Elias S. Helou

University of São Paulo

AlgorithmMathematical optimizationIterative reconstructionConvex optimizationMathematics

32Publications

7H-index

148Citations

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Publications 30

Newest

#1Marcelo V. W. Zibetti (NYU: New York University)H-Index: 10

#2Elias S. Helou (USP: University of São Paulo)H-Index: 7

Last. Ravinder R. Regatte (NYU: New York University)H-Index: 35

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NMR relaxometry can provide information about the relaxation of the magnetization in different tissues, increasing our understanding of molecular dynamics and biochemical composition in biological systems. In general, tissues have complex and heterogeneous structures composed of multiple pools. As a result, bulk magnetization returns to its original state with different relaxation times, in a multicomponent relaxation. Recovering the distribution of relaxation times in each voxel is a difficult ...

Analysis of a New Sequential Optimality Condition Applied to Mathematical Programs with Equilibrium Constraints

#1Elias S. Helou (USP: University of São Paulo)H-Index: 7

#2Sandra A. Santos (State University of Campinas)H-Index: 21

Last. Lucas E. A. Simões (State University of Campinas)H-Index: 4

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Abstract In this study, a novel sequential optimality condition for general continuous optimization problems is established. In the context of mathematical programs with equilibrium constraints, the condition is proved to ensure Clarke stationarity. Originally devised for constrained nonsmooth optimization, the proposed sequential optimality condition addresses the domain of the constraints instead of their images, capturing indistinctly the features of the complementarity and the ordinary const...

#1Elias S. HelouH-Index: 7

#2Sandra A. SantosH-Index: 21

Last. Lucas E. A. SimõesH-Index: 4

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#1Yair CensorH-Index: 44

#2Edgar GarduñoH-Index: 9

Last. Gabor T. HermanH-Index: 63

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The superiorization methodology is intended to work with input data of constrained minimization problems, that is, a target function and a set of constraints. However, it is based on an antipodal way of thinking to what leads to constrained minimization methods. Instead of adapting unconstrained minimization algorithms to handling constraints, it adapts feasibility-seeking algorithms to reduce (not necessarily minimize) target function values. This is done by inserting target-function-reducing p...

#1R. M. Oliveira (USP: University of São Paulo)

#2Elias S. Helou (USP: University of São Paulo)H-Index: 7

Last. Eduardo F. Costa (USP: University of São Paulo)H-Index: 13

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ABSTRACTWe present a method to solve constrained convex stochastic optimization problems when the objective is a finite sum of convex functions . Our method is based on Incremental Stochastic Subgradient Algorithms and String-Averaging techniques, with an assumption that the subgradient directions are affected by random errors in each iteration. Our analysis allows the method to perform approximate projections onto the feasible set in each iteration. We provide convergence results for the case w...

#1Elias S. Helou (USP: University of São Paulo)H-Index: 7

#2Marcelo V. W. Zibetti (NYU: New York University)H-Index: 10

Last. Gabor T. Herman (CUNY: City University of New York)H-Index: 63

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Estimation of the Discrete-Space Fourier Transform (DSFT) at points of a finite domain arises in many two-dimensional signal processing applications. As a new approach to tackling this task, the notion of a Golden Angle Linogram Fourier Domain (GALFD) is presented, together with a computationally fast and accurate tool, named Golden Angle Linogram Evaluation (GALE), for the approximation of the DSFT at points of a GALFD. The sampling pattern in a GALFD resembles those in the linogram approach, w...

#1Marcelo V. W. Zibetti (NYU: New York University)H-Index: 10

#2Elias S. Helou (USP: University of São Paulo)H-Index: 7

Last. Gabor T. Herman (CUNY: City University of New York)H-Index: 63

view all 4 authors...

An improvement of the monotone fast iterative shrinkage-thresholding algorithm (MFISTA) for faster convergence is proposed in this paper. Our motivation is to reduce the reconstruction time of compressed sensing problems in magnetic resonance imaging. The proposed modification introduces an extra term, which is a multiple of the proximal-gradient step, into the so-called momentum formula used for the computation of the next iterate in MFISTA. In addition, the modified algorithm selects the next ...

#1Elias S. Helou (USP: University of São Paulo)H-Index: 7

#2Sandra A. Santos (State University of Campinas)H-Index: 21

Last. Lucas E. A. Simões (State University of Campinas)H-Index: 4

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This paper proposes an algorithm for the unconstrained minimization of a class of nonsmooth and nonconvex functions that can be written as finite-max functions. A gradient and function-based sampling method is proposed which, under special circumstances, either moves superlinearly to a minimizer of the problem of interest or improves the optimality certificate. Global and local convergence analysis are presented, as well as examples that illustrate the obtained theoretical results.

Superiorization of Preconditioned Conjugate Gradient Algorithms for Tomographic Image Reconstruction

#1Elias S. HelouH-Index: 7

#2Gabor T. HermanH-Index: 63

Last. Marcelo V. W. ZibettiH-Index: 10

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Properties of Superiorized Preconditioned Conjugate Gradient (SupPCG) algorithms in image reconstruction from projections are examined. Least squares (LS) is usually chosen for measuring data-inconsistency in these inverse problems. Preconditioned Conjugate Gradient algorithms are fast methods for finding an LS solution. However, for ill-posed problems, such as image reconstruction, an LS solution may not provide good image quality. This can be taken care of by superiorization. A superiorized al...

#1Eduardo X. MiquelesH-Index: 7

#2Nikolay Koshev (CSIC: Spanish National Research Council)H-Index: 2

Last. Elias S. Helou (CSIC: Spanish National Research Council)H-Index: 7

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Fast image reconstruction techniques are becoming important with the increasing number of scientific cases in high resolution micro and nano tomography. The processing of the large scale 3D data demands new mathematical tools for the tomographic reconstruction. Due to the high computational complexity of most current algorithms, big data sizes demands powerful hardware and more sophisticated numerical techniques. Several reconstruction algorithms are dependent on a mathematical tool called backp...

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