Tomographic absorption spectroscopy (TAS) is experiencing a surge of interest due to recent progress in laser technology and advanced imaging concepts such as nonlinear tomography and compressed sensing. Nevertheless, even though numerous algorithms have been adapted from other tomographic areas such as medical imaging and engineering process control, and applied in TAS applications, systematic comparison between those methods has not been investigated. In this work, we aim to test major inversion algorithms on both the so-called rank-deficient (RD) and discrete ill-posed (DIP) problems. Comparative studies were performed on extensive cases, and the results for three representative phantoms are reported here. Other important topics such as determination of control parameters and the semiconvergent behavior of iterative methods have also been studied. According to our study, Landweber outperformed other methods for two RD cases and is slightly inferior to the maximum likelihood expectation maximization (MLEM) algorithm for the third one. It has also been found that Landweber and MLEM feature better immunity to semiconvergence than the others; however, since MLEM is sensitive to an initial guess, it is less robust than Landweber. On the other hand, the truncated singular value decomposition (TSVD) method is recommended for DIP problems due to its superior performance as it can effectively suppress detrimental effects from noise, which will be amplified during the inversion procedure. It should be emphasized that even though this study was conducted under the context of TAS, we expect it to provide useful insights for other tomographic modalities.
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20 March 2017: Corrections were made to Ref. 17 and Refs. 49–55.