一种快速迭代软阈值稀疏角CT重建算法

吴俊峰; 牟轩沁; 张砚博

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一种快速迭代软阈值稀疏角CT重建算法

更新时间：2025-07-09

- 一种快速迭代软阈值稀疏角CT重建算法
- A Fast Iterative Soft-Threshold Algorithm for Few-View CT Reconstruction
- 西安交通大学学报 2012年46卷第12期页码：24-29
- 作者机构：
  
  西安交通大学电子与信息工程学院,西安,710049
- 作者简介：
- 基金信息：
  
  : 2012-04-27. 作者简介: 吴俊峰(1980-),女, 博士生;牟轩沁(通信作者), 男, 教授,博士生导师. 基金项目: 国家自然科学基金资助项目(61072069)
- DOI：
  中图分类号： TN911.73
- 网络首发：2012-12-10，
  
  纸质出版：2012
- 稿件说明：
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吴俊峰, 牟轩沁, 张砚博. 一种快速迭代软阈值稀疏角CT重建算法[J]. 西安交通大学学报, 2012,46(12):24-29.

A Fast Iterative Soft-Threshold Algorithm for Few-View CT Reconstruction[J]. 2012, 46(12): 24-29.
吴俊峰, 牟轩沁, 张砚博. 一种快速迭代软阈值稀疏角CT重建算法[J]. 西安交通大学学报, 2012,46(12):24-29. DOI：

A Fast Iterative Soft-Threshold Algorithm for Few-View CT Reconstruction[J]. 2012, 46(12): 24-29. DOI：

摘要

针对目前迭代软阈值稀疏角CT重建算法收敛速度较慢的问题

提出了一种基于全变分约束的快速迭代软阈值稀疏角CT重建算法.该算法首先对CT稀疏投影数据采用联合代数重建算法(SART)进行重建

以获得满足数据一致性的重建图像

然后计算SART重建图像的离散梯度变换

并对其进行软阈值滤波

最后利用离散梯度变换的伪逆更新重建图像.由于在迭代过程中利用了前2次迭代重建图像作为下一次迭代的初始图像

因而加快了重建算法的收敛速度.对Shepp-Logan模体进行仿真的实验结果表明:在无噪、5×10

和2×10

光子泊松噪声情况下

与SART重建算法、基于Harr小波的快速迭代软阈值算法以及基于全变分约束的迭代软阈值重建算法相比

该重建算法的收敛速度有明显提高

同时能够有效减小图像的相对重建误差.

Abstract

A fast iterative soft-threshold algorithm is proposed to accelerate the convergence of iterative soft-threshold algorithm for image reconstruction from few-view projections.The algorithm bases on total variation minimization. Simultaneous algebraic reconstruction technique(SART)is used to reconstruct image from few-view projections and to meet the constraint of the projection data. Then discrete gradient transform(DGT)of the reconstructed image is calculated and the soft-threshold filtering is performed on the DGT. Finally the reconstructed image is updated using the pseudo-inverse of the DGT. The proposed algorithm takes the images in previous two iterations as the input image for a new iteration

and hence the convergence is accelerated. Experimental results and comparisons with the SART algorithm

the fast iterative soft-thr

eshold algorithm with Harr wavelet constraint

and the iterative soft-threshold filtering algorithm with total variation constraint on the projections of Shepp-Logan phantom under the conditions without noise and corrupted by Poisson noise assuming with 5×10

and 2×10

photons per detector element show that the proposed algorithm can not only speed up the convergence

but also reduce the relative reconstruction error of images.

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references

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