arXiv subjects

Eduardo X. Miqueles

Publications and source records attributed to Eduardo X. Miqueles.

5 recordsLinked to original sources

arXiv2023

Alternative Fan-beam Backprojection and Adjoint Operators

We present in this work alternative analytic formulations for the fan-beam tomographic backprojection operation and its associated adjoint transform in standard (equiangular) and linear (equidistant) detector geometries. The proposed formulations are obtained from a recent backprojection theorem in parallel tomography. Such formulations are written as a Bessel-Neumann series in the frequency domain that can be implemented as an $O(N^{2.3729})$ matrix multiplication. Proofs are provided together with numerical simulations compared with conventional fan-beam $O(N^{3})$ backprojection representations showing more robustness when dealing with highly noisy data.

math.NA↗

arXiv2017

Low-complexity Distributed Tomographic Backprojection for large datasets

In this manuscript we present a fast GPU implementation for tomographic reconstruction of large datasets using data obtained at the Brazilian synchrotron light source. The algorithm is distributed in a cluster with 4 GPUs through a fast pipeline implemented in C programming language. Our algorithm is theoretically based on a recently discovered low complexity formula, computing the total volume within O(N3logN) floating point operations; much less than traditional algorithms that operates with O(N4) flops over an input data of size O(N3). The results obtained with real data indicate that a reconstruction can be achieved within 1 second provided the data is transferred completely to the memory.

cs.DC↗

arXiv2017

Phase-Retrieval as a Regularization Problem

It was recently shown that the phase retrieval imaging of a sample can be modeled as a simple convolution process. Sometimes, such a convolution depends on physical parameters of the sample which are difficult to estimate a priori. In this case, a blind choice for those parameters usually lead to wrong results, e.g., in posterior image segmentation processing. In this manuscript, we propose a simple connection between phase-retrieval algorithms and optimization strategies, which lead us to ways of numerically determining the physical parameters

math.NA↗

arXiv2016

Superiorization of Incremental Optimization Algorithms for Statistical Tomographic Image Reconstruction

We propose the superiorization of incremental algorithms for tomographic image reconstruction. The resulting methods follow a better path in its way to finding the optimal solution for the maximum likelihood problem in the sense that they are closer to the Pareto optimal curve than the non-superiorized techniques. A new scaled gradient iteration is proposed and three superiorization schemes are evaluated. Theoretical analysis of the methods as well as computational experiments with both synthetic and real data are provided.

math.OC↗

arXiv2016

Fast Backprojection Techniques for High Resolution Tomography

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 three-dimensional data demands new mathematical tools for the tomographic reconstruction task because of the big computational complexity of most current algorithms as the sizes of tomographic data grow with the development of more powerful acquisition hardware and more refined scientific needs. In the present paper we propose a new fast back-projection operator for the processing of tomographic data and compare it against other fast reconstruction techniques.

math.NA↗