Notes on reconstructing the data cube in hyperspectral image processing

The hyperspectral imaging technique described in [12] leads to the interesting problem of reconstructing a three-dimensional data cube from measured data. This problem involves three separate steps in which we must estimate values of a function from values of its Fourier transform. Depending on which of the two functions involved at each step has bounded support, that is, is zero off of a bounded set, the estimation process can take one of two forms, which we call Type One and Type Two problems. We discuss these two types and suggest techniques for solving both of them. For Type Two problems there is a good opportunity to incorporate whatever prior information we may have about the shape of the function being reconstructed. Since the data sets are large we recommend the use of iterative methods, such as the algebraic reconstruction technique (ART).