Blind Poissonian reconstruction algorithm via curvelet regularization for an FTIR spectrometer.

Area of Science:

• Spectroscopy
• Analytical Chemistry
• Signal Processing

Background:

• Fourier Transform Infrared (FTIR) spectroscopy is prone to spectral degradation.
• Common issues include band overlap and Poisson noise, complicating data interpretation.
• Existing methods may struggle to fully resolve these degradation effects.

Purpose of the Study:

• To develop a robust method for mitigating infrared (IR) spectrum degradation.
• To address challenges of band overlap and Poisson noise in FTIR data.
• To enhance the accuracy of spectral feature extraction and material identification.

Main Methods:

• Formulated spectrum degradation as a maximum a posteriori (MAP) problem.
• Utilized a cost function with likelihood (Poisson noise model) and prior terms (curvelet transform, Gauss-Markov IRF).
• Employed the split Bregman iteration method for efficient minimization.

Main Results:

• Successfully removed Poisson noises from FTIR spectra.
• Preserved crucial spectral structure information.
• Achieved joint estimation of the instrument response function (IRF) and latent spectrum.
• Significantly reduced spectral degradation effects.

Conclusions:

• The proposed MAP framework offers effective IR spectrum reconstruction.
• The method enhances the convenience of spectral feature extraction.
• Improved spectral quality facilitates the interpretation of chemical and biological materials.