Robust Averaged Projections Onto Convex Sets

Abstract

We present a new robust method for recovering the spectral sensitivity of digital cameras and scanners. It is well known that the recovery of camera spectral sensitivities is an ill-posed problem. To stabilize the solution to the problem constraints are often imposed on the solution space. Among common constraints are: non-negativity, degree of smoothness, number of peaks, noise level bounding and that estimated curves result in the lowest possible error between predicted and measured data. These constraints are not always physically justified; and imposing them on the solution space can result in poor estimates that adhere only to our expectations of sensor curves.Knowing that all previous methods result in perfect sensor prediction when the data is noise-free, we introduce a robust algorithm that enables the user to heavily dampen the impact of noise and outliers on the solution. By controlling the effect of noise we show that the only additional constraint needed is the physically feasible non-negativity. Despite being iterative the method is computationally fast and simple to implement.To evaluate the new method, we used data from real trichromatic camera systems as well as simulated data. The results support our assertions that controlling the noise results in better sensor estimates.