Model-based spectral reconstruction of interferometric acquisitions

Spectral information of the scene can be reconstructed from processing observations acquired by interferometric devices. In the case of devices that have multiple wave interference (e.g., Fabry-Perot etalons), a simple inversion such as inverse Fourier transform (e.g., for Michelson-like interferometers) of the measured interferograms is not straightforward due to the ill-posedness of the problem. In this paper, we represent the system through an infinity-wave model. The spectral reconstruction is done by a model-based approach as we have a good knowledge of the system. Specifically, we propose to use Loris-Verhoeven algorithm with proximal solvers and induced sparsity on the Fourier domain of the desired spectrum. Our proposal is more robust to noise compared to conventional reconstruction algorithms, as demonstrated by experiments that are carried with interferograms computed from real spectral acquisitions.