Journal of Computational and Applied Mathematics ( IF 2.1 ) Pub Date : 2020-09-01 , DOI: 10.1016/j.cam.2020.113174 Andrés Jerez , Miguel Márquez , Henry Arguello
Computed tomography (CT) is a non-invasive scanning technique that allows the visualization of the internal structure of an object from X-ray projections. These projections are frequently affected by different artifacts, including the beam hardening (BH) effect, among others. The BH effect is produced by high X-ray attenuation due to dense elements inside the object of interest. Traditionally, BH artifacts are addressed by applying oversampling techniques. However, the prolonged X-ray exposition represents a risk to the patient’s health. To overcome this drawback, undersampling CT approaches have been developed, e.g., the coded aperture computed tomography (CA-CT) which is based on the compressive sensing (CS) theory. Nevertheless, CA-CT has not been extended for addressing the BH effect. This work proposes an adaptive coded aperture sensing methodology based on a fan-beam X-ray architecture to reduce the BH artifacts. The proposed methodology uses an initial sampling to identify high-density elements and an adaptive sampling to avoid the acquisition of those dense elements. Specifically, the proposed method is summarized into three main steps: (i) sensing matrix analysis via Gershgorin theorem; (ii) coded aperture optimization criteria based on view angles, pixels of the object, and dense elements; (iii) coded aperture optimization algorithm through the sensing matrix analysis and the proposed optimization criteria. Simulation results show that the reconstructed images by the proposed adaptive methodology gain up to in averaged peak signal-to-noise ratio (PSNR) compared to the traditional CA-CT approach which implements non-designed coded apertures.
中文翻译:
自适应编码孔径设计用于压缩计算机断层扫描
计算机断层扫描(CT)是一种非侵入性扫描技术,可通过X射线投影可视化对象的内部结构。这些投影经常受不同伪影的影响,其中包括射束硬化(BH)效应等。BH效应是由于感兴趣的对象内部的密集元素导致的高X射线衰减而产生的。传统上,BH伪影通过应用过采样技术来解决。但是,长时间的X射线暴露会对患者的健康构成威胁。为了克服该缺点,已经开发了欠采样CT方法,例如基于压缩感测(CS)理论的编码孔径计算机断层摄影(CA-CT)。然而,CA-CT尚未扩展用于解决BH效应。这项工作提出了一种基于扇形X射线架构的自适应编码孔径传感方法,以减少BH伪影。所提出的方法使用初始采样来识别高密度元素,并使用自适应采样来避免获取那些密集元素。具体而言,所提出的方法概括为三个主要步骤:(i)通过Gershgorin定理检测矩阵;(ii)基于视角,物体像素和密集元素的编码光圈优化标准;(iii)通过感测矩阵分析和提出的优化标准来编码孔径优化算法。仿真结果表明,所提出的自适应方法所重建的图像的增益达到最大值。所提出的方法使用初始采样来识别高密度元素,并使用自适应采样来避免获取那些密集元素。具体而言,所提出的方法概括为三个主要步骤:(i)通过Gershgorin定理检测矩阵;(ii)基于视角,物体像素和密集元素的编码光圈优化标准;(iii)通过感测矩阵分析和提出的优化标准来编码孔径优化算法。仿真结果表明,所提出的自适应方法所重建的图像的增益达到最大值。所提出的方法使用初始采样来识别高密度元素,并使用自适应采样来避免获取那些密集元素。具体而言,所提出的方法概括为三个主要步骤:(i)通过Gershgorin定理检测矩阵;(ii)基于视角,物体像素和密集元素的编码光圈优化标准;(iii)通过感测矩阵分析和提出的优化标准来编码孔径优化算法。仿真结果表明,所提出的自适应方法所重建的图像的增益达到最大值。(ii)基于视角,物体像素和密集元素的编码光圈优化标准;(iii)通过感测矩阵分析和提出的优化标准来编码孔径优化算法。仿真结果表明,所提出的自适应方法所重建的图像的增益达到最大值。(ii)基于视角,物体像素和密集元素的编码光圈优化标准;(iii)通过感测矩阵分析和提出的优化标准来编码孔径优化算法。仿真结果表明,所提出的自适应方法所重建的图像的增益达到最大值。 与采用非设计编码孔径的传统CA-CT方法相比,平均峰值信噪比(PSNR)有所降低。