This study proposes different fitting methods for different types of targets in the 400–900 nm wavelength range, based on convex optimization algorithms, to achieve the effect of high-precision spectral reconstruction for small space-borne spectrometers. This article first expounds on the mathematical model in the imaging process of the small spectrometer and discretizes it into an AX = B matrix equation. Second, the design basis of the filter transmittance curve is explained. Furthermore, a convex optimization algorithm is used, based on 50 filters, and appropriate constraints are added to solve the target spectrum. First, in terms of spectrum fitting, six different ground object spectra are selected, and Gaussian fitting, polynomial fitting, and Fourier fitting are used to fit the original data and analyze the best fit of each target spectrum. Then the transmittance curve of the filter is equally divided, and the corresponding AX = B discrete equation set is obtained for the specific object target, and a random error of 1% is applied to the equation set to obtain the discrete spectral value. The fitting is performed for each case to determine the best fitting method with errors. Subsequently, the transmittance curve of the filter with the detector characteristics is equally divided, and the corresponding AX = B discrete equation set is obtained for the specific object target. A random error of 1% is applied to the equation set to obtain the error. After the discrete spectral values are obtained, the fitting is performed again, and the best fitting method is determined. In order to evaluate the fitting accuracy of the original spectral data and the reconstruction accuracy of the calculated discrete spectrum, the three evaluation indicators MSE, ARE, and RE are used for evaluation. To measure the stability and accuracy of the spectral reconstruction of the fitting method more accurately, it is necessary to perform 500 cycles of calculations to determine the corresponding MSE value and further analyze the influence of the fitting method on the reconstruction accuracy. The results show that different fitting methods should be adopted for different ground targets under the error conditions. The three indicators, MSE, ARE, and RE, have reached high accuracy and strong stability. The effect of high-precision reconstruction of the target spectrum is achieved. This article provides new ideas for related scholars engaged in hyperspectral reconstruction work and promotes the development of hyperspectral technology.
Computational spectral imaging technology is an effective method to miniaturize the imaging spectrometer. Stable spectral reconstruction has been achieved with on-chip spectrometers using broad-bandpass filter dot-arrays. The imaging spectrometer using broad-bandpass filter line-arrays is developed for computational spectral imaging. Due to the processing difficulty of actual filter line arrays, 20-line arrays of the broad bandpass filter were selected in the pre-study. The discrete linear model is developed by analyzing the system response of the imaging spectrometer. The sparse constraint is introduced into the current underdetermined solution system to guarantee a unique and accurate solution; since the solution of hyperspectral bands cannot be performed using a small number of filters. The incoherence analysis of the system response and the dictionary is carried out to identify the general orthogonal systems such as the discrete cosine transform (DCT), etc. that can be used as the dictionary. The OMP was used for the final implementation of the simulation to realize the spectral reconstruction in the Visible-NIR. The results of the reconstruction show that the DCT as the dictionary has the highest accuracy: mean square error≤8.24×10 -4 . The different accuracy of various spectral reconstructions using different sparse transforms indicates the existence of different sparse transforms with different sensitivity to the detail and the global of the target spectrum.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.