Elias Salomão Helou Neto

• Outcome Evaluation and Pricing in Superiorization and in Multiobjective Optimization, AR.EXT

• Abstract

  Reduction of computational time in high resolution image reconstruction is essential in basic research and applications as well. This reduction is important for different types of traditional non diffractive tomography in medical diagnosis as well as for applications in nanomaterials research, related to modern technologies.Alternatives to alleviate the computationally intense part of eac…

  Fast computation of the generalized Backprojection operator with applications in tomographic image reconstruction, AP.R
• Inverse Problems and Applications, AR.EXT

(Only some records are available in English at this moment)

• Abstract

  The most successful stochastic gradient methods in deep learning have an incremental characteristic and are executed on multiple Graphics Processing Units (GPUs) in large training data sets. It is expected to divide the large group of training data into mini-batches, each containing a subset of this data, to keep the processing of each iteration of the method computationally viable (calle…

  Study of the String-Averaging algorithmic topology for Stochastic Gradient methods with applications to supervised machine learning in deep neural networks, BP.IC

• Abstract

  "String averaging" algorithms for the convex feasibility problem, recently shown interesting properties in applications to computerized tomography when generalized appropriately. Until now the theory covers the differentiable convex case restricted to non-negative octant, but non-differentiable functions and more general constraints are of practical interest. This project aims to approach…

  Incremental methods and String-Averaging for non-differentiable convex optimization with inaccurate Subgradients, BP.DR

• Abstract

  The present work plan describes the goals and planned activities for PhD Nikolay Koshev's proposed postdoctoral stage. The activities are associated with CEPID/CeMEAI (FAPESP 2013/07375-0), which aims at integrating state-of-art applied mathematics techniques to industry. The main subjecs are implementation and development of fast tomographic reconstruction of high-resolution datasets. Ap…

  Rapid rear projection techniques applied to micro-tomography by synchrotron illumination, BP.PD

(Only some records are available in English at this moment)

• Abstract

  The present project approaches two relevant current themes in applied mathematics. The first branch aims at studying Stein-like estimators that are exact, in average and except for a constant term, replacements for non-computable mean squared errors in denoising and inverse problems. We propose to extend current techniques to operate with more general Bregman-divergences and, more importa…

  Computational and theoretical advances in inverse problems with applications to tomographic image reconstruction, BE.PQ