A Blind Source Separation Technique for Document Restoration
Antonio Boccuto, Ivan Gerace, Valentina Giorgetti · SIAM Journal on Imaging Sciences · 2019
We examine an instance of the blind source separation problem, namely, the reconstruction of digital documents degraded by bleed-through and show-through effects. We introduce a nonstationary, locally linear data model and a solution approach based on the assumption of cross-correlated ideal sources. In order to solve the ill-posed local linear problem, we impose that the sum of all rows of the mixture matrix is equal to one, and we assume that the ideal sources are nonnegative and with an estimated level of overlapping (i.e., estimated cross-correlation). The solutions we obtain are related to a factorization of the covariance matrix of the data, which allows the given constraints to be satisfied at best. Our experimental results confirm the effectiveness of the method we propose.