Bayesian framework with wavelet gradient prior for denoising gas Fourier transform infrared spectra
Yuhao Wang, Liang Xu, Jianguo Liu, Hanyang Xu · Optical Engineering · 2025
Noise in Fourier transform infrared spectroscopy critically affects both qualitative and quantitative analyses, particularly when the instrument’s measurement time is limited. Traditional denoising methods are widely believed to struggle in balancing noise reduction and detail preservation, especially within high-resolution (≤1 cm−1) gas Fourier transform infrared spectroscopy. For example, Savitzky–Golay filters may offer minimal noise reduction. To confront these challenges, we propose a denoising method based on a wavelet gradient prior within a Bayesian framework. This approach formulates the spectrum denoising problem as a maximum a posteriori estimate, optimized using the split Bregman iteration technique. We evaluated our method against Savitzky–Golay filtering, wavelet denoising, and other statistical techniques, including total variation and second-order total generalized variation denoising, based on mean-square error and visual quality. Validation on both simulated and real datasets with a noise level around 1×10−4 shows that our method reduces mean-square error by at least 25% compared with the original noisy spectra. Furthermore, it outperforms traditional methods by at least 13% and other commonly used statistical denoising techniques by at least 5%. These results demonstrate the effectiveness of our method in reducing spectral noise, leading to progressively more accurate gas analysis for industrial applications.