Compressive recovery of smartphone RGB spectral sensitivity functions

Spectral response (or sensitivity) functions of a three-color image sensor (or trichromatic camera) allow a mapping from spectral stimuli to RGB color values. Like biological photosensors, digital RGB spectral responses are device dependent and significantly vary from model to model. Thus, the information on the RGB spectral response functions of a specific device is vital in a variety of computer vision as well as mobile health (mHealth) applications. Theoretically, spectral response functions can directly be measured with sophisticated calibration equipment in a specialized laboratory setting, which is not easily accessible for most application developers. As a result, several mathematical methods have been proposed relying on standard color references. Typical optimization frameworks with constraints are often complicated, requiring a large number of colors. We report a compressive sensing framework in the frequency domain for accurately predicting RGB spectral response functions only with several primary colors. Using a scientific camera, we first validate the estimation method with direct spectral sensitivity measurements and ensure that the root mean square errors between the ground truth and recovered RGB spectral response functions are negligible. We further recover the RGB spectral response functions of smartphones and validate with an expanded color checker reference. We expect that this simple yet reliable estimation method of RGB spectral sensitivity can easily be applied for color calibration and standardization in machine vision, hyperspectral filters, and mHealth applications that capitalize on the built-in cameras of smartphones.