Most color-acquisition devices capture spectral signals by acquiring only three samples, critically undersampling the spectral information. We analyze the problem of estimating high-dimensional spectral signals from low-dimensional device responses. We begin with the theory and geometry of linear estimation methods. These methods use linear models to characterize the likely input signals and reduce the number of estimation parameters. Next, we introduce two submanifold estimation methods. These methods are based on the observation that for many data sets the deviation between the signal and the linear estimate is systematic; the methods incorporate knowledge of these systematic deviations to improve upon linear estimation methods. We describe the geometric intuition of these methods and evaluate the submanifold method on hyperspectral image data.
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