Shanghai Key Lab of Modern Optical Systems, School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, 200093, P, Shanghai, R, China.
School of Medicine, Stanford University, 269 Campus Drive, Stanford, CA, 94305, USA.
BMC Med Imaging. 2020 Jan 6;20(1):2. doi: 10.1186/s12880-019-0407-4.
The Rician noise formed in magnetic resonance (MR) imaging greatly reduced the accuracy and reliability of subsequent analysis, and most of the existing denoising methods are suitable for Gaussian noise rather than Rician noise. Aiming to solve this problem, we proposed fuzzy c-means and adaptive non-local means (FANLM), which combined the adaptive non-local means (NLM) with fuzzy c-means (FCM), as a novel method to reduce noise in the study.
The algorithm chose the optimal size of search window automatically based on the noise variance which was estimated by the improved estimator of the median absolute deviation (MAD) for Rician noise. Meanwhile, it solved the problem that the traditional NLM algorithm had to use a fixed size of search window. Considering the distribution characteristics for each pixel, we designed three types of search window sizes as large, medium and small instead of using a fixed size. In addition, the combination with the FCM algorithm helped to achieve better denoising effect since the improved the FCM algorithm divided the membership degrees of images and introduced the morphological reconstruction to preserve the image details.
The experimental results showed that the proposed algorithm (FANLM) can effectively remove the noise. Moreover, it had the highest peak signal-noise ratio (PSNR) and structural similarity (SSIM), compared with other three methods: non-local means (NLM), linear minimum mean square error (LMMSE) and undecimated wavelet transform (UWT). Using the FANLM method, the image details can be well preserved with the noise being mostly removed.
Compared with the traditional denoising methods, the experimental results showed that the proposed approach effectively suppressed the noise and the edge details were well retained. However, the FANLM method took an average of 13 s throughout the experiment, and its computational cost was not the shortest. Addressing these can be part of our future research.
磁共振成像（MR）中形成的瑞利噪声极大地降低了后续分析的准确性和可靠性，而大多数现有的去噪方法适用于高斯噪声而不适用于瑞利噪声。针对这一问题，我们提出了模糊 c-均值和自适应非局部均值（FANLM），它将自适应非局部均值（NLM）与模糊 c-均值（FCM）相结合，作为一种新的方法来降低研究中的噪声。
该算法根据改进的中值绝对偏差（MAD）估计器对瑞利噪声的噪声方差自动选择最佳搜索窗口大小。同时，它解决了传统 NLM 算法必须使用固定大小搜索窗口的问题。考虑到每个像素的分布特征，我们设计了三种大小的搜索窗口，分别为大、中、小，而不是使用固定大小。此外，与 FCM 算法的结合有助于达到更好的去噪效果，因为改进的 FCM 算法对图像的隶属度进行了划分，并引入了形态重建来保留图像细节。
实验结果表明，所提出的算法（FANLM）可以有效地去除噪声。此外，与其他三种方法：非局部均值（NLM）、线性最小均方误差（LMMSE）和非下采样小波变换（UWT）相比，它具有最高的峰值信噪比（PSNR）和结构相似性（SSIM）。使用 FANLM 方法，可以很好地保留图像细节，同时去除大部分噪声。
与传统的去噪方法相比，实验结果表明，所提出的方法有效地抑制了噪声，同时很好地保留了边缘细节。然而，FANLM 方法在整个实验过程中平均需要 13 秒，其计算成本不是最短的。解决这些问题可以是我们未来研究的一部分。
