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Anne Gelb

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Research Professor
Faculty, TEMPE Campus, Mailcode 1804
Research Professor
Faculty, TEMPE Campus, Mailcode 1804
Adjunct Faculty
Faculty, TEMPE Campus, Mailcode 1804
Biography

Anne Gelb is a numerical analyst who is interested in developing accurate and robust numerical algorithms in two focus areas: (i) simulating models that describe important physical processes; and (ii) retrieving important information from sampled data. In the first case, the models are usually comprised of partial differential equations that describe problems in electro-magnetics or fluid dynamics. In the second, the collected data are typically indirect, under-sampled, and noisy, which makes standard numerical methods for solving inverse problems difficult to apply. Specific applications include magnetic resonance imaging (MRI) and synthetic aperture radar (SAR).

Education

PhD, 1996, Brown University, Providence

Anne Gelb's faculty webpage

Publications
  • Adam Martinez, Anne Gelb, and Alexander Gutierrez. Edge Detection from Non-Uniform Fourier Data Using the Convolutional Gridding Algorithm. Journal of Scientific Computing (2014).
  • Anne Gelb and Guohui Song. A Frame Theoretic Approach to the Non-Uniform Fast Fourier Transform. SIAM Journal of Numerical Analysis (2014).
  • D. Cochran, A. Gelb, and Y. Wang. Edge Detection From Truncated Fourier Data Using Spectral Mollifiers. Advances in Computational Mathematics (2013).
  • Guohui Song and Anne Gelb. Approximating the Inverse Frame Operator from Localized Frames. Applied and Computational Harmonic Analysis (2013).
  • A. Petersen, A. Gelb, and R. Eubank. Hypothesis Testing for Fourier Based Edge Detection Methods. Journal of Scientific Computing (2012).
  • Adityavikram Viswanathan, Douglas Cochran, and Anne Gelb. Iterative Design of Concentration Factors for Jump Detection. Journal of Scientific Computing (2012).
  • Anne Gelb and Taylor Hines. Recovering Exponential Accuracy from Non-Harmonic Fourier Data Through Spectral Reprojection. Journal of Scientific Computing (2012).
  • Wolfgang Stefan, Adityavikram Viswanathan, Anne Gelb and Rosemary Renaut. A High Order Edge Detection Method for Blurred and Noisy Fourier Data. Journal of Scientific Computing (2012).
  • . Special Issue on Mathematical Methods in Medical Imaging. (2012).
  • Anne Gelb and Taylor Hines. Detection of Edges from Nonuniform Fourier Data. Journal of Fourier Analysis and Applications (2011).
  • D. Cochran, A. Gelb, and Y. Wang. Edge Detection From Truncated Fourier Data Using Spectral Mollifiers. Advances in Computational Mathematics (2011).
  • Adityavikram Viswanathan, Anne Gelb, Douglas Cochran, Rosemary Renaut. On Reconstruction from Non-uniform Spectral Data. Journal of Scientific Computing (2010).
  • W. Stefan, R. Renaut, and A. Gelb. Improved total variation-type regularization using higher-order edge detectors. SIAM Journal on Imaging Sciences (2010).
  • Anne Gelb, Dennis Cates. Segmentation of Images from Fourier Spectral Data. Communications in Computational Physics (2009).
  • R. Archibald, A. Gelb, R. Saxena, and D.B. Xiu. Discontinuity Detection in Multivariate Space for Stochastic Simulations. Journal of Computational Physics (2009).
  • R. Platte and A. Gelb. A Hybrid Fourier-Chebyshev Method for Partial Differential Equations. Journal of Scientific Computing (2009).
  • Rishu Saxena, Anne Gelb, Hans Mittelmann. A High Order Method for Determining the Edges in the Gradient of a Function. Communications in Computational Physics (2009).
  • Anne Gelb, Dennis Cates. Detection of Edges in Spectral Data III - Improvements in the Presence of Noise. Journal of Scientific Computing (2008).
  • Anne Gelb, Rodrigro Platte, W Rosenthal. The Discrete Orthogonal Polynomial Least Squares Method for Approximationand Solving Partial Differential Equations. Communications in Computational Physics (2008).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-uniform Grid Point Data. Journal of Scientific Computing (2007).
  • Chris Blakely, Anne Gelb, Antonio Navarra. An Automated Method for Recovering Piecewise Smooth Functions on Spheres Free from Gibbs Oscillations. Sampling Theory in Signal and Image Processing (2007).
  • Dennis Cates, Anne Gelb. Determining the Locations of the Discontinuities in Derivatives of Functions Using Spectral Methods. Numerical Algorithms (2007).
  • R Archibald, Anne Gelb, J Yoon. Determining the Locations of the Discontinuities in the Derivatives of Functions. Applied Numerical Mathematics (2007).
  • Anne Gelb, E Tadmor. Adaptive Edge Detectors for Piecewise Smooth Data Based on the MinMod Limiter. Journal of Scientific Computing (2006).
  • Anne Gelb, Z Jackiewicz. Determining analyticity for parameter optimization of the Gegenbauer reconstruction method. SIAM Journal on Scientific Computing (2006).
  • R Archibald, Anne Gelb, S Gottlieb, J Ryan. One-sided post-processing for the discontinuous Galerkin method using ENO type stencil choosing and the local edge detection method. Journal of Scientific Computing (2006).
  • Anne Gelb, J Tanner. Robust Reprojection Methods for the Resolution of the Gibbs Phenomenon. Applied and Computational Harmonic Analysis (2005).
  • R Archibald, Anne Gelb, J Yoon. Polynomial Fitting for Edge Detection in Irregularly Sampled Signals and Images. SIAM Journal on Numerical Analysis (2005).
  • Y Ha, Carl Gardner, Anne Gelb, C Shu. Numerical Simulation of High Mach Number Astrophysical Jets with Radiative Cooling. Journal of Scientific Computing (2005).
  • Anne Gelb. Parameter Optimization and Reduction of Round Off Error for the Gegenbauer Reconstruction Method. Journal of Scientific Computing (2004).
  • J Gleeson, O Roche, J West, Anne Gelb. Modelling Annular Micromixers. SIAM J. Appl. Math (2004).
  • R Archibald, J Hu, Anne Gelb, G Farin. Improving the Accuracy of Volumetric Segmentation Using Pre-Processing Boundary Detection and Image Reconstruction. IEEE Transactions on Image Pocessing (2004).
  • J Gleeson, O Roche, J West, Anne Gelb. Modelling Annular Micromixers. Proceedings of Nanotech 2003 (2003).
  • R Archibald, K Chen, Anne Gelb, R Renaut. Improving Tissue Segmentation of Human Brain MRI Through Pre-Processing by theGegenbauer Reconstruction Method. NeuroImage (2003).
  • Gleeson, J, Roche, O, West, J, Gelb, Anne. Modelling Annular Micromixers. (2003).
  • Anne Gelb, E Tadmor. Spectral Reconstruction of Piecewise Smooth Functions from Their Discrete Data. Mathematical Modelling and Numerical Analysis (2002).
  • Anne Gelb, Zdzislaw Jackiewicz, B Welfert. Absorbing Boundary Conditions of the Second Order for the Pseudospectral Chebyshev Methods for Wave Propagation. Journal of Scientific Computing (2002).
  • C Gardner, Anne Gelb, J Hernandez. A Comparison of Modern Hyperbolic Methods for Semiconductor Device Simulation: NTK Central Scheme vs. CLAWPACK. VLSI Design (2002).
  • R Archibald, Anne Gelb. A Method to Reduce the Gibbs Ringing Artifact in MRI Scans While Keeping Tissue Boundary Integrity. IEEE Medical Imaging (2002).
  • R Archibald, Anne Gelb. Reducing the Effects of Noise in Image Reconstruction. Journal of Scientific Computing (2002).
  • Archibald, R, Gelb, Anne. Reducing the Effects of Noise in MRI Reconstruction. (2002).
  • Gelb, Anne, Archibald, R. Reducing the Gibbs Ringing Artifact in MRI Scans While Maintaining Tissue Boundary Integrity. (2002).
  • Anne Gelb. A Hybrid Approach to Spectral Reconstruction of Piecewise Smooth Functions. Journal of Scientific Computing (2001).
  • Anne Gelb, J Gleeson. Spectral Viscosity for Shallow Water Equations in Spherical Geometry. Monthly Weather Review (2001).
  • Anne Gelb, E Tadmor. Detection of Edges in Spectral Data II: Nonlinear Enhancement. SIAM Journal on Numerical Analysis (2000).
  • Anne Gelb, E Tadmor. Enhanced Spectral Viscosity Approximations for Conservation Laws. Applied Numerical Mathematics (2000).
  • Anne Gelb and Sigal Gottlieb. The Resolution of the Gibbs Phenomenon for Fourier Spectral Methods. Advances in the Gibbs Phenomenon (0).
Research Activity
Fall 2017
Course NumberCourse Title
MAT 792Research
APM 799Dissertation
Summer 2017
Course NumberCourse Title
APM 792Research
Spring 2017
Course NumberCourse Title
MAT 792Research
APM 792Research
Fall 2016
Course NumberCourse Title
APM 792Research
MAT 792Research
APM 799Dissertation
Summer 2016
Course NumberCourse Title
APM 792Research
Spring 2016
Course NumberCourse Title
MAT 492Honors Directed Study
MAT 493Honors Thesis
MAT 495Undergraduate Research
APM 524Spectral Methods
APM 792Research
MAT 792Research
APM 799Dissertation
Fall 2015
Course NumberCourse Title
MAT 272Calc w/Analytic Geometry III
MAT 492Honors Directed Study
MAT 493Honors Thesis
APM 792Research
MAT 792Research
APM 799Dissertation
Summer 2015
Course NumberCourse Title
MAT 499Individualized Instruction
MAT 792Research
APM 792Research
Spring 2015
Course NumberCourse Title
MAT 492Honors Directed Study
MAT 493Honors Thesis
MAT 495Undergraduate Research
APM 506Computational Methods
APM 792Research
MAT 792Research
APM 799Dissertation
Fall 2014
Course NumberCourse Title
MAT 272Calc w/Analytic Geometry III
MAT 492Honors Directed Study
MAT 493Honors Thesis
MAT 792Research
APM 792Research
Summer 2014
Course NumberCourse Title
MAT 492Honors Directed Study
MAT 499Individualized Instruction
MAT 792Research
APM 792Research
Spring 2014
Course NumberCourse Title
MAT 493Honors Thesis
APM 506Computational Methods
APM 792Research
MAT 792Research
APM 799Dissertation
Fall 2013
Course NumberCourse Title
MAT 272Calc w/Analytic Geometry III
MAT 492Honors Directed Study
MAT 792Research
APM 792Research
Summer 2013
Course NumberCourse Title
MAT 499Individualized Instruction
MAT 792Research
APM 792Research
Spring 2013
Course NumberCourse Title
MAT 493Honors Thesis
MAT 590Reading and Conference
MAT 792Research
APM 792Research
Presentations
  • Anne Gelb. Numerical Approximation Methods for Non-Uniform Fourier Data. Laboratoire Jacques-Louis Lions Universite Pierre & Marie Curie, Paris, (Nov 2012).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-Uniform Fourier Coefficients. Case Western Reserve Colloquium (Oct 2011).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-Uniform Fourier Coefficients. 2nd Midwest Conference on Mathematical Conferences for Images and Surfaces (Aug 2011).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions. Northern Arizona University Honors Week (Apr 2011).
  • Anne Gelb. Applications for High Order Numerical Methods. Northern Arizona University Honors Week (Apr 2011).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-Uniform Fourier Coefficients. University of Wisconsin, Madison (Apr 2011).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-Uniform Fourier Coefficients. CSUMS Seminar (Apr 2011).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-Uniform Fourier Coefficients. Arizona State University Applied Math Seminar (Feb 2011).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-Uniform Fourier Coefficients. ASU Seminar (Feb 2011).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-Uniform Fourier Coefficients. February Fourier Talks at the Norbert Weiner Center for Harmonic Analysis and Applications (Feb 2011).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-Uniform Fourier Coefficients. Mathematics and Computer Science Colloquium Colorado School of Mines (Apr 2010).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-Uniform Fourier Coefficients. Mathematics Colloquium University of Wyoming (Apr 2010).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-Uniform Fourier Coefficients. Michigan State University Department of Mathematics Colloquium (Mar 2010).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-Uniform Fourier Coefficients. Mathematics Colloquium University of Alabama (Mar 2010).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-Uniform Fourier Coefficients. Mathematics Colloquium Michigan State University (Mar 2010).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-Uniform Fourier Coefficients. Cal Tech Applied Mathematics Colloquium (Jan 2010).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-Uniform Fourier Coefficients. Conference (Dec 2009).
  • Anne Gelb. Numerical Methods for Image Reconstruction. University of Wyoming REU summer program seminar series (Jul 2009).
  • Anne Gelb. High Order Methods for Image Analysis. Conference minisymposium (Jun 2009).
  • Anne Gelb. Reconstruction of Piecewise Smooth Functions from Non-Uniform Fourier Coefficients. Conference (Apr 2009).
  • Gelb, Anne. Reconstructing Piecewise Smooth Images from Fourier Spectral Data. International Conference on Spectral and Higher Order Methods (ICOSAHOM) 2007 (Jun 2007).
  • Gelb, Anne. Image Reconstruction from Fourier Data. REU seminar (Jul 2006).
  • Platte, Rodrigo, Gelb, Anne. A Hybrid Fourier-Chebyshev Pseudo-Spectral Method for Non-Periodic Hyperbolic Problems. SIAM annual meeting (Jul 2006).
  • Gelb, Anne. Recent Advances in Reconstruction Methods for Piecewise Smooth Functions. Department Colloquium (Apr 2006).
  • Gelb, Anne. Spectral Viscosity for Shallow Water Equations on a Sphere. Conference (Jun 2005).
  • Gelb, Anne. Multivariate Edge Detection. ICOSAHOM (Jun 2004).
  • Gelb, Anne. Multivariate Edge Detection. SIAM conference on imaging science (May 2004).
  • Gelb, Anne. High Order Reconstruction Algorithms for Medical Imaging. Seminar (Apr 2004).
  • Gelb, Anne. Reconstructing Images from Fourier Spectral Data. Colloqium
Service
  • Dean's Strategic Planning and Academic Resources Advisory Council, member (2014 - Present)
  • Personnel Committee, Member at Rank (2014 - Present)
  • SIAM Journal on Scientific Computing, reviewer (2014 - Present)
  • ICOSAHOM, organizing committee (2014 - Present)
  • SIAM Journal on Scientific Computing, Associate Editor (2014 - Present)
  • visiting position search committee, Chair (2013 - Present)
  • Review Committee, chair (2013 - Present)
  • Graduate committee, Member (2013 - Present)
  • AWM, Panelist/Speaker (2013 - Present)
  • co-organizer for MBI conference, co-organizer (2013 - Present)
  • SIAM representative for the Joint Committee of Women, member (2013 - Present)
  • Nanyang Technological University (NTU), Singapore, promotion review (2011 - Present)
  • Applied Mathematics and Computation, referee (2010 - Present)
  • ICOSAHOM, referee (2010 - Present)
  • Journal of Computational Physics, Peer Review of Article (2010 - Present)
  • Review Committee, member (2007 - Present)
  • Department of Mathematics and Statistics, Graduate Chair (2007 - Present)
  • Applied Numerical Mathematics, Associate Editor (2006 - Present)
  • Applied Numerical Mathematics, Associate Editor (2006 - Present)
  • Applied Numerical Mathematics, Associate Editor (2006 - Present)
  • Applied Numerical Mathematics, Associate Editor (2006 - Present)
  • Applied Numerical Mathematics, Associate Editor (2006 - Present)
  • Applied Numerical Mathematics, Associate Editor (2006 - Present)
  • Journal of Scientific Computing, Associate Editor (2006 - Present)
  • Journal of Scientific Computing, Associate Editor (2006 - Present)
  • Journal of Scientific Computing, Associate Editor (2006 - Present)
  • Journal of Scientific Computing, Associate Editor (2006 - Present)
  • Journal of Scientific Computing, Associate Editor (2006 - Present)
  • Journal of Scientific Computing, Associate Editor (2006 - Present)
  • Journal of Scientific Computing, Associate Editor (2006 - 2017)
  • SIAM Science Policy Committee, member (2014 - 2016)
  • SIAM representative for the Joint Committee of Women, member (2013 - 2014)
  • Applied Numerical Mathematics, Associate Editor (2006 - 2014)
  • co-organizer (lead) for the ICERM cluster program, co-organizer (2014 - 2014)
  • Personnel Committee, Member at Rank (2011 - 2013)
  • Personnel Committee, Member at Rank (2009 - 2010)
  • visiting position search committee, Chair (2009 - 2010)
  • Applied Mathematics and Computation, Peer Reviewer of Article (2009 - 2009)
  • Communications in Computational Physics, peer reviewer (2009 - 2009)
  • NSF -Postdoctoral Fellows Review Panel, Review Panelist (2009 - 2009)
  • Journal of Scientific Computing, Peer Reviewer of Article (2009 - 2009)
  • Journal of Fourier Analysis and Applications, Peer reviewer of article (2009 - 2009)
  • U.S. Israel Binational Science Foundation, External Reviewer (2009 - 2009)
  • Review Committee, member (2007 - 2009)
  • Scholarpedia, Peer Reviewer of Article (2009 - 2009)
  • University of Wyoming, Presenter (2009 - 2009)
  • Department of Mathematics and Statistics, Graduate Chair (2007 - 2009)
  • IMA Journal of Numerical Analysis, Peer Review of Article (2008 - 2008)
  • Department of Mathematics and Statistics, search committee member (2008 - 2008)
  • Journal of Approximation Theory, Peer Review of Article (2008 - 2008)
  • hiring committee chair (2007 - 2008)
  • Applied Numerical Mathematics, Peer review of article (2007)
  • Communications in Computational Physics, peer reviewer (2007)
  • Journal of Fourier Analysis and Applications, Peer reviewer of article (2007)
  • Qualifying exam committee, Member (2007 - 2007)
  • Faculty Senate, Department Senator (2005 - 2007)
  • Colloquium Committee, Member (2006 - 2007)
  • Graduate reorganization committee, Member (2006 - 2007)
  • PFMF, Assistant (2005 - 2007)
  • Lockheed Martin, Consultant (2005 - 2007)
  • Preparing Future Math Faculty, Mentor (2007)
  • ELCVIA, Peer Review of Article (2006)
  • Journal of Computational Physics, Peer Review of Article (2006)
  • Mathematics of Computation, Peer Review of Article (2006)
  • Pattern Recognition Letters, Peer Review of Article (2006)
  • NSF -CAREER Review Panel, Review Panelist (2006 - 2006)
  • Swedish Research Coucil, Proposal Reviewer (2006 - 2006)
  • Northern Arizona University, Presenter (2006)
  • Graduate mentoring committee, Chair (2005 - 2006)
  • J. Comp and Appl. Math, Peer Review (2005)
  • Journal of Approximation Theory, Peer Review of Article (2005)
  • Mathematical Biosciences and Engineering, Peer Review of Article (2005)
  • Sampling Theory in Signal and Image Processing, Peer Review of Article (2005)
  • Swedish Research Coucil, Proposal Reviewer (2005 - 2005)
  • NSF, External Reviewer (2005 - 2005)
  • University of Delaware, Panelist (2005)
  • Graduate committee, Member (2003 - 2004)
  • Personnel Committee, Member at Rank (2003 - 2004)
  • Department of Mathematics and Statistics, Hiring committee for tenure track position in computational Biology (2004)
  • ICCS Conference proceedings, Peer Review (2004)
  • J. Comp and Appl. Math, Peer Review (2004)
  • Mathematics of Computation, Peer Review (2004)
  • Swedish Research Coucil, Proposal Reviewer (2004)
  • Journal of Scientific Computing, Peer Review of Article (2003)
  • NSF -FRG Review Panel, Referee (2003)
  • SIAM Review, Peer Review of Article (2003)