Trade-offs between color saturation and noise sensitivity in image sensors

A color correction matrix is usually used to transform the raw color image obtained from color image sensors to adjust for factors such as variations in illumination and deviations of the actual filter characteristics from the ideal. Color correction matrices that have high condition numbers can greatly amplify noise, while it can be difficult to achieve good color saturation with low condition number matrices. Noise can be a significant problem for digital camera images which have limited bit-depth. We explore the trade-off between noise reduction and color saturation analytically, and using digital camera images. We present an orthonormality criterion to define optimality with respect to noise sensitivity and color saturation in the case of signal-independent, orthogonal sensor measurement noise in each color channel