提出快速算法加速光声成像重建，显著提升计算效率。
Fast algorithms enabling optimization and deep learning for photoacoustic tomography in a circular detection geometry
- 基于圆形探测几何，设计了高效前向与伴随算子算法
- 图像尺寸为n×n时，计算复杂度降至O(n² log n)
- 已用于多种重建方法，适合医学成像与深度学习研究者
光声断层成像等耦合物理模态中的反源问题通常通过迭代算法求解，依赖代价函数最小化。当前研究也探索深度学习技术以改进优化方法。这些方法均需多次计算正向问题及其伴随算子。本文针对圆形探测几何，提出新的渐近快速算法，实现前向与伴随算子的高效数值计算。对于n×n图像，算法计算复杂度为O(n² log n)。我们在数值模拟中验证了其性能，将其作为经典变分方法（如非负最小二乘、总变差正则化最小二乘）和深度学习方法（如学习型原始对偶网络）的核心组件。算法的Python实现及计算示例已公开提供。
原文摘要 · Abstract (English)
The inverse source problem arising in photoacoustic tomography and in several other coupled-physics modalities is frequently solved by iterative algorithms. Such algorithms are based on the minimization of a certain cost functional. In addition, novel deep learning techniques are currently being investigated to further improve such optimization approaches. All such methods require multiple applications of the operator defining the forward problem, and of its adjoint. In this paper, we present new asymptotically fast algorithms for numerical evaluation of the forward and adjoint operators, applicable in the circular acquisition geometry. For an $(n \times n)$ image, our algorithms compute these operators in $\mathcal{O}(n^2 \log n)$ floating point operations. We demonstrate the performance of our algorithms in numerical simulations, where they are used as an integral part of several iterative image reconstruction techniques: classic variational methods, such as non-negative least squares and total variation regularized least squares, as well as deep learning methods, such as learned primal dual. A Python implementation of our algorithms and computational examples is available to the general public.
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