The use of entropy minimization for the solution of blind source separation problems in image analysis

Entropy minimization is closely associated with pattern recognition. The present contribution uses a direct minimization of an entropy like function to solve the blind source separation problem for image reconstruction. The mixture patterns are decomposed using SVD and then global stochastic optimization is used to find the first irreducible image pattern. Further images are then subsequently reconstructed, by imposing a 2D correlation coefficient for dissimilarity to prevent repeated images, until all images are exhaustively enumerated. Three test cases are used, including (1) a set of three black and white texturally different photographs (2) a set of three RGB geometrically similar photographs and (3) an underdetermined problem involving an imbedded watermark. Cases 1 and 2 are easily solved with outstanding image quality. Both searches are conducted in an unsupervised manner—no a priori information is used. In Case 3, the watermark is enhanced after targeting the region for entropy minimization. The present results have a wide variety of applications, including image and spectroscopic analysis.