Biomedical Applications

Total variation superiorization schemes in proton computed tomography image reconstruction

  • Yair Censor
  • Scott Penfold
  • Anatoly Rosenfeld
  • Reinhard W. Schulte
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Other Topics Tags ,

    Purpose: Iterative projection reconstruction algorithms are currently the preferred reconstruction method in proton computed tomography (pCT). However, due to inconsistencies in the measured data arising from proton energy straggling and multiple Coulomb scattering, noise in the reconstructed image increases with successive iterations. In the current work, we investigated the use of total variation superiorization (TVS) … Read more

    MultiRTA: A simple yet accurate method for predicting peptide binding affinities for multiple class II MHC allotypes

  • Andrew J. Bordner
  • Hans D Mittelmann
    • Categories Biomedical Applications

    Background: The binding of peptide fragments of antigens to class II MHC is a crucial step in initiating a helper T cell immune response. The identification of such peptide epitopes has potential applications in vaccine design and in better understanding autoimmune diseases and allergies. However, comprehensive experimental determination of peptide-MHC binding affinities is infeasible due … Read more

    Perturbation resilience and superiorization of iterative algorithms

  • Yair Censor
  • Ran Davidi
  • Gabor T. Herman
    • Categories Biomedical Applications, Constrained Nonlinear Optimization Tags , , , ,

    Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little demand on computer resources. For other problems, such as finding that point in the intersection at which the … Read more

    Prediction Range Estimation from Noisy Raman Spectra

  • Matthew Glucksberg
  • Sanjay Mehrotra
  • Richard Van Duyne
  • Joseph Walsh
  • Lyandres Olga
    • Categories Basic Sciences Applications, Biomedical Applications, Robust Optimization Tags , , ,

    Inferences need to be drawn in biological systems using experimental multivariate data. The number of samples collected in many such experiments is small, and the data is noisy. We present and study the performance of a robust optimization (RO) model for such situations. We adapt this model to generate a minimum and a maximum estimation … Read more

    On the Effectiveness of Projection Methods for Convex Feasibility

  • Yair Censor
  • Patrick L. Combettes
  • Wei Chen
  • Ran Davidi
  • Gabor T. Herman
    • Categories Applications - Science and Engineering, Biomedical Applications, Linear, Cone and Semidefinite Programming

    The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications. This is supported by experimental evidence provided in this paper on problems of various sizes (up to tens of thousands of … Read more

    Metal Artefact Reduction by Least-Squares Penalized-Likelihood Reconstruction with a Fast Polychromatic Projection Model

  • Jean-Pierre Dussault
  • Yves Goussard
  • Benoit Hamelin
    • Categories Biomedical Applications, Bound-constrained Optimization Tags , , , , ,

    We consider penalized-likelihood reconstruction for X-ray computed tomography of objects that contain small metal structures. To reduce the beam hardening artefacts induced by these structures, we derive the reconstruction algorithm from a projection model that takes into account the photon emission spectrum and nonlinear variation of attenuation to photon energy. This algorithm requires excessively long … Read more

    Molecular distance geometry methods: from continuous to discrete

  • Carlile Lavor
  • Leo Liberti
  • Antonio Mucherino
  • Nelson Maculan
    • Categories Biomedical Applications, Combinatorial Optimization Tags , , ,

    Distance geometry problems arise from the need to position entities in the Euclidean $K$-space given some of their respective distances. Entities may be atoms (molecular distance geometry), wireless sensors (sensor network localization), or abstract vertices of a graph(graph drawing). In the context of molecular distance geometry, the distances are usually known because of chemical properties … Read more

    Prediction of the binding affinities of peptides to class II MHC using a regularized thermodynamic model

  • Andrew J. Bordner
  • Hans D Mittelmann
    • Categories Biomedical Applications

    The binding of peptide fragments of extracellular peptides to class II MHC is a crucial event in the adaptive immune response. Each MHC allotype generally binds a distinct subset of peptides and the enormous number of possible peptide epitopes prevents their complete experimental characterization. Computational methods can utilize the limited experimental data to predict the … Read more

    A Note on the Behavior of the Randomized Kaczmarz Algorithm of Strohmer and Vershynin

  • Yair Censor
  • Gabor T. Herman
  • Ming Jiang
    • Categories Biomedical Applications, Convex Optimization Tags , ,

    In a recent paper by Strohmer and Vershynin (J. Fourier Anal. Appl. 15:262–278, 2009) a “randomized Kaczmarz algorithm” is proposed for solving consistent systems of linear equations {ai, x = bi }m i=1. In that algorithm the next equation to be used in an iterative Kaczmarz process is selected with a probability proportional to ai2. … Read more

    Block-Iterative and String-Averaging Projection Algorithms in Proton Computed Tomography Image Reconstruction

  • Vladimir Bashkirov
  • Yair Censor
  • Scott McAllister
  • Scott Penfold
  • Anatoly Rosenfeld
  • Keith Schubert
  • Reinhard W. Schulte
    • Categories Applications - Science and Engineering, Biomedical Applications Tags , , ,

    Proton computed tomography (pCT) is an imaging modality that has been suggested as a means for reducing the range uncertainty during proton radiation treatments. By measuring the spatial location of individual protons pre- and post-patient, as well as the energy lost along the proton path, three dimensional maps of patient water equivalent electron densities can … Read more