Biomedical subjects

Mariano Rivera

Publications and source records attributed to Mariano Rivera.

5 recordsLinked to original sources

PubMed2006

Second-order robust regularization cost function for detecting and reconstructing phase discontinuities.

We propose a robust method for computing discontinuous phase maps from a fringe pattern with carrier frequency. Our algorithm is based on the minimization of an edge-preserving regularized cost function, specifically, on a robust regularized potential that uses a paradigm called the plate with adaptive rest condition, i.e., a second-order edge-preserving potential. Given that the proposed cost function is not convex, our method uses as its initial point an overly smoothed phase computed with a standard fringe analysis method and then reconstructs the phase discontinuities. Although the method is general purpose, it is introduced in the context of interferometric gauge-block calibration. The performance of the algorithm is demonstrated by numerical experiments with both synthetic and real data.

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PubMed2006

Fast half-quadratic regularized phase tracking for nonnormalized fringe patterns.

Although one of the simplest and powerful approaches for the demodulation of a single fringe pattern with closed fringes is the regularized phase-tracking (RPT) technique, this technique has two important drawbacks: its sensibility at the fringe-pattern modulation and the time employed in the estimation. We present modifications to the RPT technique that consist of the inclusion of a rough estimate of the fringe-pattern modulation and the linearization of the fringe-pattern model that allows the minimization of the cost function through stable numerical linear techniques. With these changes, the demodulation of nonnormalized fringe patterns is made with a significant reduction in the processing time, preserving the demodulation accuracy of the original RPT method.

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PubMed2005

Robust phase demodulation of interferograms with open or closed fringes.

We present two robust algorithms for fringe pattern analysis with partial-field and closed fringes. The algorithm for partial-field fringe patterns is presented as a refinement method for precomputed coarse phases. Such an algorithm consists of the minimization of a regularized cost function that incorporates an outlier rejection strategy, which causes the algorithm to become robust. On the basis of the phase refinement method, we propose a propagative scheme for phase retrieval from closed-fringe interferograms. The algorithm performance is demonstrated by demodulating closed-fringe interferograms with complex spatial distribution of stationary points and gradients in the illumination components.

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PubMed2004

Half-quadratic cost functions for phase unwrapping.

We present a generic regularized formulation, based on robust half-quadratic regularization, for unwrapping noisy and discontinuous wrapped phase maps. Two cases are presented: the convex case and the nonconvex case. The unwrapped phase with the convex formulation is unique and robust to noise; however, the convex function solution deteriorates as a result of real discontinuities in phase maps. Therefore we also present a nonconvex formulation that, with a parameter continuation strategy, shows superior performance.

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PubMed2002

Quadratic cost functional for wave-front reconstruction.

A quadratic cost functional for reconstruction of a high-resolution wave front from a coarse wave front is presented. The functional uses as data the position and the direction of the coarse wave front that had previously been computed with a ray-tracing method. This functional uses an optical relationship between the ray information and the wave front's shape to reconstruct a high-density wave front. The performance of the proposed functional is illustrated by reconstruction of complicated wave fronts for which this functional has an accuracy that is superior to that of conventional interpolation methods.

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