A piecewise constant levelset approach for semi-blind deconvolution: Application to barcode decoding
This work provides a theoretically grounded method for decoding blurred barcodes, a specific application domain, but the approach is incremental as it builds on an existing framework.
The paper addresses semi-blind deconvolution for blurred linear barcodes using a piecewise constant level set approach with augmented Lagrangians, achieving stable approximate solutions under noise. Numerical experiments validate effectiveness across various blur and noise levels.
We consider a semi-blind deconvolution problem arising in the decoding of blurred linear barcodes. Building on the Piecewise Constant Level Set (PCLS) framework introduced in [De\,Cezaro et al., Inv.\,Probl., 29 (2013), 015003], we propose and analyze a solution method based on augmented Lagrangians to obtain stable approximate solutions to the corresponding inverse problem with respect to noisy measurements. 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 required to prove regularization properties of the approximate solutions produced by the proposed strategy. Furthermore, we present an associated ADMM-type iterative scheme for the explicit computation of approximate barcodes. Numerical experiments are carried out for various variance values (responsible for the blurred effect) and several levels of noise, validating the effectiveness of the proposed method.