Estimation of Spatially Variable Level Field of Rician Noise and its Application to MR Image Denoising
1 School of Biomedical Engineering, Southern Medical University, Guangzhou 510515,China
2 Shenzhen Entryexit Inspection and Quarantine Industrial Detection Technology Center, Shenzhen 518067, China
Abstract：The levels of Rician noise in MR images vary spatially. A method to estimate the noise level field (NLF) was proposed in this paper for denoising the spatially variable noise. The NLF was fitted using the estimations of local noise levels and a NLF model with the sparsity constraint. Then, the noisy MR images were made to be homoscedastic by the spatially adaptive variancestabilization transformations with the estimated NLF. Thus, BM3D algorithm was adopted to suppress the noise in the transformed images. Experimental results on the synthetic and real images demonstrate that the proposed method effectively estimates the NLF and the estimated NLF is useful for denoising the spatially variable Rician noise. The mean relative error of the estimated noise levels was less than 0.2%. Compared with other denoising methods for MR images, the method with NLF performed better and PSNR was improve about 2 dB. The results demonstrate that the proposed method can effectively estimate the Rician noise level field and can be used to suppress the spatially variable Rician noise.
［1］陈武凡. 并行磁共振成像的回顾、现状与发展前景［J］.中国生物医学工程学报, 2005,24(6):649-654.
［2］Buades A, Coll B, Morel JM. A review of image denoising algorithm, with a new one ［J］. SIAM Multiscale Modeling and Simulation, 2005, 4(2): 490-530.
［3］Dabov K, Foi A, Katkovnik V, at al. Image denoising by sparse3D transformdomain collaborative filtering ［J］. IEEE Trans Image Process, 2007, 16(8):2080-2095.
［4］Foi A. Noise estimation and removal in MR imaging: the variancestabilization approach［C］// IEEE International Symposium on Biomedical Imaging. Chicago: IEEE, 2011:1809-1814.
［5］Manjón JV, Coupé P, Martí-Bonmatí L, et al. Adaptive nonlocal means denoising of MR images with spatially varying noise levels ［J］. Magn Reson Imaging, 2010, 31(1):192-203.
［6］Sijbers J, Poot D, Dekker AJ, et al. Automatic estimation of the noise variance from the histogram of a magnetic resonance image ［J］. Phys Med Biol, 2007, 52(5):1335-1348.
［7］Foi A. Optimization of variancestabilizing transformations ［OL］.http://www.cs.tut.fi/～foi/.
［8］Zheng Yuanjie. Estimation of image bias field with sparsity constraints ［C］//Computer Vision and Pattern Recognition (CVPR). San Francisco: IEEE Computer Society, 2010: 255-262.
［9］王浩.求解正则化问题的算法研究［D］.北京:北京航空航天大学,2010.
［10］Kim SJ, Koh K, Lustig M, at al. An interiorpoint method for largescale l1regularized least squares ［J］.IEEE Signal Processing, 2007,1(4):606-617.
［11］Rousseeuw PJ, Verboven S. Robust estimation in very small samples ［J］. Comp Stat Data Anal, 2002, 40(4): 741-758.
［12］Maximov II,Farrher E, Grinberg F,at al. Spatially variable Rician noise in magnetic resonance imaging ［J］.Med Image Anal, 2012,16(2):536-548.
［13］Coupé P, Manjón JV, Gedamu E, at al. Robust Rician noise estimation for MR images ［J］. Med Image Anal, 2010, 14(4): 483-493.
［14］Koay CG, Basser PJ. Analytically exact correction scheme for signal extraction from noisy magnitude MR signals ［J］. J Magn Reson, 2006, 179(2):317-322.
［15］Zhu Xiang, Milanfar P. Automatic parameter selection for denoising algorithms using a noreference measure of image content ［J］.IEEE Trans Image Process, 2010, 19(12):3116-3132.
［16］Portilla J, Strela V, Wainwright M, et al. Image senoising using scale mixtures of gaussians in the wavelet domain ［J］. IEEE Trans on Image Process, 2003, 12(11):1338-1351.
