光子学报, 2015, 44 (5): 0517002, 网络出版: 2015-05-26  

稀疏计算层析成像重构中迭代去噪方法的分析

Analysis of Iterative Denoising Method in Sparse Computed Tomography Reconstruction
作者单位
天津大学 精密仪器与光电子工程学院, 光电信息技术教育部重点实验室, 天津 300072
摘要
研究了稀疏计算层析成像重构中的迭代去噪模型及其求解算法, 理论推导及模拟实验验证了代数重构技术的抑噪能力.根据稀疏计算层析成像成像过程的噪音特征, 提出了基于欧氏范数不等式约束和基于无穷范数不等式约束的去噪模型.提出了基于凸集投影方法求解去噪模型的算法, 并给出了算法推导过程.结果表明: 欧氏范数去噪模型优于无穷范数去噪模型, 代数重构技术具有抑制噪音的作用.
Abstract
The iterative denoising models and their solving algorithms in the sparse computed tomoyraphy reconstruction were researched. The theoretical derivations and simulation experiments demonstrate that the Algebraic Reconstruction Technique (ART) have the denoising ability. Two models for the sparse computed tomoyraphy denoise were proposed. One is based on the Euclidean norm inequality constraint, and the other is based on the infinity norm inequality constraint. Inspaired by the iterative method in ART, we use projection onto convex sets method to solve these two denoising models. The algorithm derivation is provided. The results indicate that the Euclidean norm based denoise model is better than the infinity norm based denoise model, and the ART method has the ability of denoising.
参考文献

[1] DONOHO D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.

[2] CANDS E J, WAKIN M B. An introduction to compressive sampling[J]. IEEE Signal Processing Magazine, 2008, 25(2): 21-30.

[3] 刘海英, 李云松, 吴成柯. 一种数字微镜阵列分区控制和超分辨重建的压缩感知成像法[J]. 光子学报, 2014, 43(5): 0510002.

    LIU Hai-ying, LI Yun-song, WU Cheng-ke. A method for compressive sensing of images based on zone control of digital micromirror device and super-resolution[J]. Acta Photonica Sinica, 2014, 43(5): 0510002.

[4] 卢佩, 刘效勇, 卢熙, 田敏, 等. 基于压缩感知及光学理论的图像信息加密[J]. 光子学报, 2014, 43(9): 0910002.

    LU Pei, LIU Xiao-yong, LU Xi, et al. Image information encryption by compressed sensing and optical theory[J]. Acta Photonica Sinica, 2014, 43(9): 0910002.

[5] 计振兴,孔繁锵. 基于谱间线性滤波的高光谱图像压缩感知[J]. 光子学报, 2012, 41(1): 82-86.

    JI Zhen-Xin, KONG Pan-Qiang. Hyperspectral image compressed sensing based on linear filter between bands[J]. Acta Photonica Sinica, 2012, 41(1): 82-86.

[6] ZHANG T, CHOWDHURY S, LUSTIG M, et al. Clinical performance of contrast enhanced abdominal pediatric MRI with fast combined parallel imaging compressed sensing reconstruction[J]. Journal of Magnetic Resonance Imaging, 2013: n/a-n/a.

[7] BERRINGTON D G A, MAHESH M, KIM K P, et al. Projected cancer risks from computed tomographic scans performed in the United States in 2007[J]. Archives of Internal Medicine, 2009, 169(22): 2071-2077.

[8] LIU Y, LIANG Z, MA J, et al. Total variation-stokes strategy for sparse-view X-ray CT image reconstruction[J]. IEEE Transactions on Medical Imaging, 2014, 33(3): 749-763.

[9] CHEN Z, JIN X, LI L, et al. A limited-angle CT reconstruction method based on anisotropic TV minimization[J]. Physics in Medicine and Biology, 2013, 58(7): 2119.

[10] WU D, LI L, ZHANG L. Feature constrained compressed sensing CT image reconstruction from incomplete data via robust principal component analysis of the database[J]. Physics in Medicine and Biology, 2013, 58(12): 4047-4070.

[11] 方静, 程乐红, 张玉萍,等. 基于扇束双投影方向的改进迭代层析成像算法[J]. 光子学报, 2014, 43(10): 1011003.

    FANG Jing, CHENG Le-hong, ZHANG Yu-ping, et al. Improved iterative tomography algorithm based on fan-beam geometry of double projections[J]. Acta Photonica Sinica, 2014, 43(10): 1011003.

[12] GORDON R, BENDER R, HERMAN G T. Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography[J]. Journal of Theoretical Biology, 1970, 29(3): 471-481.

[13] LI H, CHEN X, WANG Y, et al. Sparse CT reconstruction based on multi-direction anisotropic total variation (MDATV)[J]. BioMedical Engineering OnLine, 2014, 13(1): 92.

[14] LI T, LI X, WANG J, et al. Nonlinear sinogram smoothing for low-dose X-ray CT[J]. IEEE Transactions on Nuclear Science, 2004, 51(5): 2505-2513.

[15] ROSS S M, Introduction to probability and statistics for engineers and scientists[M]: Elsevier Science, 2009. 2.3.2.

[16] LUO Z Q, TSENG P. On the convergence of the coordinate descent method for convex differentiable minimization[J]. Journal of Optimization Theory and Applications, 1992, 72(1): 7-35.

[17] BECKER S, BOBIN J, CANDS E. NESTA: a fast and accurate first-order method for sparse recovery[J]. SIAM Journal on Imaging Sciences, 2011, 4(1): 1-39.

[18] NESTEROV Y. Smooth minimization of non-smooth functions[J]. Mathematical Programming, 2005, 103(1): 127-152.

[19] FESSLER J. Image reconstruction toolbox[OL]. http: //web.eecs.umich.edu/~fessler/code/.

[20] CANDS E J, ROMBERG J, TAO T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.

[21] BRACEWELL R N. Strip integration in radio astronomy[J]. Australian Journal of Physics, 1956, 9(2): 198-217.

李宏霄, 陈晓冬, 李俊威, 汪毅, 郁道银. 稀疏计算层析成像重构中迭代去噪方法的分析[J]. 光子学报, 2015, 44(5): 0517002. LI Hong-xiao, CHEN Xiao-dong, LI Jun-wei, WANG Yi, YU Dao-yin. Analysis of Iterative Denoising Method in Sparse Computed Tomography Reconstruction[J]. ACTA PHOTONICA SINICA, 2015, 44(5): 0517002.

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