Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise

The acquisition of the colorimetric information about an object using a color image acquisition device is important at an early stage in a color management system. The accuracy of the colorimetric values estimated by the device responses depends not only on the spectral sensitivities of a set of sensors but also on the noise present in the devices. We address the optimization of a set of spectral sensitivities with Gaussian distribution functions based on a colorimetric evaluation model. It is demonstrated that the design of optimal sensors is contingent on finding the right balance between the human visual subspace and the subspace that maximizes the singular values of a matrix 1/2 to increase the robustness to noise, where , , , and represent a sensor matrix, a diagonal matrix for an illuminant, a basis matrix, and a diagonal matrix with eigenvalues of an autocorrelation matrix of reflectance spectra, respectively.