In-Flight Estimation of Instrument Spectral Response Functions Using Sparse Representations for Remote Sensing Missions

Core Concepts

A new sparse representation-based method for accurate in-flight estimation of Instrument Spectral Response Functions (ISRFs) is proposed and evaluated on datasets from various remote sensing spectrometers. The method outperforms state-of-the-art parametric models in terms of ISRF estimation accuracy.

Abstract

This paper proposes a new method, called SPIRIT (SParse representation of Instrument spectral Response functions using a dIcTionary), for accurate in-flight estimation of Instrument Spectral Response Functions (ISRFs) for high-resolution spectrometers used in remote sensing missions. The key highlights are: Existing parametric models like Gaussian and generalized Gaussian (Super-Gauss) have limited flexibility to represent the diverse ISRF shapes encountered in practice. SPIRIT decomposes ISRFs as sparse linear combinations of atoms in a well-chosen dictionary, providing much greater flexibility. Two dictionary construction methods are investigated: using Singular Value Decomposition (SVD) of ISRF examples, and the K-SVD algorithm. Sparse coding is performed using Orthogonal Matching Pursuit (OMP) or LASSO optimization. SPIRIT is evaluated on datasets from 6 different spectrometers (Avantes, GOME-2, OMI, TROPOMI, OCO-2, MicroCarb) and shown to significantly outperform parametric models, achieving normalized ISRF estimation errors below 1%. The method is robust to noise corruption of the spectral measurements and can adapt to ISRF changes due to varying scene illumination. Overall, SPIRIT with OMP and SVD-based dictionary provides the best performance across the different instruments and scenarios.

Stats

The normalized ISRF estimation errors for the Gaussian model are typically above 10%. The normalized ISRF estimation errors for the Super-Gaussian model are typically around 2-5%. The normalized ISRF estimation errors for the SPIRIT method with OMP and SVD are typically below 1%.

Quotes

"The proposed SPIRIT method allows us to obtain normalized errors less than 1%, which are significantly below those of parametric methods." "For this spectrometer, LASSO has more difficulty to approximate the ISRFs than OMP, possibly due to the l1 regularization, LASSO may struggle to select the correct coefficients." "To conclude, OMP combined with SVD provides the overall best results for ISRF estimation, also in the presence of additive noise."

Key Insights Distilled From

In-Flight Estimation of Instrument Spectral Response Functions Using Sparse Representations

by Jihanne El H... at arxiv.org 04-09-2024

https://arxiv.org/pdf/2404.05298.pdf

Deeper Inquiries

How could the proposed SPIRIT method be extended to jointly estimate the ISRFs and other instrument parameters like wavelength calibration

The proposed SPIRIT method could be extended to jointly estimate the ISRFs and other instrument parameters like wavelength calibration by incorporating these parameters into the dictionary. Instead of solely focusing on the ISRFs, the dictionary could include atoms representing the different instrument parameters that affect the spectral response. By including these parameters in the dictionary, the sparse representation approach can be used to simultaneously estimate the ISRFs and the other instrument parameters. This would involve expanding the dictionary to encompass a wider range of possible variations in the instrument parameters, allowing for a more comprehensive estimation of the instrument characteristics.

What are the potential limitations of the sparse representation approach if the ISRF shapes exhibit very high variability across wavelengths or instruments

The potential limitations of the sparse representation approach arise when the ISRF shapes exhibit very high variability across wavelengths or instruments. In such cases, the dictionary may not adequately capture the diverse range of ISRF shapes, leading to suboptimal estimation results. If the ISRF shapes are highly complex and cannot be effectively represented by the atoms in the dictionary, the sparse representation approach may struggle to accurately model the ISRFs. Additionally, the performance of the sparse representation approach may be limited by the choice of dictionary and the number of atoms used for representation. If the dictionary is not sufficiently diverse or if the number of atoms is too limited, the approach may not be able to effectively capture the variability in the ISRF shapes.

Could the SPIRIT framework be applied to other types of instrument characterization problems beyond just ISRFs

Yes, the SPIRIT framework could be applied to other types of instrument characterization problems beyond just ISRFs. The underlying principle of using sparse representations in a dictionary to model complex instrument responses can be extended to various instrument parameters and characteristics. For example, the SPIRIT framework could be adapted to estimate point spread functions, detector responses, or other optical properties of instruments. By constructing dictionaries that encompass the different aspects of instrument behavior, the SPIRIT approach can be utilized for a wide range of instrument characterization tasks. This flexibility allows for the application of the SPIRIT framework to diverse instruments and measurement scenarios, providing a versatile tool for instrument calibration and characterization.