Estimating Instrument Spectral Response Functions Using Sparse Representations and Quadratic Envelopes

The estimation of high resolution spectrometer Instrument Spectral Response Functions (ISRFs) is crucial because an imperfect knowledge of these functions can induce errors in the measurements. The state-of-the-art for this problem currently relies on the use of parametric models, which frequently lack flexibility to accurately model real-world ISRFs. To address this limitation, this paper proposes and investigates the use of sparse representations for modeling and estimating ISRFs, where the ISRFs are decomposed in a fixed dictionary of atoms. To estimate the sparse coefficient vector, a novel sparsity inducing regularization of the problem based on quadratic envelopes is studied and compared to the classical LASSO estimator and to a greedy method based on the Orthogonal Matching Pursuit (OMP) algorithm. Results for simulated ISRFs from the MicroCarb mission indicate that the proposed spectral representations yield excellent ISRF estimates, and that the use of quadratic envelopes can yield significantly better precision than competing methods.