We have described two different acceleration techniques and demonstrated their application in both instrument restoration for production of the datacube, and deconvolution to improve spectral resolution. The non-search acceleration is ideal in deconvolution problems and can reduce the number of iterations from one to three orders of magnitude. It has also been found to be ideal in single-color image restoration, reducing the number of iterations to just three. A power exponentiation acceleration has been found useful in restoration of spectral instruments where the applications require high spectral resolution information. For applications with broadband spectra where the spectral information is relatively low resolution, both the power law exponentiation and non-search acceleration work acceptably. Restoration of these type of spectra require only a few iterations and gain from an accelerated restorations is limited. In these latter instances,iterations can be reduced from between 10-20 to between 5-10. It is anticipated that the acceleration techniques can reduce overall iteration time more than on order of magnitude in processing hyperspectral datacubes from tomographic instruments and will aid in developing instruments which have throughput which allows their many physical advantages to be put more fully to use in hyperspectral applications.
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