磁共振成像（MRI）实验时常采用多次扫描累加平均提高图像信噪比（SNR），但当扫描过程中运动引起图像变形时，简单地累加平均就无法奏效.为此，本研究组曾提出一种匹配加权平均方法（MWA）提高图像的信噪比.在此基础上，该文提出一种旋转不变的非局域均值算法（RINLM），即选取圆形邻域区域并将其划分为一系列以中心像素为圆心的等面积圆环，再计算模式的相似性.RINLM算法可以更好地利用图像中旋转的冗余信息、找到更多的相似结构，提高算法的去噪性能.我们把该方法应用于低信噪比图像序列的平均和去噪中，可以更好地处理旋转的局部运动.与非局域均值算法（NLM）相比，RINLM算法可以进一步提高图像的信噪比；与MWA方法相比，其与RINLM算法的结合可以进一步提高磁共振图像序列信噪比，更好的保持图像边缘信息.
张波
,
谢海滨
,
严序
,
李文静
,
杨光
. 旋转不变的非局域均值算法在磁共振图像去噪中的应用[J]. 波谱学杂志, 2018
, 35(2)
: 162
-169
.
DOI: 10.11938/cjmr20172582
Averaging of multiple scans is often used in magnetic resonance imaging (MRI) to increase the signal-to-noise ratio (SNR). However, image averaging often results in movement-induced blurs of the edges and tissue details. A matched and weighted averaging (MWA) method has been proposed by our group to obtain images with reduced blurring effects in signal averaging. Here a rotation-invariant non-local means (RINLM) algorithm was proposed, which used circular patches consisted of series of rings with equal area, instead of square patches, to search for similar patches in the images. Compared with the non-local means (NLM) algorithm, the RINLM algorithm was capable of finding more similar patches in the images containing many rotated local structure. This method was used to process noisy images to improve the SNR, and validated using both phantom images and in vivo MR images. The results demonstrated that the method could improve the SNR, while better preserving the edges and details of the images.
[1] MOHAN J, KRISHNAVENI V, GUO Y H, et al. A survey on the magnetic resonance image denoising methods[J]. Biomed Signal Proces, 2014, 9:56-69.
[2] DONOHO D L, JOHNSTONE I M. Ideal spatial adaptation by wavelet shrinkage[J]. Biometrika, 1994, 81(3):425-455.
[3] DONOHO D L. De-noising by soft-thresholding[J]. IEEE T Inform Theory, 1995, 3(41):613-627.
[4] PIZURICA A, WINK A M, VANSTEENKISTE E, et al. A review of wavelet denoising in MRI and ultrasound brain imaging[J]. Current Med Imaging Rev, 2006, 2(2):247-260.
[5] MANJON J V, COUPEB P, BUADES A, et al. New methods for MRI denoising based on sparseness and self-similarity[J]. Med Image Anal, 2012, 16(1):18-27.
[6] BAO L J, ROBINI M, LIU W Y, et al. Structure-adaptive sparse denoising for diffusion-tensor MRI[J]. Med Image Anal, 2013, 17(4):442-457.
[7] AHARON M, ELAD M, BRUCKSTEIN A. rmK-SVD:an algorithm for designing over complete dictionaries for sparse representation[J]. IEEE T Signal Proces, 2006, 54(11):4311-4322.
[8] ELAD M, AHARON M. Image denoising via sparse and redundant representations over learned dictionaries[J]. IEEE Trans Image Process, 2006, 15(12):3736-3745.
[9] BUADES A, COLL B, MOREL J M, et al. A review of image denoising algorithms, with a new one, Multiscale Model[J]. Siam Journal on Multiscale Modeling & Simulation, 2005, 4(2):490-530.
[10] MANJÓN J V, COUPÉ P, BUADES A, et al. New methods for MRI denoising based on sparseness and self-similarity[J]. Med Image Anal, 2012, 16(1):18-27.
[11] CAI B, LIU W, ZHENG Z, et al. A new similarity measure for non-local means denoising[M]. ZHA H, CHEN X, WANG L, et al. Computer vision. communications in computer and information science. Heidelberg:Springer, 2015, 546:306-316.
[12] LI H J, SUEN C Y. A novel Non-local means image denoising method based on grey theory[J]. Pattern Recogn, 2016, 49:237-248.
[13] PRASATH V B S, KALAVATHI P. Adaptive nonlocal filtering for brain MRI restoration[M]. THAMPI S, BANDYOPADHYAY S, KRISHNAN S, et al. Advances in signal processing and intelligent recognition systems. Switzerland:Springer International Publishing, 2016, 425:571-580.
[14] MANJON J V, COUPE P, MARTI-BONMATI L, et al. Adaptive non-local means denoising of MR images with spatially varying noise levels[J]. J Magn Reson Imaging, 2010, 31(1):192-203.
[15] COUPE P, YGER P, PRIMA S, et al. An optimized blockwise nonlocal means denoising filter for 3-D magnetic resonance images[J]. IEEE Trans Med Imaging, 2008, 27(4):425-441.
[16] MAHMOUDI M, SAPIRO G. Fast image and video denoising via nonlocal means of similar neighborhoods[J]. IEEE Signal Proc Let, 2005, 12(12):839-842.
[17] LI W J, XIE H B, YAN X, et al. MR image average based on local offset correction[J]. Chinese J Magn Reson, 2017, 34(3):294-301. 李文静, 谢海滨, 严序, 等. 基于局部位移校正的磁共振图像相干平均[J]. 波谱学杂志, 2017, 34(3):294-301.
[18] HE L L, GREENSHIELDS I R. A nonlocal maximum likelihood estimation method for rician noise reduction in MR images[J]. IEEE Trans Med Imaging, 2009, 28(2):165-172.
[19] SALMON J. On two parameters for denoising with non-local means[J]. IEEE Signal Proc Let, 2010, 17(3):269-272.
[20] VAN DE VILLE D, KOCHER M. Nonlocal means with dimensionality reduction and sure-based parameter selection[J]. IEEE T Image Process, 2011, 20(9):2683-2690.
[21] http://brainweb.bic.mni.mcgill.ca/brainweb/selection_normal.html[OL]
[22] WANG Z, SIMONCELLI E P, BOVIK A C, et al. Multiscale structural similarity for image quality assessment[C]. Pacific Grove:Conference Record of the Thirty-Seventh Asilomar Conference on Signals, Systems and Computers, 2004. DOI:10.1109/ACSSC.2003. 1292216
