DeepLight: A Sobolev-trained Image-to-Image Surrogate Model for Light Transport in Tissue

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.

A Method for Accurate Spatial Focusing Simulation via Numerical Integration and its Application in Optoacoustic Tomography

The spatial sensitivity of an ultrasound transducer, which strongly influences its suitability for different applications, depends on the shape of the transducer surface. Accurate simulation of these spatial effects is important for transducer characterization and design, and for system response modelling in imaging applications. In optoacoustic imaging, broadband transducers are used to capitalize on the rich frequency content of the signals, but their usage makes highly accurate simulations with general wave equation solvers prohibitively memory- and time-intensive. Therefore, specialized tools for simulating the isolated spatial focusing properties described by the spatial impulse response (SIR) have been developed. However, the challenging numerics of the SIR and the necessity to convolve the SIR with the wave shape generated by the optoacoustic absorber to simulate the system response lead to numerical inaccuracies of SIR-based methods. In addition, the approximation error of these methods cannot be controlled a priori. To circumvent the problems associated with the explicit calculation of SIR, we propose directly computing the convolution of the required wave shape with the SIR, which we call the spatial pulse response (SPR). We demonstrate that by utilizing an h-adaptive cubature algorithm, SPR can be computed with significantly higher accuracy than an SIR-based reference method, and the approximation error can be controlled with a tolerance parameter. In addition, the integration of accurate SPR simulations into model-based optoacoustic image reconstruction is shown to improve image contrast and reduce noise artifacts. Precise system characterization and simulation leads to improved imaging performance, ultimately increasing the value of optoacoustic imaging systems for clinical applications.