基于块空间中低维流形恢复的图像去噪

摘要

For patch-based image denoising,a novel assumption recently is proposed that there are several low dimensional manifolds contain most of patches in the clear image.These manifolds are corrupted by noise in noisy image.So it is possible to de-noise by recovering these manifolds.The assumption is varified by two dimensional patches distribution.Then an iterative algorithm is presented for denosing by recovering the low dimensional manifolds from noisy image.Consequently image denoising is modeled as an optimization problem to minimize the rank of matrix correspondence to the manifold according to the assumption.Preliminary experiments show that proposed algorithm performs well in image denoising.%针对基于块处理的图像去噪,最近出现一种新的假设:真实无噪的图像块在块空间中的分布有一定的规律,即会形成若干个低维流形,而在带噪图像中这些流形受到噪声污染而变形,若能恢复这些低维流形便可去噪.若干真实图像的二维块分布表明了该假设的正确性.接下来根据该假设给出了在块空间中通过复原受噪声污染流形来去噪的一个迭代算法.最后还考察了基于该假设图像去噪的最优化模型,即最小化这些流形所对应矩阵的秩.初步实验表明,该算法能取得良好的去噪效果,与当今最好的去噪算法有可比性.