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 $12\left[\mathrm{dB}\right]$ in averaged peak signal-to-noise ratio (PSNR) compared to the traditional CA-CT approach which implements non-designed coded apertures.

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。$12\left[\mathrm{D\; b}\right]$ 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。