Untrained neural network for linear tomographic absorption spectroscopy

Linear tomographic absorption spectroscopy (LTAS) is a non-destructive diagnostic technique widely employed for gas sensing. The inverse problem of LTAS represents a classic example of an ill-posed problem. Linear iterative algorithms are commonly employed to address such problems, yielding generally poor reconstruction results due to the incapability to incorporate suitable prior conditions within the reconstruction process. Data-driven deep neural networks (DNN) have shown the potential to yield superior reconstruction results; however, they demand a substantial amount of measurement data that is challenging to acquire. To surmount this limitation, we proposed an untrained neural network (UNN) to tackle the inverse problem of LTAS. In conjunction with an early-stopping method based on running variance, UNN achieves improved reconstruction accuracy without supplementary training data. Numerical studies are conducted to explore the optimal network architecture of UNN and to assess the reliability of the early-stopping method. A comparison between UNN and superiorized ART (SUP-ART) substantiates the exceptional performance of UNN.