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>i)</i> automatically adjusts the regularization strength based on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msup> </mml:math> norm of the input sinogram, and <i>ii)</i> 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.