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We investigate methods for the recovery of reflectance spectra from the responses of trichromatic camera systems and the application of these methods to the problem of camera characterization. The recovery of reflectance from colorimetric data is an ill-posed problem, and a unique solution requires additional constraints. We introduce a novel method for reflectance recovery that finds the smoothest spectrum consistent with both the colorimetric data and a linear model of reflectance. Four multispectral methods were tested using data from a real trichromatic camera system. The new method gave the lowest maximum colorimetric error in terms of camera characterization with test data that were independent of the training data. However, the average colorimetric performances of the four multispectral methods were statistically indistinguishable from each other but were significantly worse than conventional methods for camera characterization such as polynomial transforms.