Liangfeng Guo

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.

A combination of spectral re-alignment and BTEM for the estimation of pure component NMR spectra from multi-component non-reactive and reactive systems

The deconvolution of multi-component mixtures in NMR spectroscopy is a challenging problem due to the spectral non-linearities. In the present contribution, two data sets were studied (A) 10 samples of a four-component non-reactive mixture measured with 1H, 13C, 19F, 31P NMR and (B) a three-solute cyclo-addition reaction measured with 13C NMR. Both data sets were treated with a re-alignment procedure to correct for the non-stationary chemical shifts, followed by band-target entropy minimization (BTEM) analysis. For data set A, quite good spectral estimates of the two hydrogen-containing species, four carbon-containing species, two fluorine-containing species and two phosphorus-containing species were obtained from the multi-component data. For data set B quite good spectral estimates of all three carbon-containing reactants were obtained as well as their relative concentration profiles. The present contribution using model systems indicates the usefulness of re-alignment procedures for correcting non-stationary characteristics, prior to self-modeling curve resolution (SMCR), and the potential for investigating more complex problems.