Measuring the physical properties of galaxies such as redshift frequently requires the use of Spectral Energy Distributions (SEDs). SED template sets are, however, often small in number and cover limited portions of photometric color space. Here we present a new method to estimate SEDs as a function of color from a small training set of template SEDs. We first cover the mathematical background behind the technique before demonstrating our ability to reconstruct spectra based upon colors and then compare to other common interpolation and extrapolation methods. When the photometric filters and spectra overlap we show reduction of error in the estimated spectra of over 65% compared to the more commonly used techniques. We also show an expansion of the method to wavelengths beyond the range of the photometric filters. Finally, we demonstrate the usefulness of our technique by generating 50 additional SED templates from an original set of 10 and applying the new set to photometric redshift estimation. We are able to reduce the photometric redshifts standard deviation by at least 22.0% and the outlier rejected bias by over 86.2% compared to original set for z $leq$ 3.
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