核范数最小化在低剂量CT去噪中的研究

Denoising of low-dose CT images based on the nuclear norm minimization method

目的加权核范数最小化(weighted nuclear norm minimization,WNNM)算法是一种低秩矩阵逼近去噪方法,目前主要应用于自然图像去噪。本文拟探究WNNM方法在低剂量CT图像去噪中应用价值。方法将WNNM算法与三维块匹配滤波(block-matching and 3D filtering,BM3D)算法相结合,提出BM3D-WNNM图像后处理方法。使用该方法对Shepp-Logan仿真低剂量CT图像做去噪处理,并将其结果与BM3D算法、WNNM算法以及基于直觉模糊熵和加权方差的各向异性扩散算法(anisotropic diffusion algorithm based on intuitionistic fuzzy entropy and weighted variance,IFE-WV-AD)的结果进行对比分析,定量比较4种算法对Shepp-Logan仿真低剂量CT图像去噪结果的峰值信噪比(peak signal to noise ratio,PSNR)和结构相似性(structural similarity,SSIM)。结果BM3D-WNNM方法处理后的图像在视觉观察和定量分析中均优于另外3种方法,该方法处理后的图像中肉眼可分辨的斑点状噪声和条形伪影少于另外3种算法处理后的图像,且PSNR和SSIM均大于另外3种算法的结果。结论BM3D-WNNM算法可以有效去除Shepp-Logan仿真低剂量CT图像中的噪声,在低剂量CT图像去噪中具有应用价值。

Objective The weighted nuclear norm minimization(WNNM)algorithm is a low rank matrix approximation denoising method,which is currently mainly applied to natural image denoising.This paper intends to explore the application value of WNNM method in low-dose CT images denoising.Methods Combining the WNNM algorithm with a block-matching and 3d filtering(BM3D)algorithm,an image post-processing method(BM3D-WNNM algorithm)is proposed.This method is used to denoise the Shepp-Logan simulated low-dose CT images.The results are compared with the results of BM3D algorithm,WNNM algorithm and anisotropic diffusion algorithm based on intuitionistic fuzzy entropy and weighted variance(IFE-WV-AD),and quantitatively compared the peak signal to noise ratio(PSNR)and structural similarity(SSIM)of the Shepp-Logan simulated low-dose CT images denoised by four algorithms.Results The images processed by BM3D-WNNM algorithm are superior to the other three methods both in visual observation and quantitative analysis.The visually distinguishable speckle noise and stripe artifacts in images processed by the proposed method are less than those processed by the other three algorithms,the PSNR and SSIM values of the images processed by this method are larger than the results of the other three algorithms.Conclusions The BM3D-WNNM algorithm can effectively remove the noise in Shepp-Logan simulation low-dose CT images,and has application value in low-dose CT image denoising.