Spectral semi-blind deconvolution with least trimmed squares regularization

• Least trimmed squares (LTS) regularization is modeled to preserve spectral details.
• Spectral semi-blind deconvolution method with LTS regularization is proposed.
• Numerical solution procedure of SBD-LTS is deduced in detail.
• The effectiveness of SBD-LTS is verified by some deconvolution experiments.

A spectral semi-blind deconvolution with least trimmed squares regularization (SBD-LTS) is proposed to improve spectral resolution. Firstly, the regularization term about the spectrum data is modeled as the form of least trimmed squares, which can help to preserve the peak details better. Then the regularization term about the PSF is modeled as L1-norm to enhance the stability of kernel estimation. The cost function of SBD-LTS is formulated and the numerical solution processes are deduced for deconvolving the spectra and estimating the PSF. The deconvolution results of simulated infrared spectra demonstrate that the proposed SBD-LTS can recover the spectrum effectively and estimate the PSF accurately, as well as has a merit on preserving the details, especially in the case of noise. The deconvolution result of experimental Raman spectrum indicates that SBD-LTS can resolve the spectrum and improve the resolution effectively.