Hyperspectral Image Dimensionality Reduction with Metamer Discrimination Preservation

Hyperspectral imaging, even when restricted to the visible spectrum range, allows what is indiscriminable to the human visual system to become discriminable. The typical human visual system (HVS) projects the light spectrum, the determinant of color, into a threedimensional subspace. The basis is determined by the spectral response of the three types of cones. The response has been modeled as the 1964 10 degree CIE Standard Colorimetric Observer Data, which we take to be our standard. The response is shown in Figure 1. Atypical people may have visual systems that perform twoor four-dimensional subspace projections. Contrariwise, hyperspectral images are able to sample the light spectrum in much finer detail, producing 30 or more linear functionals at each pixel location. A sample hyperspectral image from the database of [1] is shown in Figure 2. As can be noted from the figure, unlike remote sensing hyperspectral image data, there are no junk bands where there is significant noise due to atmospheric interference [2]; all bands seem useful and so we would like to make use of them. In the subimage format of Figure 2, however, the image is hard to interpret; we would like to reduce the dimensionality to facilitate interpretation by a human observer. When the HVS does the dimensionality reducing projection, there are points in the higher-dimensional space that are mapped to the same point in the low-dimension space. The projection of the hyperspectral image in Figure 2 using the representors shown in Figure 1 is shown in Figure 3. Points in the high-dimensional space that are projected to the same point in low-dimensional space are referred to as metamers. The in-subspace component of metamers is the same, but the out-of-subspace component can be arbitrary, therefore there is an infinite collection of metamers: the dimensionality-reduction problem is undercomplete. Two spectra that yield the same point in the three-dimensional HVS subspace are shown in Figure 4. The goal of this project is to reduce the dimensionality of hyperspectral images, so that they can be easily displayed and interpreted by people. One could simply project to the HVS subspace; however this would result in metamers. We would like to preserve the benefit of hyperspectral imagery, the ability to discriminate metamers, by a suitable modification of the projection process. We would also like to meet many of the desiderata delineated by [3] for the