Tomographic absorption spectroscopy based on dictionary learning.

Area of Science:

• Optical diagnostics
• Spectroscopy
• Combustion science

Background:

• Tomographic absorption spectroscopy (TAS) offers advantages for combustor diagnostics due to limited optical access requirements.
• Practical TAS applications are often hindered by incomplete projection data, leading to ill-posed reconstruction problems.

Purpose of the Study:

• To investigate the use of dictionary learning (DL) for extracting a priori information from existing datasets.
• To incorporate this DL-derived information into the TAS reconstruction process to enhance accuracy and robustness.

Main Methods:

• Development of two novel dictionary learning (DL) algorithms tailored for TAS data.
• Incorporation of DL priors to regularize the ill-posed inverse problem in TAS reconstruction.
• Comparative analysis against classical Tikhonov reconstruction and inverse Radon transform.

Main Results:

• Numerical simulations demonstrated that DL algorithms outperform Tikhonov reconstruction under moderate noise.
• Experimental data validation showed significant suppression of reconstruction artifacts using DL methods.
• DL-based reconstructions yielded more physically plausible solutions compared to the inverse Radon transform.

Conclusions:

• Dictionary learning is an effective strategy for improving TAS reconstructions with limited projection data.
• DL-based methods offer enhanced accuracy and artifact reduction for practical combustor diagnostics.
• This approach provides a pathway to more reliable and physically meaningful optical imaging in combustion.