A New Method for Analysis of Differential Optical Absorption Spectra using Wavelet Transform and Independent Component Analysis

This paper presents a new method for analysis of differential optical absorption spectroscopy (DOAS), which has been used for nondestructive air monitoring and has used the LS (least squares) method to calculate trace gas concentrations due to its computational simplicity. Since the LS method is insufficient to recover the desired spectra perfectly due to sparsity characteristic, we applies the ICA (independent component analysis) method to the DOAS system. If the sparsity of reference spectra in the DOAS system imposes the assumption of independence, the ICA algorithm can be used to regress the observed spectrum on the estimates of the reference spectra. In this paper, for enhancing this sparsity, we apply the wavelet transform into the DOAS spectra, and estimate the independent components from the decomposition signal that the wavelet transform can yield the input in the ICA. The ICA algorithm can be seen as a preprocessing method where the ICs of the references are used as the input in the regression. When the measured spectrum data is reconstructed by regression with the ICs of the decomposition signal, the concentration is calculated by LS method with the reconstruction spectrum. The performance of the proposed method is evaluated in simulation studies using synthetic data and real measured data.