Yu Hengyong, Wang Ge
Department of Biomedical Engineering, Wake Forest University Health Sciences, Winston-Salem, NC 27157, USA ; Biomedical Imaging Division, VT-WFU School of Biomedical Engineering and Sciences, Winston-Salem, NC 27157, USA.
Biomedical Imaging Cluster, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA.
IEEE Access. 2014;2:602-613. doi: 10.1109/ACCESS.2014.2326165.
The [Formula: see text] regularization problem has been widely used to solve the sparsity constrained problems. To enhance the sparsity constraint for better imaging performance, a promising direction is to use the [Formula: see text] norm (0 1) and solve the [Formula: see text] minimization problem. Very recently, Xu developed an analytic solution for the [Formula: see text] regularization via an iterative thresholding operation, which is also referred to as half-threshold filtering. In this paper, we design a simultaneous algebraic reconstruction technique (SART)-type half-threshold filtering framework to solve the computed tomography (CT) reconstruction problem. In the medical imaging filed, the discrete gradient transform (DGT) is widely used to define the sparsity. However, the DGT is noninvertible and it cannot be applied to half-threshold filtering for CT reconstruction. To demonstrate the utility of the proposed SART-type half-threshold filtering framework, an emphasis of this paper is to construct a pseudoinverse transforms for DGT. The proposed algorithms are evaluated with numerical and physical phantom data sets. Our results show that the SART-type half-threshold filtering algorithms have great potential to improve the reconstructed image quality from few and noisy projections. They are complementary to the counterparts of the state-of-the-art soft-threshold filtering and hard-threshold filtering.
[公式：见正文]正则化问题已被广泛用于解决稀疏约束问题。为了增强稀疏约束以获得更好的成像性能，一个有前景的方向是使用[公式：见正文]范数（0 < p < 1）并解决[公式：见正文]最小化问题。最近，Xu通过迭代阈值操作开发了一种用于[公式：见正文]正则化的解析解，这也被称为半阈值滤波。在本文中，我们设计了一种同时代数重建技术（SART）型半阈值滤波框架来解决计算机断层扫描（CT）重建问题。在医学成像领域，离散梯度变换（DGT）被广泛用于定义稀疏性。然而，DGT是非可逆的，并且不能应用于CT重建的半阈值滤波。为了证明所提出的SART型半阈值滤波框架的实用性，本文的一个重点是为DGT构建一个伪逆变换。所提出的算法使用数值和物理体模数据集进行评估。我们的结果表明，SART型半阈值滤波算法在从少量有噪声投影中提高重建图像质量方面具有很大潜力。它们与最先进的软阈值滤波和硬阈值滤波的对应算法互补。
