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Ricardo Legarda-Saenz

Publications and source records attributed to Ricardo Legarda-Saenz.

5 recordsLinked to original sources
arXiv2023

Wavefront reconstruction of discontinuous phase objects from optical deflectometry

One of the challenges in phase measuring deflectometry is to retrieve the wavefront from objects that present discontinuities or non-differentiable gradient fields. Here, we propose the integration of such gradients fields based on an Lp-norm minimization problem. The solution of this problem results in a nonlinear partial differential equation, which can be solved with a fast and well-known numerical methods and doesn't depend on external parameters. Numerical reconstructions on both synthetic and experimental data are presented that demonstrate the capability of the proposed method.

math.NA↗
arXiv2023

A variational model for wrapped phase denoising

In this paper, we introduce a total variation based variational model for denoising wrapped phase images. Our model improves on former methods by preserving discontinuities of the phase map and enforcing the fundamental Pythagorean trigonometric identity between the real and imaginary parts of the phase map enhancing the quality of the restored phase. The existence and uniqueness of the solution of our model is proven using standard methods. Further, we provide a fast fixed point method for finding the numerical solution and prove its convergence. Experiments on both synthetic and real patterns verify our findings.

math.NA↗
arXiv2022

On the performance of preconditioned methods to solve \(L^p\)-norm phase unwrapping

In this paper, we analyze and evaluate suitable preconditioning techniques to improve the performance of the $L^p$-norm phase unwrapping method. We consider five preconditioning techniques commonly found in the literature, and analyze their performance with different sizes of wrapped-phase maps. Keywords.- Phase unwrapping, $L^p$-norm based method, Preconditioning techniques.

math.NA↗
arXiv2020

Variational phase recovering without phase unwrapping in phase-shifting interferometry

We present a variational method for recovering the phase term from the information obtained from phase-shifting methods. First we introduce the new method based on a variational approach and then describe the numerical solution of the proposed cost function, which results in a simple algorithm. Numerical experiments with both synthetic and real fringe patterns shows the accuracy and simplicity of the resulting algorithm.

eess.IV↗
arXiv2020

Augmented Lagrangian method for a TV-based model for demodulating phase discontinuities

In this work we reformulate the method presented in App. Opt. 53:2297 (2014) as a constrained minimization problem using the augmented Lagrangian method. First we introduce the new method and then describe the numerical solution, which results in a simple algorithm. Numerical experiments with both synthetic and real fringe patterns show the accuracy and simplicity of the resulting algorithm.

math.NA↗