  We consider the problem of joint three-dimensional (3D) localization and
material classification of unresolved space debris using a multispectral
rotating point spread function (RPSF). The use of RPSF allows one to estimate
the 3D locations of point sources from their rotated images acquired by a
single 2D sensor array, since the amount of rotation of each source image about
its x, y location depends on its axial distance z. Using multi-spectral images,
with one RPSF per spectral band, we are able not only to localize the 3D
positions of the space debris but also classify their material composition. We
propose a three-stage method for achieving joint localization and
classification. In Stage 1, we adopt an optimization scheme for localization in
which the spectral signature of each material is assumed to be uniform, which
significantly improves efficiency and yields better localization results than
possible with a single spectral band. In Stage 2, we estimate the spectral
signature and refine the localization result via an alternating approach. We
process classification in the final stage. Both Poisson noise and Gaussian
noise models are considered, and the implementation of each is discussed.
Numerical tests using multispectral data from NASA show the efficiency of our
three-stage approach and illustrate the improvement of point source
localization and spectral classification from using multiple bands over a
single band.
