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The theory of optimal image restoration is well established for monochrome imagery. However, a variety of sensors acquire multi-spectral or polychrome imagery. The restoration of multispectral imagery by optimal (Wiener) methods is developed in this paper. It is shown that optimal restoration must take place in the Karhunen-Loeve domain. It is further shown that high quality approximate multispectral restorations must be achieved at less computational cost than exact restoration. This latter point is applied to the development of a fast approximate procedure for restoration of conventional color photography.