  Shadow detection and removal is a challenging problem in the analysis of
hyperspectral images. Yet, this step is crucial for analyzing data for remote
sensing applications like methane detection. In this work, we develop a shadow
detection and removal method only based on the spectrum of each pixel and the
overall distribution of spectral values. We first introduce Iterative Logistic
Regression (ILR) to learn a spectral basis in which shadows can be linearly
classified. We then model the joint distribution of the mean radiance and the
projection coefficients of the spectra onto the above basis as a parametric
linear combination of Gaussians. We can then extract the maximum likelihood
mixing parameter of the Gaussians to estimate the shadow coverage and to
correct the shadowed spectra. Our correction scheme reduces correction
artefacts at shadow borders. The shadow detection and removal method is applied
to hyperspectral images from MethaneAIR, a precursor to the satellite
MethaneSAT.
