Levenberg–Marquardt algorithm with adaptive Tikhonov regularization for bandwidth correction of spectra

ABSTRACT

Spectrometers are widely used in many fields. However, the spectrum is distorted due to the bandwidth limitations. This study analyzes the problem of using the least square method for bandwidth correction, introduces the common regularization methods and the existing problems of Tikhonov regularization, and proposes a new bandwidth correction method based on Levenberg–Marquardt algorithm with adaptive Tikhonov regularization. The proposed method was used to optimize spectral parameters. White light-emitting diodes and Raman were used as light sources, and a comparative simulation was conducted. Subsequently, the uncertainty and root mean square error of different regularization parameters were calculated. Results show that the proposed method exhibits satisfactory bandwidth correction effect and small estimation error.

KEYWORDS:

• Bandwidth correction
• deconvolution
• Levenberg–Marquardt algorithm
• adaptive Tikhonov regularization

Acknowledgments

The authors would like to thank the anonymous reviewers for their helpful comments and constructive suggestions and to Shinewrite for providing the touch-up service.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Key Research and Development Program of Anhui Province [grant number 1804d08020310].