学习用于半球形测量几何的光声计算机断层扫描的滤波反投影重建方法
Learning a Filtered Backprojection Reconstruction Method for Photoacoustic Computed Tomography with Hemispherical Measurement Geometries
AI总结：
针对半球形PACT半扫描数据缺乏闭式重建公式的问题，提出用学习方法近似半扫描FBP中的未知滤波算子，并通过虚拟与体内乳腺实验验证其准确且泛化稳定。
摘要：
在光声计算机断层扫描（PACT）的某些三维（3D）应用中，包括体内乳腺成像，会采用将目标包围在其凸包内的半球形测量孔径来进行数据采集。由于这种测量几何仅使用完整球形测量孔径的一半，因此所采集的数据被称为半扫描数据。尽管先前研究已经证明，半扫描数据能够唯一且稳定地重建所寻求的目标，但尚未有适用于半扫描数据的闭式重建公式被报道。为解决这一问题，本研究开发了一种滤波反投影（FBP）形式的半解析重建方法，称为半扫描FBP方法。由于目前尚不知道半扫描FBP方法中滤波操作的显式形式，因此提出了一种基于学习的方法来近似该操作。通过采用数值乳腺体模集合和基于物理的数据采集过程模型的3D乳腺PACT虚拟成像研究，对所提出的方法进行了系统考察。随后，该方法被应用于一项体内乳腺PACT研究中采集的实验数据。结果证实，半扫描FBP方法能够从半扫描数据中准确重建3D图像。重要的是，由于所寻求的逆映射是适定的，即使将该重建方法应用于与学习滤波操作时所用数据差异很大的数据，它仍能保持准确。
英文摘要：
In certain three-dimensional (3D) applications of photoacoustic computed tomography (PACT), including \textit{in vivo} breast imaging, hemispherical measurement apertures that enclose the object within their convex hull are employed for data acquisition. Data acquired with such measurement geometries are referred to as \textit{half-scan} data, as only half of a complete spherical measurement aperture is employed. Although previous studies have demonstrated that half-scan data can uniquely and stably reconstruct the sought-after object, no closed-form reconstruction formula for use with half-scan data has been reported. To address this, a semi-analytic reconstruction method in the form of filtered backprojection (FBP), referred to as the half-scan FBP method, is developed in this work. Because the explicit form of the filtering operation in the half-scan FBP method is not currently known, a learning-based method is proposed to approximate it. The proposed method is systematically investigated by use of virtual imaging studies of 3D breast PACT that employ ensembles of numerical breast phantoms and a physics-based model of the data acquisition process. The method is subsequently applied to experimental data acquired in an \textit{in vivo} breast PACT study. The results confirm that the half-scan FBP method can accurately reconstruct 3D images from half-scan data. Importantly, because the sought-after inverse mapping is well-posed, the reconstruction method remains accurate even when applied to data that differ considerably from those employed to learn the filtering operation.
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