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\begin{document}

\title{Expanded Dimensionality for Image Spectroscopy via Machine Learning}



\author[1]{Fangcao Xu}%
\author[1]{Guido Cervone}%
\author[2]{Mark Salvador}%
\affil[1]{Pennsylvania State University Main Campus}%
\affil[2]{Zi Inc}%


\vspace{-1em}



  
  \date{June 16, 2024}


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\begin{abstract}
The generalized solution for the radiance equation is expanded by
exploiting multiple hyperspectral image scans acquired by aerial
platforms at different viewing angles. A machine learning solution based
on convolutional neural networks is used to learn the relationships
between the total radiance observed at the sensor, and different
atmospheric components of the radiance equation. The goal is to
precisely characterize the atmosphere, in order to properly solve the
radiance equation, in which atmospheric components constitute important
input. Traditionally, these atmospheric components are only estimated
from averages of pixels, or assigned using heuristics tables. Compared
to traditional image spectroscopy, this expanded radiance equation and
machine learning solution integrates quantitative mathematical modeling,
multiple scanned hyperspectral images and artificial intelligence. The
solution is able to model and predict the transmittance, downwelling and
upwelling components of the radiance equation with increased spatial and
temporal dimensionality. It's promising to use different combinations of
the multiple scans to parameterize the radiance equation and improve the
target detection in varying atmospheric conditions, where current
solutions based on a single hyperspectral image normally fail. This
works presents initial results of an expanded mathematical solution,
along with the results from the convolution networks. Synthetic data
were generated using the MODTRAN atmospheric software to simulate
different vintage points, atmospheric models, time of the day and year,
for an array of specific targets with varying reflectances. More
specifically, MODTRAN was used to simulate Longwave Infrared Red between
7.5 and 12 microns with a 17.5 nanometers spectral sensitivity, which
correspond to the range and resolution of the Blue Heron Longwave
Hyperspectral sensor. Results from the convolutional neural network
indicate our machine learning solution is computationally faster than
the traditional radiative transfer (RT) model and is able to
characterize the impact of varying atmospheric conditions on the
at-sensor radiance components.%
\end{abstract}%



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