Elias S. Helou

Elias S. Helou, Gabor T. Herman, Chuan Lin et al.

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 algorithm leads to images with the value of a secondary criterion (a merit function such as the total variation) improved as compared to images with similar data-inconsistency obtained by the algorithm without superiorization. Numerical experimentation shows that SupPCG can lead to high-quality reconstructions within a remarkably short time. A theoretical analysis is also provided.

Eduardo X. Miqueles, Nathaly L. Archilha, Marcelo R. Dos Anjos et al.

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

Nikolay Koshev, Elias S. Helou, Eduardo X. Miqueles

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.