Spectral data estimation is an ill-posed problem, since (i) it is difficult to collect sufficient linear independent data and (ii) due to the integral nature of solid-state light sensors, camera outputs do not depend continuously on input signals. To solve these problems, most methods rely on exact a priori knowledge to reduce the problem?s complexity (solution space). In this paper a new algorithm is introduced which does not require a priori information. The method is build upon a new extension of the Bayes Information Criterion for ill-posed estimation problems, that is able to extract this information from the input data. The proposed solution is quite general and can readily be applied to other ill-posed problems, which are common in computer vision and image processing.