Variational color transformation method for direct color imaging

As an imaging scheme with a single solid-state image sensor, the direct color-imaging approach is considered promising as an acquisition scheme of multi-spectral color data with high spatial-resolution. The sensor has multiple photo-sensing layers more than two along its depth direction. Although each pixel has multiple color signals, their spectral sensitivities are overlapped with each other to a considerable extent. The overlapped color signals should be transformed to color signals such as RGB color signals and/or YMC color signals that are specified by an output device. We present a color transformation method for the direct color-imaging scheme. Our method tries to recover multi-spectral color data and then to transform the sensed color signals by utilizing the recovered multi-spectral color data. We formulate the problem as the inverse problem that multi-spectral color data with a large number of color channels are recovered from observed color signals with a smaller number of color channels, e.g. five channels, and solve it by the regularization technique that minimizes the energy functional composed of a color-fidelity energy term, a spectral-regularity energy term and so on. The color-fidelity energy term quantifies back-projection errors in the linear color transformation from the recovered multi-spectral color data to the sensed color signals, whereas the spectral-regularity energy term quantifies the smoothness property that a spectral reflectance at a color channel is similar to those at its neighboring channels. We simulate the direct color-imaging scheme and our color-transformation method. The results show that in the case of more than four photo-sensing layers our method restores multi-spectral reflectance acceptably.