Scale-equivariant deep model-based optoacoustic image reconstruction

Model-based reconstruction provides state-of-the-art image quality for multispectral optoacoustic tomography. However, optimal regularization of in vivo data necessitates scan-specific adjustments of the regularization strength to compensate for fluctuations of the signal magnitudes between different sinograms. Magnitude fluctuations within in vivo data also pose a challenge for supervised deep learning of a model-based reconstruction operator, as training data must cover the complete range of expected signal magnitudes. In this work, we derive a scale-equivariant model-based reconstruction operator that i) automatically adjusts the regularization strength based on the $L^2$ norm of the input sinogram, and ii) facilitates supervised deep learning of the operator using input singorams with a fixed norm. Scale-equivariant model-based reconstruction applies appropriate regularization to sinograms of arbitrary magnitude, achieves slightly better accuracy in quantifying blood oxygen saturation, and enables more accurate supervised deep learning of the operator.