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Courses
  • CII
    Calculus II

  • VC
    Vector Calculus

  • NA
    Numerical Analysis

  • LA
    Linear Algebra

  • AAA
    Advanced Applied Analysis

  • MPNA
    Mathematical Principles of Numerical Analysis

  • AAMI
    Algorithms of Applied Mathematics I

Grants
  • Funding agency logo
    4D Transcranial Acoustoelectric Imaging for High Resolution Functional Mapping of Neuronal Currents

    Co-Investigator (COI)

    2020

    $2.1M
    Active
  • Funding agency logo
    Inverse Problems Arising in Novel Modalities of Biomedical Imaging

    Principal Investigator (PI)

    2017

    $300.4K
  • Funding agency logo
    High Resolution Electrical Brain Mapping by Real-Time and Portable 4D Acoustoelectric Imaging

    Co-Investigator (COI)

    2015

    $1.2M
  • Funding agency logo
    Collaborative Research: Wavelet Frames for Variational Models in Imaging: Bridging Discrete and Continuum

    Co-Investigator (COI)

    2014

    $170.8K
  • Funding agency logo
    Collaborative Research: Mathematics of Emerging Imaging Methods in Medicine and Homeland Security

    Principal Investigator (PI)

    2012

    $183.0K
  • Funding agency logo
    Collaborative Research: Mathematical Methods for Emerging Techniques of Biomedical Imaging

    Principal Investigator (PI)

    2009

    $109.4K
News
  • UA Researchers Develop Brain-Mapping Technology

    2015

Publications (51)
Recent
  • Weighted Radon transforms of vector fields, with applications to magnetoacoustoelectric tomography

    2023

  • On the exactness of the universal backprojection formula for the spherical means Radon transform

    2022

  • Current Source Density Imaging Using Regularized Inversion of Acoustoelectric Signals

    2022

  • Parametrix for the inverse source problem of thermoacoustic tomography with reduced data

    2021

  • Microlocally accurate solution of the inverse source problem of thermoacoustic tomography

    2020

  • Compton camera imaging and the cone transform: a brief overview

    2018

  • Theoretically exact photoacoustic reconstruction from spatially and temporally reduced data

    2018

  • Rotational magneto-acousto-electric tomography (MAET): theory and experimental validation

    2017

  • Compton Camera Imaging And The Cone Transform. A Brief Overview

    2017

  • A dissipative time reversal technique for photoacoustic tomography in a cavity

    2016

  • A NEW TIME REVERSAL TECHNIQUE FOR PHOTO-ACOUSTIC TOMOGRAPHY IN A CAVITY

    2015

  • Hybrid Methods of Imaging

    2015

  • Gradual time reversal in thermo- and photo- acoustic tomography within a resonant cavity

    2015

  • Inversion of the spherical means transform in corner-like domains by reduction to the classical Radon transform

    2015

  • Inversion of the spherical means transform by reduction to the classical Radon transform

    2014

  • Exterior/interior problem for the circular means transform with applications to intravascular imaging

    2013

  • Photoacoustic tomography in a reflecting cavity

    2013

  • Photoacoustic tomography in a rectangular reflecting cavity

    2013

  • On Reconstruction Formulas and Algorithms for the Thermoacoustic Tomography

    2012

  • A mathematical model and inversion procedure for magneto-acousto-electric tomography

    2012

  • Mathematics of photoacoustic and thermoacoustic tomography

    2011

  • Handbook of Mathematical Methods in Imaging

    2011

  • Fast reconstruction algorithms for the thermoacoustic tomography in certain domains with cylindrical or spherical symmetries

    2011

  • 2D and 3D reconstructions in acousto-electric tomography

    2010

  • Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra

    2010

  • Reconstructions in 2D acousto-electric tomography

    2010

  • Synthetic focusing in ultrasound modulated tomography

    2009

  • A survey in mathematics for industry: Mathematics of thermoacoustic tomography

    2008

  • ASYMPTOTICALLY OPTIMAL HIGH-ORDER ACCURATE ALGORITHMS FOR THE SOLUTION OF CERTAIN ELLIPTIC PDEs

    2008

  • Thermoacoustic tomography with detectors on an open curve: an efficient reconstruction algorithm

    2008

  • Mathematics of thermoacoustic tomography

    2008

  • MR2302980 (2007m: 44002) 44A12 (65R10)

    2007

  • A series solution and a fast algorithm for the inversion of the spherical mean Radon transform

    2007

  • Mathematics of thermoacoustic and photoacoustic tomography

    2007

  • Explicit inversion formulae for the spherical mean Radon transform

    2007

  • Inversion of the 3D exponential parallel-beam transform and the Radon transform with angle-dependent attenuation

    2004

  • On single-photon emission computed tomography imaging based on an exact formula for the nonuniform attenuation correction

    2002

  • Differential operators on graphs and photonic crystals

    2002

  • Analytic reconstruction algorithms in emission tomography with variable attenuation

    2001

  • Surface scattering in three dimensions: an accelerated high ndash;order solver

    2001

  • A Fast

    2001

  • A new SPECT reconstruction algorithm based on the Novikov explicit inversion formula

    2001

  • A fast, high-order algorithm for the solution of surface scattering problems. II

    2001

  • Goussis, Dimitrios A., 44

    2001

  • Surface scattering in three dimensions: An accelerated high-order solver

    2001

  • A fast, high-order algorithm for the solution of surface scattering problems: Basic implementation, tests, and applications

    2000

  • Asymptotic methods for thin high-contrast two-dimensional PBG materials

    1999

  • Spectral properties of high contrast band-gap materials and operators on graphs

    1999

  • Fast, high-order solution of surface scattering problems

    1999

  • Numerical and analytic study of problems of photonic crystals theory

    1998

  • Generalized and attenuated radon transforms: restorative approach to the numerical inversion

    1992

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