arXiv subjects

Antonio Leitão

Publications and source records attributed to Antonio Leitão.

4 recordsLinked to original sources

arXiv2026

A piecewise constant levelset approach for semi-blind deconvolution: Application to barcode decoding

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.

math.NA↗

arXiv2024

On inertial Levenberg-Marquardt type methods for solving nonlinear ill-posed operator equations

In these notes we propose and analyze an inertial type method for obtaining stable approximate solutions to nonlinear ill-posed operator equations. The method is based on the Levenberg-Marquardt (LM) iteration. The main obtained results are: monotonicity and convergence for exact data, stability and semi-convergence for noisy data. Regarding numerical experiments we consider: i) a parameter identification problem in elliptic PDEs, ii) a parameter identification problem in machine learning; the computational efficiency of the proposed method is compared with canonical implementations of the LM method.

math.NA↗

arXiv2024

On inertial iterated Tikhonov methods for solving ill-posed problems

In this manuscript we propose and analyze an implicit two-point type method (or inertial method) for obtaining stable approximate solutions to linear ill-posed operator equations. The method is based on the iterated Tikhonov (iT) scheme. We establish convergence for exact data, and stability and semi-convergence for noisy data. Regarding numerical experiments we consider: i) a 2D Inverse Potential Problem, ii) an Image Deblurring Problem; the computational efficiency of the method is compared with standard implementations of the iT method.

math.NA↗

arXiv2020

A Computational Approach for the inverse problem of neuronal conductances determination

The derivation by Alan Hodgkin and Andrew Huxley of their famous neuronal conductance model relied on experimental data gathered using neurons of the giant squid. It becomes clear that determining experimentally the conductances of neurons is hard, in particular under the presence of spatial and temporal heterogeneities. Moreover it is reasonable to expect variations between species or even between types of neurons of a same species. Determining conductances from one type of neuron is no guarantee that it works across the board. We tackle the inverse problem of determining, given voltage data, conductances with non-uniform distribution computationally. In the simpler setting of a cable equation, we consider the Landweber iteration, a computational technique used to identify non-uniform spatial and temporal ionic distributions, both in a single branch or in a tree. Here, we propose and (numerically) investigate an iterative scheme that consists in numerically solving two partial differential equations in each step. We provide several numerical results showing that the method is able to capture the correct conductances given information on the voltages, even for noisy data.

math.NA↗