The Geometry of Noise in Color and Spectral Image Sensors

Digital images are always affected by noise and the reduction of its impact is an active field of research. Noise due to random photon fall onto the sensor is unavoidable but could be amplified by the camera image processing such as in the color correction step. Color correction is expressed as the combination of a spectral estimation and a computation of color coordinates in a display color space. Then we use geometry to depict raw, spectral and color signals and noise. Geometry is calibrated on the physics of image acquisition and spectral characteristics of the sensor to study the impact of the sensor space metric on noise amplification. Since spectral channels are non-orthogonal, we introduce the contravariant signal to noise ratio for noise evaluation at spectral reconstruction level. Having definitions of signal to noise ratio for each steps of spectral or color reconstruction, we compare performances of different types of sensors (RGB, RGBW, RGBWir, CMY, RYB, RGBC).