Generalized Inverse-Approach Model for Spectral-Signal Recovery

Abstract

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.

A general metric for the magnitude of observer metamerism

“…The performance of spectral reconstruction methods from sensor responses is generally assessed by colorimetric and spectral metrics. The spectral difference between a reference spectrum and a recovered one is evaluated by spectral metrics such as the goodness‐of‐fit coefficient or the root mean square value.…”

“…In the present paper, a linear approximation formula of Eqn (20) was developed that links an arbitrary (small) observer CMF change to the colorimetric shift of a reflecting sample. The application of this formula to a metameric pair of reflecting samples gave another linear approximation formula of Eqn (23), which transforms an arbitrary small observer CMF change to the truly metameric effectthe colour difference vector between metameric samples after the observer's CMFs have been slightly changed. As the linear model of Eqn (23) is expected to predict a small colour difference due to small observer change DT, the accuracy of Eqn (23) in predicting the observer-metameric CIELAB colour difference value, ðDL à ; Da à ; Db Ã Þ T metameric…”

Visible Light Spectrum Extraction from Diffraction Images by Deconvolution and the Cepstrum

“…The most relevant previous work considered the task of estimating the reflectance spectrum with a computational method from an image acquired with a monochromatic or a trichromatic camera, typically equipped with passive color filters. Several methods combining multispectral imaging with algorithms that estimate the reflectance spectrum (and subsequently, the color) by explicitly assuming it to be smooth were proposed [ 7 , 8 , 9 , 10 ]. Similarly, the observation that most of the variance in the reflectance spectra can be explained by a small number of principal components[ 7 , 11 ] has been used for estimating them using principal component analysis of multispectral images [ 8 , 12 ].…”

“…Similarly, the observation that most of the variance in the reflectance spectra can be explained by a small number of principal components[ 7 , 11 ] has been used for estimating them using principal component analysis of multispectral images [ 8 , 12 ]. Other works assumed that Gaussian distributions are good estimates for reflectance spectra [ 10 , 13 ] and used these for the recovery of the spectrum. An alternative to using color filters is to use multiple illuminants for multispectral image capture [ 14 ].…”

“…Our approach shares the conceptual motivation of the previous research covered above, but uses a simpler optical construction and makes less assumptions about the spectra. In particular, we used a purely passive add-on device attached to ordinary consumer cameras and did not require knowing its spectral response, and our computational method requires only mild smoothness assumption, in contrast to the strong parametric assumptions of, e.g., [ 8 , 10 , 12 , 13 ]. The core idea of our approach is in the use of a specific diffractive element—a transmissive diffraction grating—placed in front of the camera sensor.…”