Coded aperture X-ray computed tomography (CAXCT) systems reconstruct high quality images of the inner structure of an object from a few coded illumination measurements. Since the computed tomography (CT) system matrix is highly structured, random coded apertures lead to lower quality image reconstructions. In this paper, the noisy forward models of CAXCT in both Gaussian noise and Poisson noise are formulated and analyzed. In addition, a coded aperture optimization approach based on sparse principal component analysis is proposed to maximize the information sensed by a set of fan-beam projections. The complexity of the proposed optimization method is on the same order of magnitude as that of state-of-the-art methods but provide superior image quality. Computational experiments using simulated datasets and real datasets show gains up to $\sim$4.3 dB with SNR = 25 dB in the reconstruction image quality compared with that attained by random coded apertures.

中文翻译：

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通过稀疏主成分分析在 X 射线断层扫描中优化编码孔径

编码孔径 X 射线计算机断层扫描 (CAXCT) 系统通过少量编码照明测量重建物体内部结构的高质量图像。由于计算机断层扫描 (CT) 系统矩阵是高度结构化的，随机编码孔径导致图像重建质量较低。本文对高斯噪声和泊松噪声中CAXCT的噪声前向模型进行了阐述和分析。此外，提出了一种基于稀疏主成分分析的编码孔径优化方法，以最大化一组扇形光束投影所感知的信息。所提出的优化方法的复杂性与最先进方法的复杂性处于同一数量级，但提供了卓越的图像质量。使用模拟数据集和真实数据集的计算实验显示增益高达 $\sim$4。