一种基于各向异性总变分最小化的CT图像重建算法

CT Image Reconstruction Algorithm Based on Anisotropic Total Variation Minimization

摘要: 由于受数据采集时间、照射剂量、成像系统扫描的几何位置等因素的约束，计算机断层成像(CT)技术目前只能在有限角度范围或在较少的投影角度得到数据，这些都属于不完全角度重建问题。图像重建问题中的总变分(Total-Variation, TV)最小化模型使用基于交替方向法(alternating direction method, ADM)的稀疏优化算法能够在不完全角度的图像重建中获得较优的重建结果。然而，在极稀疏的角度数量下，各向同性TV最小化算法的重建精度不是很理想，存在进一步改善空间。本文针对该问题，通过基于稀疏优化的交替方向方法推导基于各向异性TV最小化的CT图像重建算法。实验结果表明，在稀疏角度重建中，本文提出的基于各向异性TV最小化重建算法与各向同性TV最小化重建算法相比，在稀疏性保持良好的基础上，重建精度上存在优势，综合性能方面表现更优异。

Abstract: In many practical applications, due to the data acquisition time, dose, and geometric constraint scanning, only in a limited Angle range, various data is available to acquire. It is the so-called few-view problem. In recent years, the Total Variation (TV) minimization model, using alternating direction method (ADM) in sparse optimization algorithm shows better reconstruction results among these TV-based algorithms. However, Isotropic TV minimization based algorithms for few- view reconstruction has not so good accuracy and there is further improvement to achieve. Aiming at this problem, Anisotropic TV minimization algorithm is proposed in this paper. The algorithm is based on ADM and uses sparse optimization theory. Experimental results demonstrate that the proposed method compared with Isotropic TV minimization algorithm, has higher reconstruction accuracy and a more excellent comprehensive performance.