Spectral imaging has advanced to reproduce the real colors under different illuminants. Since the high-precision spectral camera is expensive, multi-band cameras with 6∼16 channels have been widely used. On the other hand, human vision is basically tri-chromatic and perceives a color based on metamerism. According to matrix-R theory, any spectral input C is decomposed into fundamental C* and metameric black B. Human vision perceives the fundamental C* as visible component but bypasses the metameric black B as invisible component. On the conditional color matching under a fixed illuminant, we need only the fundamental. However both of fundamental and metameric black are necessary under the different illuminants, because the objective spectrum C=C*+B changes with the illuminant. This paper proposes a new spectral sensing model with XYZ+K four-band filters. The additional filter K is designed to rescue the “metameric black” and restores the spectral reflectance in combination with “fundamental” captured by XYZ colorimetric tri-color filters. The paper clarifies the mathematical design concept for the spectral sensitivity curve of filter K based on matrix-R theory and shows how the proposed XYZ+K sensing model works well when applied to the parametric or non-parametric spectral estimators keeping with the colorimetric color reproduction. The paper also introduces a simulation on spectral image restoration under the different illuminants.