Learning a Fully Connected U-Net for Spectrum Reconstruction of Fourier Transform Imaging Spectrometers

Fourier transform imaging spectrometers (FTISs) are widely used in global hyperspectral remote sensing due to the advantages of high stability, high throughput, and high spectral resolution. Spectrum reconstruction (SpecR) is a classic problem of FTISs determining the acquired data quality and application potential. However, the state-of-the-art SpecR algorithms were restricted by the length of maximum optical path difference (MOPD) of FTISs and apodization processing, resulting in a decrease in spectral resolution; thus, the applications of FTISs were limited. In this study, a deep learning SpecR method, which directly learned an end-to-end mapping between the interference/spectrum information with limited MOPD and without apodization processing, was proposed. The mapping was represented as a fully connected U-Net (FCUN) that takes the interference fringes as the input and outputs the highly precise spectral curves. We trained the proposed FCUN model using the real spectra and simulated pulse spectra, as well as the corresponding simulated interference curves, and achieved good results. Additionally, the performance of the proposed FCUN on real interference and spectral datasets was explored. The FCUN could obtain similar spectral values compared with the state-of-the-art fast Fourier transform (FFT)-based method with only 150 and 200 points in the interferograms. The proposed method could be able to enhance the resolution of the reconstructed spectra in the case of insufficient MOPD. Moreover, the FCUN performed well in visual quality using noisy interferograms and gained nearly 70% to 80% relative improvement over FFT for the coefficient of mean relative error (MRE). All the results based on simulated and real satellite datasets showed that the reconstructed spectra of the FCUN were more consistent with the ideal spectrum compared with that of the traditional method, with higher PSNR and lower values of spectral angle (SA) and relative spectral quadratic error (RQE).