解决投影角度和位置未知的二维断层成像问题
Two-Dimensional Tomographic Reconstruction From Projections With Unknown Angles and Unknown Spatial Shifts
- 基于图拉普拉斯算法改进，同时估计投影角度与空间偏移
- 在噪声肋骨图像上重建效果优于忽略偏移的基线方法
- 适合工业与生物医学中几何参数未知的成像场景
平行束计算机断层扫描（CT）中，物体通过不同角度的投影进行重建。但在某些工业与生物医学成像应用中，投影几何信息未知或部分缺失。本文提出一种二维（2D）断层成像技术，可同时处理投影角度与空间偏移未知的问题。现有二维未知视角断层成像（UVT）算法多假设投影中心对齐，即无空间偏移。为此，我们首先改进一种基于图拉普拉斯的2D UVT算法以支持空间偏移，再将其作为初始化，用于所提出的三路交替最小化算法，联合估计二维结构、投影角度及对应偏移量。在含噪声的核糖体图像投影数据上评估，结果表明该方法重建质量显著优于忽略偏移的基线方法。
原文摘要 · Abstract (English)
In parallel beam computed tomography (CT), an object is reconstructed from a series of projections taken at different angles. However, in some industrial and biomedical imaging applications, the projection geometry is unknown, completely or partially. In this paper, we present a technique for two-dimensional (2D) tomography in which both viewing angles and spatial shifts associated with the projections are unknown. There exists literature on 2D unknown view tomography (UVT), but most existing 2D UVT algorithms assume that the projections are centered; that is, there are no spatial shifts in the projections. To tackle these geometric ambiguities, we first modify an existing graph Laplacian-based algorithm for 2D UVT to incorporate spatial shifts, and then use it as the initialization for the proposed three-way alternating minimization algorithm that jointly estimates the 2D structure, its projection angles, and the corresponding shifts. We evaluate our method on noisy projections of ribosome images and demonstrate that it achieves superior reconstruction compared to the baseline that neglects shifts.
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