A content-adaptive unstructured grid based integral equation method with the TV regularization for SPECT reconstruction
A content-adaptive unstructured grid based integral equation method with the TV regularization for SPECT reconstruction
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DOI：
10.3934/ipi.2019062
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发表时间：
2020
影响因子：
1.3
通讯作者：
Yun Chen;Jiasheng Huang;Si Li;Yao Lu;Yuesheng Xu
中科院分区：
文献类型：
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作者：
Yun Chen;Jiasheng Huang;Si Li;Yao Lu;Yuesheng Xu
现有的单光子发射计算机断层成像（SPECT）重建方法大多基于离散模型，导致重建精度低。针对SEPCT成像中离散模型精度不足的问题，提出了基于高阶分段多项式离散的积分方程模型（IEM）重建方法。基于像素网格的IEM的离散化导致大维度的系统，这可能需要更高的计算成本来求解。我们开发了一种SPECT重建方法，该方法采用了SPECT数据采集过程的IEM，并在内容自适应非结构化网格（CAUG）上进行离散化，并采用全变分（TV）正则化，旨在减少积分方程法的计算成本。具体来说，我们设计了一个CAUG的图像域的离散化的IEM，并提出了一个TV正则化定义的CAUG所产生的不适定问题。然后，我们应用一个预处理的不动点邻近算法来解决由此产生的非光滑优化问题，并提供算法的收敛性分析。数值实验证明了该方法在抑制噪声、保持边缘和减少计算量方面优于其他方法。
Existing reconstruction methods for single photon emission computed tomography (SPECT) are most based on discrete models, leading to low accuracy in reconstruction. Reconstruction methods based on integral equation models (IEMs) with a higher order piecewise polynomial discretization on the pixel grid for SEPCT imaging were recently proposed to overcome the accuracy deficiency of the discrete models. Discretization of IEMs based on the pixel grid leads to a system of a large dimension, which may require higher computational costs to solve. We develop a SPECT reconstruction method which employs an IEM of the SPECT data acquisition process and discretizes it on a content-adaptive unstructured grid (CAUG) with the total variation (TV) regularization aiming at reducing computational costs of the integral equation method. Specifically, we design a CAUG of the image domain for the discretization of the IEM, and propose a TV regularization defined on the CAUG for the resulting ill-posed problem. We then apply a preconditioned fixed-point proximity algorithm to solve the resulting non-smooth optimization problem, and provide convergence analysis of the algorithm. Numerical experiments are presented to demonstrate the superiority of the proposed method over the competing methods in terms of suppressing noise, preserving edges and reducing computational costs.