Per Christian Hansen

Section for Scientific Computing

Professor of Scientific Computing Head of HD-Tomo research project Office DTU Compute Section for Scientific Computing Building 303 (the West Wing), Room 114 Technical University of Denmark DK-2800 Lyngby, Denmark Email: pcha@dtu.dk URL: http://www2.compute.dtu.dk/~pcha Phone: +45 45.25.30.97 Mobil: +45 23.65.27.98

Personal Data

• Curriculum vitae: PDF file.   Short CV: PDF file.   Long CV: PDF file.  
• List of publications: PDF file.   H-index : 45 (January 2017), see Google Scholar.
• SIAM Fellow for contributions to algorithms for rank-deficient and discrete ill-posed problems and regularization techniques.
• Editor of SIAM J. Scientific Computing

Workshop: Uncertainty in Image Reconstruction

• Jonathan M. Bardsley, University of Montana. Bayesign Methods and Uncertainty Quantification for Linear Inverse Problems, Bayesign Methods and Uncertainty Quantification for Nonlinear Inverse Problems.
• James G. Nagy, Emory University. Object Motion and Image Reconstruction, Compact Multi-Frame Blind Deconvolution,
• Ioannis Sechopoulos, Dutch Reference Centre for Screening. (Un)certainties in Radion Dosimetry in Breast Imaging, Uncertainty in Mecial Imaging.
• Sarang Joshi, SCI Institute, University of Utah. Motion Modeling in CT Imaging.

Short Course: An Introduction to Uncertainty Quantification (UQ)

• Prof. Jan S. Hesthaven, EPFL: UQ for PDE problems. Lecture 1, Lecture 2, Lecture 3, Lecture 4.
• Prof. Oliver G. Ernst, Technische Universität Chemnitz: UQ for inverse problems. Complete lecture.

Jan S. Hesthaven's Lectures about Reduced Order Models for Parameterized Problems

• Slides: Lecture 1, Lecture 2, Lecture 3.
• Text book: Hesthaven, Rozza, and Stamme: Cerfified Reduced Methods for Parametrized PDEs.

Research Projects

Books and Stuff to Download

Matlab Software for Reconstruction and Imaging

Talks and Seminars

• Invited speaker at the International Workshop on Mathematical Imaging and Emerging Modalities, June 27-30, 2016 with the talk ART Performance.
• Invited speaker at the COST workshop Advanced X-Ray Tomography: Experiment, Modeling, and Algorithms, Feb. 10-14, 2014.
• Invited speaker at the Householder Symposium on Numerical Linear Algebra, Spa, Belgium, June 8-13, 2014.
• Selected to participate in the Oberwolfach Workshop on Mathematics and Algorithms in Tomography, August 10-16, 2014.

• Regularization in Tomography - Dealing with Ambiguity and Noise
• Image Deblurring with Krylov Subspace Methods
• A Paramter-Choice Method that Exploits Residual Information
• Image Deblurring in the Light of the Cosine Transform
• Semi-Convergence Properties of Kaczmarz's Method (ART)
• AIR Tools - A MATLAB Package of Algebraic Iterative Reconstruction Methods
• Semi-Convergence and Relaxation Paramters for a Class of SIRT Algorithms
• Total Variation and Tomographic Imaging from Projections

Various Projects

• Bachelor Projects
  Examples of projects I have supervised:
  • Iterative Tomographic Reconstruction with Priorconditioning (2016).
  • GPU Implementation of a Toolbox for Tomographic Reconstruction (2015).
  • Robust Computed Tomography with Incomplete Data (2015). Joint with School of Mathematics, Manchester University.
  • Models and Computational Methods for Multi-Spectral Tomography (2014).
  • Computational Methods for Depth Resolution in Potential-Field Inverseion (2013).
  • Expansion of "Regularization Tools" with Large-Scale Problems (2013).
• Master Thesis Projects
  Examples of projects I have supervised (links to pdf files are currently disabled by the DTU Library):
  • Block Algebraic Methods for 3D Image Reconstruction on GPUs (2014). Thesis.
  • Reconstruction Algorithms for Phase-Contrast Tomography using Laboratory X-Rays (2014).
  • Hybrid Methods for Large-Scale tomographic Reconstructions (2012). IMM-M.Sc.-2012-16.
  • Ray-Tracing Problems for Tomographic Reconstruction in Materials Science (2011). IMM-M.Sc.-2011-79.
  • Omni-Directional Image Deblurring (2011). IMM-M.Sc.-2011-11.
    This project received the Master Thesis Award (Specialeprisen) 2011 from the Danish Mathematical Society.
  • Implementation and Evaluation of a Splitting Method for Total Variation Deblurring (2011). IMM-M.Sc.-2011-12
  • Depth Resolution in 3D Imaging (2010). IMM-M.Sc.-2010-36
  • Sound Source Reconstruction with Covariance Matrix Fitting (2010). IMM-M.Sc.-2010-08
  • Matlab Package for Algebraic Reconstruction Techniques (2010). IMM-M.Sc.-2010-18
• PhD Projects
  Current PhD students and their projects:
  • Hari Om Aggrawal (co-supervisor) - Priors for Temporal Tomographic Image Reconstruction
  • Federica Sciacchitano (co-supervisor) - Image Reconstruction Under Non-Gaussian Noise.
  See also my list of former Ph.D. students and projects.
• Research Projects
  • HT-Tomo - High-Definition Tomography (through the use of prior information (funded by the European Research Council).
  • Improved Impedance Tomography with Hybrid Data (funded by the Danish Council for Independent research | Natural Sciences.
  Past projects that I have previously headed:
  • CSI - Computational Science in Imaging (funded by FTP 2007-2012).
  • Scientific GPU Computing - Desktop Scientific Computing on Consumer Graphics Cards (funded by FTP 2010-2013).
  • SASI - Stabiliserings-Algoritmer til Storskala Inversion (Stabilization Algorithms for Large-Scale Inversion, funded by SNF 2004-2006).
  • SCOSI - Scientific Computing in Optimization, Simulation, and Inversion (funded by SNF 2000-2002).

Publications, Software, Technical Reports, Etc.

• Published and submitted papers, technical reports, etc.
  
  • Link to a continuously updated list of my works.
• Books.
  
  • The monograph Rank-Deficient and Discrete Ill-Posed Problems (second printing) is published by SIAM.
    • SIAM's book description.
    • The table of contents.
    • List of misprints and corrections for the first printing (pdf file).
  • The book Deblurring Images: Matrices, Spectra, and Filtering, written jointly with James G. Nagy and Dianne P. O'Leary, is also published by SIAM.
    • SIAM's book description.
    • The book's home page includes Matlab functions, images and other material related to the book.
    • List of misprints and corrections.
  • The textbook Discrete Inverse Problems: Insight and Algorithms is another book published by SIAM.
    • SIAM's book description.
    • The book's home page has a suggestion for a short course based on the book, including overheads, and a list of misprints.
  • The monograph Least Squares Data Fitting with Applications is written jointly with Victor Pereyra and Godela Scherer, and it is published by Johns Hopkins University Press.
    • The publisher's book description.
    • The book's home page with some overheads and a list of misprints.
• Matlab Software for Regularization of Discrete Ill-Posed Problems.
  • Regularization Tools (Version 4.0 for Matlab 7.3) is a Matlab package for analysis and solution of discrete ill-posed problems. The software and the manual is available, as well as some additional functions that provide new functionality.
  • AIR Tools is a Matlab package of algebraic iterative reconstruction methods.
  • mxTV, a software package for Total Variation image reconstruction. The core software is written in C, and with mex interfact to Matlab.
  • TVReg, a software package for 3D tomography using Total Variation regularization. The core software is written in C, and with mex interfact to Matlab.
• Matlab Software for Rank-Deficient Problems.
  • UTV Tools is a package of 46 Matlab functions for computing and modifying rank-revealing decompositions, with focus on URV and ULV decompositions.
  • UTV Expansion Pack, with extensions and new algorithms, is also available.

Professional Memberships

• SIAM - Society for Industrial and Applied Mathematics.
• Danish Academy of Technical Sciences (ATV).
• Danish Academy of Naltural Sciences (DNA).

Some Interesting Links

• Freely available software for linear algebra.
• Matrix Market.
• NA-Net Home Page.
• Netlib Home Page.
• Top 500 supercomputers.
• History of Mathematics archive.