In optoacoustic imaging, recovering the absorption coefficients of tissue by inverting the light transport remains a challenging problem. Improvements in solving this problem can greatly benefit the clinical value of optoacoustic imaging. Existing variational inversion methods require an accurate and differentiable model of this light transport. As neural surrogate models allow fast and differentiable simulations of complex physical processes, they are considered promising candidates to be used in solving such inverse problems. However, there are in general no guarantees that the derivatives of these surrogate models accurately match those of the underlying physical operator. As accurate derivatives are central to solving inverse problems, errors in the model derivative can considerably hinder high fidelity reconstructions. To overcome this limitation, we present a surrogate model for light transport in tissue that uses Sobolev training to improve the accuracy of the model derivatives. Additionally, the form of Sobolev training we used is suitable for high-dimensional models in general. Our results demonstrate that Sobolev training for a light transport surrogate model not only improves derivative accuracy but also reduces generalization error for in-distribution and out-of-distribution samples. These improvements promise to considerably enhance the utility of the surrogate model in downstream tasks, especially in solving inverse problems.

翻译：在光声成像中，通过反演光传输来恢复组织的吸收系数仍然是一个具有挑战性的问题。解决该问题的改进可以极大地提升光声成像的临床价值。现有的变分反演方法需要一个精确且可微的光传输模型。由于神经代理模型能够对复杂物理过程进行快速且可微的模拟，它们被认为是解决此类反问题的有希望的候选方案。然而，通常无法保证这些代理模型的导数与底层物理算子的导数精确匹配。由于精确的导数是解决反问题的核心，模型导数中的误差会严重阻碍高保真重建。为了克服这一限制，我们提出了一种用于组织光传输的代理模型，该模型使用Sobolev训练来提高模型导数的准确性。此外，我们所采用的Sobolev训练形式通常适用于高维模型。我们的结果表明，对光传输代理模型进行Sobolev训练不仅提高了导数精度，还降低了分布内和分布外样本的泛化误差。这些改进有望显著增强代理模型在下游任务中的实用性，特别是在解决反问题方面。