GTA Seminar | Speaker: Mirjana Milijevic,  University of Banja Luka, Bosnia and Herzegovina
 

Title: Geometry of Statistical Manifolds

Abstract: We consider a semi-blind deconvolution problem arising in the decoding of blurred linear barcodes. We propose and analyze a novel regularization method based on augmented Lagrangians for obtaining stable approximate solutions to the resulting inverse problem. We establish the existence of generalized multipliers for the augmented Lagrangian functional under consideration, as well as the absence of duality gaps. These results provide the theoretical foundation for establishing regularization properties of the approximate solutions produced by the proposed method. Furthermore, we develop an associated ADMM-type iterative scheme for the explicit computation of approximate barcodes. Numerical experiments are conducted for a range of variance values (which determine the degree of blurring) and several levels of noise. The results demonstrate the effectiveness of the proposed method in reconstructing blurred and noisy barcodes.