

Image Denoising with Blind Source Separation Based on Convex Hull Optimization

The work aims to propose image denoising method with blind source separation based on convex hull optimization in consideration of the problem of removing Gaussian white noise and impulse noise from a image simultaneously for a lot of outliers in the noisy image. This proposed method treated the mixed noise and the clean image as two source signals of a noisy image. A model of blind source separation was built according to additive relationship between the mixed noise and the clean image in the noisy image. The convex hull optimization method was adopted to construct the affine hull of source signals (those were the extreme points of convex hull). Then, a clean image was separated from two noisy images by minimizing the projection error of the affine hull onto convex hull (the noisy image) for the purpose of removing mixed noise and recovering the clean image. According to the experimental results, peak signal-to-noise ratio (PSNR) value and mean structure similarity index measurements (MSSIM) value of the denoised images in the proposed method were respectively over 39.9129 dB and 0.9 even if the Gaussian and impulse mixed noise was very strong. Results of denoising experiments show that the proposed method has good performance in removing the Gaussian and impulse mixed noise and recovering the clean image from the perspective of blind source separation.