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
医用光学 迭代方法 稀疏计算层析成像 重构去噪方法 凸集投影方法 Medical optics Iterative method Sparse computed tomography Reconstruction denoising method Projection onto convex sets
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.
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.