Bayes Information Criterion for Tikhonov Problems with Linear Constraints: Application to Radiometric Image Correction

Ill-conditioned or singular data modeling problems are commonly observed in image processing. To solve these problems some constraints, such as smoothness and boundary conditions have to be formulated. Further, the optimal structure of the model is not always self-evident. There are several criteria that can be applied for ”optimal” regularization gain or model selection. However, these measures (i) are not for problems with linear constraints and, further (ii) are usually not simultaneously suitable for model and regularization gain selection. In this paper the Bayes Information Criterion is extended for Tikhonov problems with linear constraints. Using this measure, a new radiometric image correction method is introduced. All known radiometric correction algorithms assume that radiometric distortions remain stable over time. Our algorithm enables image correction under time varying distortions. The method decomposes radiometric image distortions into multiplicative and additive errors, whose optimal models are computed with the extended Bayes Information Criterion (BICIC).