We have studied the transformation system of a spectral signal to the response of the system as a linear mapping from higher to lower dimensional space in order to look more closely at inverse-approach models. The problem of spectral-signal recovery from the response of a transformation system is generally stated on the basis of the generalized inverse-approach theorem, which provides a modular model for generating a spectral signal from a given response value. The controlling criteria, including the robustness of the inverse model to perturbations of the response caused by noise, and the condition number for matrix inversion, are proposed, together with the mean square error, so as to create an efficient model for spectral-signal recovery. The spectral-reflectance recovery and color correction of natural surface color are numerically investigated to appraise different illuminant-observer transformation matrices based on the proposed controlling criteria both in the absence and the presence of noise.