可扩展的光声断层成像实现：考虑换能器空间脉冲响应
Scalable photoacoustic tomography implementations accounting for the spatial impulse response of transducers
另 4 家 · 查看机构详情
- Université de Toulouse, CNRS（图卢兹大学）
- UPS（艾克斯-马赛大学）
- Aix Marseille Univ, CNRS, Institut de Mathématiques de Marseille（索邦大学）
- Sorbonne Université, CNRS, Inserm, Laboratoire d’Imagerie Biomédicale, LIB（科学技术研究局）
- Agency for Science, Technology and Research（南洋理工大学）
- Nanyang Technological University（新加坡国立大学）
- National University of Singapore
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中文总结 AI 辅助
本文提出可扩展的光声断层成像实现，通过闭式面积或求积法计算换能器空间脉冲响应，并加速椭圆积分，实现快速精确的三维模型重建，优于反投影方法。
中文摘要 AI 辅助
光声断层成像中的迭代模型重建反复应用将初始压力映射到换能器信号的正向算子及其伴随算子。在当前三维系统的规模下，该算子无法存储，必须以无矩阵方式求值，同时需考虑换能器有限且聚焦的表面，其空间脉冲响应若被忽略会降低分辨率。通过用紧支撑径向函数表示初始压力，我们证明测量信号恰好是系统核（汇集径向函数与电脉冲响应）与纯几何量（表示一个时间步内从体素发射的波所到达的换能器表面部分）之间的时间卷积。我们提出了两种实现，仅在该量的求值方式上有所不同：一种是对表面上的点进行求积（如现有工作），另一种是闭式面积，从不离散表面。我们推导了平面和柱面聚焦换能器的闭式表达式，并在后一种情况下提供了所得椭圆积分的两种加速方法：查找表法和梯形近似法，以及文献中常用的分段平面近似。这些实现减少了逐体素的几何计算，并作为面向图形处理单元的开源Python包发布。这些算子的性能首先在合成体模上得到验证，其中基于查找表的算子达到精确求值的精度，速度快十倍，且在精度和运行时间上均优于点离散化。第二个实验表明，它们能够以全尺寸处理真实的血管体模，与反投影对应方法相比，具有更高的峰值信噪比和更好的分辨率。所发布的实现是向采用有限且聚焦换能器的三维模型光声重建迈出的重要一步。
英文摘要
Iterative model-based reconstruction in photoacoustic tomography repeatedly applies the forward operator mapping the initial pressure to the transducer signals, and its adjoint. At the scale of current three-dimensional systems, this operator cannot be stored and must be evaluated matrix-free, while accounting for the finite, focused surface of the transducers, whose spatial impulse response degrades the resolution when ignored. Representing the initial pressure by compactly supported radial functions, we show that the measured signal is exactly a temporal convolution between a system kernel gathering the radial function and the electrical impulse response, and a purely geometric quantity accounting for the portion of the transducer surface reached by the wave emitted from a voxel during one time step. Two implementations are proposed, differing only in how this quantity is evaluated: a quadrature over points of the surface, as in existing works, or a closed-form area, which never discretizes the surface. We derive closed forms for planar and cylindrically focused transducers and provide, in the latter case, two accelerations of the resulting elliptic integrals, a lookup table and a trapezoidal approximation, together with the piecewise planar approximation customary in the literature. These implementations reduce the per-voxel geometric computations and are released as an open-source Python package for graphics processing units. The performance of these operators is first demonstrated on a synthetic phantom, where the lookup-table-based operator reaches the accuracy of the exact evaluation ten times faster and outperforms the point discretization on both accuracy and runtime. A second experiment shows that they enable the processing of a realistic vascular phantom at full scale, with a higher peak signalto-noise ratio and a better resolution than the back-projection counterpart. The released implementations are an important step towards the adoption of three-dimensional modelbased photoacoustic reconstructions with finite and focused transducers.
