Tomographic absorption spectroscopy based on dictionary learning.

Tomographic absorption spectroscopy (TAS) has an advantage over other optical imaging methods for practical combustor diagnostics: optical access is needed in a single plane only, and the access can be limited. However, practical TAS often suffers from limited projection data. In these cases, priors such as smoothness and sparseness can be incorporated to mitigate the ill-posedness of the inversion problem. This work investigates use of dictionary learning (DL) to effectively extract useful a priori information from the existing dataset and incorporate it in the reconstruction process to improve accuracy. We developed two DL algorithms; our numerical results suggest that they can outperform classical Tikhonov reconstruction under moderate noise conditions. Further testing with experimental data indicates that they can effectively suppress reconstruction artifacts and obtain more physically plausible solutions compared with the inverse Radon transform.