Home Page of Peter Massopust, PhD

 

AFFILIATION:

Senior Researcher

Marie Curie Excellence Team

Mathematical Methods in Biological Image Analysis (MAMEBIA)

 

Helmholtz Zentrum Munich - Institute of Biomathematics and Biometry

Ingolstädter Landstrasse 1

D-85764 Neuherberg

Tel.: +49 (0)89 3187 2436

Email: peter.massopust@gsf.de

 

and

 

Centre of Mathematics, M6

Technical University Munich

Boltzmannstrasse 3

D-85747 Garching bei München

Tel.: +49 (89) 289 16839

Fax: +49 (89) 289 16809

Email: massopust@ma.tum.de

 

 

EDUCATION:

 

PhD in Mathematics                        Georgia Institute of Technology, USA 1986

                                                        Advisor: Michael Barnsley

MS in Applied Mathematics             Georgia Institute of Technology, USA 1985

MS in Physics                                 Georgia Institute of Technology, USA 1981

BS (Vordiplom) in Mathematics       Ludwig-Maximilians University, Germany 1980

BS (Vordiplom) in Physics              Ludwig-Maximilians University, Germany 1980

 

 

SCHOLARSHIPS and FELLOWSHIPS:

 

 

 

RESEARCH EXPERIENCE / COLLABORATIONS:

·       Georgia Institute of Technology, Atlanta, Georgia

·       Vanderbilt University, Nashville, Tennessee

·       Rice University, Houston, Texas

·       Sandia National Laboratories, Albuquerque, New Mexico

·       Tuboscope Pipeline Services, Houston, Texas

·       Arnold Engineering and Development Center (AEDC), Tullahoma, Tennessee

 

 

BOOKS:

 

Authored:

 

1.     Fractal Functions, Fractal Surfaces, and Wavelets, Research monograph, 384 pp, Academic Press 1995.

2.     Interpolation and Approximation with Splines and Fractals, in production for Oxford University Press.

 

Edited:

 

1.     Frames and Operator Theory in Analysis and Signal Processing, Contemporary Mathematics, Vol. 451, AMS Book Series, 291 pp., Providence, 2008 (with D. Larson, M. Nguyen, M. Papadakis, Z. Nashed, and A. Zayed).

2.     Radon Transforms, Geometry, and Wavelets, Contemporary Mathematics, Vol. 464, AMS Book Series 265 pp., Providence, 2008 (with E. Grinberg, D. Larson, P. E. T. Jorgensen, G. Olafsson, E. T. Quinto, and B. Rubin).

 

MAIN  AREAS  OF  INTEREST:

 

·       Abstract and Applied Harmonic Analysis

·       Wavelets and Frames

·       Biomathematics

·       Approximation and Interpolation Theory

·       Fractal Analysis and Fractal Geometry

 

 

PUBLICATIONS:

 

1.     The Capacity for a Class of Fractal Functions, Commun. Math. Phys., 105 (1986), 455 - 460 (with D.P. Hardin)

2.     Dynamical Systems, Fractal Functions, and Dimension, Topology Proceedings, 12 (1987), 93 - 110.

3.     Fractal Modeling of Biological Structures, Ann. NY Acad. Sci., 504 (1987), 179 - 194 (with M.F. Barnsley, H. Strickland, and A. D. Sloan)

4.     Fractals and their Geometry, The Georgia Mathematics Newsletter, Issue No. 13, Fall 1989.

5.     Fractal Peano Curves, J. of Geometry, 34 (1989), 127 - 138.

6.     Hidden Variable Fractal Interpolation Functions, SIAM J. Math. Anal., 20(5) (1989), 1218 - 1248(with M. F. Barnsley, J. Elton, and D. P. Hardin)

7.     Fractal Surfaces, J. Math. Anal. and Appl., 151(1) (1990), 275 – 290.

8.     Vector-Valued Fractal Interpolation Functions and their Box Dimension, Aequationes Mathematicae, 42(1991), 1 - 22.

9.     The Exact Hausdorff Dimension for a Class of Fractal Functions, J. Math. Anal. and Appl., 168(1992), 171 - 183 (with S. Gibert).

10.  Multiresolution Analyses Based on Fractal Functions, J. Approx. Theory, 71(1) (1992), 104 - 120 (with D. Hardin and B. Kessler)

11.  Fractal Interpolation Functions from Rn to Rm and their Projections, Zeitschrift für Analysis u. i. Anwend., 12 (1993),535 - 548 (with D. P. Hardin)

12.  Smooth Interpolating Curves and Surfaces Generated by Iterated Function Systems, Zeitschrift für Analysis u. i. Anwend., 12 (1993), 201 - 210.

13.  A Study of Wavelet-Galerkin Methods for Numerical Solutions of Differential Equations Using Multigrid Relaxation Methods, Technical Report, AFOSR Faculty Summer Research Program, July 1993.

14.  Characterization of all Solutions to a Perturbed Laplace Equation II, Rocky Mountain J. Math., 24, No. 2(1994), 549 - 562 (with J. Kelingos)

15.  Fractal Surfaces, Multiresolution Analyses, and Wavelet Transforms, NATO ASI Series F, Vol. 106(1994), 275 - 290 (with J. S. Geronimo and D. P. Hardin)

16.  An Application of Coxeter Groups to the Construction of Wavelet Bases in Rn, Lecture Notes in Pure and Applied Mathematics: Fourier Analysis - Analytic and Geometric Theory, Vol. 157 (1994), 187 - 196 (with J. S. Geronimo and D. P. Hardin)

17.  Fractal Functions and Wavelets Expansions Based on Several Scaling Functions, J. Approx. Th., 78(3)(1994), 373 - 401 (with J. S. Geronimo and D. P. Hardin)

18.  A Wavelet-Multigrid Approach to Solving Partial Differential Equations Based on Fractal Functions, Technical Report, AFOSR Faculty Summer Research Program, August 1994.

19.  An Introduction to Fractal Functions and Fractal Surfaces and their Connection to Wavelet Theory, Lecture Notes for a three-day minicourse sponsored by the Mathematical Association of America (MAA), 1995.

20.  Multiresolution Schemes for Solving Conservation Laws, Technical Report, AFOSR Faculty Summer Research Program, August 1995.

21.  A Characterization of Solutions to a Radially Perturbed Laplace Equation in the unit n-ball, J. Math. Anal. and Appl., 199 (1996), 728 - 747 (with J. Kelingos).

22.  Construction of Orthogonal Wavelets Using Fractal Interpolation Functions, SIAM J. Math. Anal., 27(4) (1996), 1158 - 1192 (with G. Donovan, J. Geronimo, and D. Hardin)

23.  On the Support Properties of Scaling Vectors, Applied and Computational Harmonic Analysis, 3(1996), 229 - 238 (with D. Ruch and P. Van Fleet)

24.  Fractal Functions and Multiwavelets, Proceedings of Fractals in Engineering 97, Arcachon, France, June 1997.

25.  Fractal Functions and their Applications, Chaos, Solitons, and Fractals, 8(2) (1997), 171 -190.

26.  Scaling Vectors and Multiwavelets in Numerical Differential Equations -- Some Approximation-Theoretic and Numerical Issues, Sandia Technical Report, SAND97-2133, UC-405, September 1997.

27.  Multiwavelets and their Applications, Lectures Notes for a week-long short course sponsored by the Mathematical Association of America (MAA), 1997.

28.  Generalized Multiresolution Schemes, J. Math. Anal. and Applications, 221 (1998), 574 -594.

29.  A Multiwavelet Based on Piecewise C1 Fractal Functions and Related Applications to Differential Equations, Bol. Soc. Mat. Méxicana, (3), Vol 4 (1998), 249 -283.

30.  Local Stable Splittings and Wavelet Packets, Technical Report for Sandia National Laboratories, May 1998.

31.  Nonlinear Approximation, Wavelet Packets, and Interpolation, Technical Report for Sandia National Laboratories, July 1998.

32.  Divergence-Free Multiwavelets, Approximation Theory IX (C. K. Chui and L. L. Schumaker, eds.),2(1998), 161 - 168 (with J. Lakey and C. Pereyra)

33.  Translation Invariant Multiwavelet Transforms, Technical Report CML TR 98-06, Computational Mathematics Laboratory, Rice University, 1998 (with Kathrin Berkner)

34.  On Magnetic Fields Generated by Cartesian, Cylindrical, Spherical, and Parabolic Defects. Part I: Analytical Solutions, Tuboscope Technical Report TR-1999-01, 1999.

35.  Circumferential Sensor Evaluation, Tuboscope Technical Report TR-1999-02, 1999.

36.  On Angularly Perturbed Laplace Equations in the Unit Ball of Rn+2 and their Distributional Boundary Values, in Analysis of Divergence, (W. O. Bray and C. V. Stanojevic, eds.) (1999), 359 -378.

37.  Fourier and Wavelet Analysis of Defects, Tuboscope Technical Report TR-2000-01, 2000.

38.  MFL Signal Enhancement via Wavelet-Based Denoising, Tuboscope Technical Report TR-2000-05, 2000 (with A. Belanger)

39.  Axial and Circumferential Local Curvature Calculations for Strain Estimation and their Error Analyses, Tuboscope Technical Report TR-2000-06, 2000.

40.  Hierarchical rule based classification of MFL signals obtained from natural gas pipeline inspection, IEEE-INNS-ENNS international joint conference on neural networks, Vol. 5, pp. 71-76, 2000 (mit J. Y. Lee, M. Afzal, S. Udpa, und L. Udpa).

41.  Two-Dimensional Wavelet-Based Denoising, Tuboscope Technical Report TR-2001-02, 2001.

42.  Knot Removal and Knot Insertion for Two-Dimensional Mechanical Damage Data, Tuboscope Technical Report TR-2001-03, 2001.

43.  Computation of the Strain Tensor Field for Mechanical Damage Data, Tuboscope Technical Report TR-2001-04, 2001.

44.  Multisensor Fusion for 3-D Characterization Using Wavelet Basis Neural Network, Review of Progress in Quantitative Nondestructive Evaluation, D. O. Thompson and D. E. Chimenti, Eds, Vol. 20A, American Institute of Physics, pp. 679-694, 2001 (mit J. Lim, S. Udpa, L. Udpa, und M. Afzal).

45.  Modified Exact Solutions, Tuboscope Technical Report TR-2002-02, 2002.

46.  Pipeline Integrity Assessment Algorithms: Statistical Foundations, Tuboscope Technical Report TR-2002-04, 2002.

47.  A Short Note on Hysteresis and Odd Harmonics, Tuboscope Technical Report TR-2002-05, 2002.

48.  Compression of ILI data Using Wavelet Packets, Tuboscope Technical Report TR-2002-07, 2002.

49.  A Short Note on ILI Data Correction Due to Pipe Deformation, Tuboscope Technical Report TR-2002-08, 2002.

50.  Mathematical Analysis of ILI Data, Tuboscope Technical Report TR-2003-02, 2003.

51.  Fractal Functions and Wavelets: Examples of Multiscale Theory, in Abstract and Applied Analysis, Proceedings of the International Conference, Hanoi, Vietnam, 13 -- 17 August,2002, (N. M. Chuong, L. Nirenberg, W. Tutschke, eds.), World Scientific Press, Singapore, 2004.

52.  The Benefits of Combining Technologies for In-Line Inspection, 3R International, (42) Heft 7,(2003) (with M. Slaughter and C. Torres)

53.  Signal Enhancement via B-Spline representations, Tuboscope Technical Report TR-2003-07, 2003 (withA. Belanger)

54.  Reconstruction of Clipped MFL Signals via B-spline Approximation and Hermite Interpolation, Tuboscope Technical Report TR-2004-04, 2004.

55.  Fractal Functions, Splines, and Besov and Triebel-Lizorkin Spaces, in Fractals in Engineering: New trends and applications (J. Lévy-Véhel, E. Lutton, eds.), 21 -- 32, Springer Verlag, London, 2005.

56.  Removal of Seamless Pipe Noise via Curvelets, Tuboscope Technical Report TR-2006-01, 2006.

57.  Inverse problems in pipeline engineering, in The Radon Transform, Inverse Problems, and Tomography, (G. Ólafsson, E. T. Quinto, eds.), AMS Proceedings on Symposia in Applied Mathematics 63, 93 – 128, Providence, Rhode Island, 2006.

58.  A Class of Solutions to Maxwell's Equations in Matter and Associated Special Functions, Advances in Deterministic and Stochastic Analysis, (N. M. Chuong, P. G. Ciarlet, P. Lax, D. Mumford and D. H. Phong, Eds.), 131 – 175, World Scientific Publishing Co., 2007.

59.  Multiwavelets: Some Approximation-Theoretic Properties, Sampling on the Interval, and Translation Invariance, Harmonic, Wavelet and p-Adic Analysis, (N. M. Chuong et al. Eds.), 37 – 57, World Scientific Publishing Co., 2007.

  1. Multivariate Complex B-Splines, Proceedings of SPIE, Wavelets XII, Vol. 6701, 670109-1 – 670109-9, 2007 (with B. Forster).
  2. Coxeter Groups and Wavelets Sets, Contemporary Mathematics, Vol. 451 (2008), 187 - 218 (with D. Larson).
  3. Some Remarks about the Connection between Fractional Divided Differences, Fractional B-Splines, and the Hermite-Genocchi Formula, International Journal of Wavelets, Multiresolution and Information Processing, Vol. 6, No. 2, 2008, 279 – 290 (with. B. Forster).
  4. Statistical Encounters with Complex B-Splines, to appear in Constructive Approximation,  (with B. Forster).
  5. Three-way Tiling Sets in Two Dimensions, to appear in Acta Applicandae Mathematicae, 2008 (with D. Larson and G. Ólafsson).
  6. Multivariate Complex B-splines and Dirichlet Averages, submitted to J. Approx. Theory (with B. Forster).
  7. Reconstruction of Smooth Functions from Incomplete Data, submitted to European Journal of Applied Mathematics, 2007.
  8. Isotropic wavelet frames based on the Riesz transform, in preparation (with B. Forster, S. Held, and M. Storath).
  9. A Class of Fractal Homeomorphisms, in preparation (with M. Barnsley).
  10. The Many Faces of Wavelet Sets: History and Open Problems, in preparation (with D. Larson and G. Ólafsson).
  11. Foldable Figures, Fuchsian Groups, and Multiscale Structure, in preparation. 

 

GRANTS AND  SPONSORED  RESEARCH:

1.     VolkswagenStiftung: Financial Support for the summer school „New Trends and Directions in Harmonic Analysis, Approximation Theory, and Image Analysis,“ Inzell, Germany, September 2007 (with B. Forster and R. Lasser).

2.     Research contract, Sandia National Laboratories, 1998.

3.     NSF Grant "Wavelets Based on Several Scaling Functions and Related Applications" (with J. Wang, D. Ruch, W. So, and P. Van Fleet), 1995-1998.

4.     Summer Faculty Research Program 1993, 1994, and 1995 (sponsored by Air Force Office of Scientific Research).

5.     NATO Grant for the Advanced Research Workshop "Shape in Picture" (The Netherlands), 1992.

6.     State University of West Georgia Faculty Research Grant (1989 - 1990).

 

 

SHORT AND  MINICOURSES  PRESENTED:

1.     Inverse Problems in Pipeline Inspection, invited presentation for the AMS Short Course entitled The Radon Transform and Applications To Inverse Problems (organized by G. Ólafsson and T. Quinto and sponsored by the AMS, Atlanta, Georgia, January 2005)

2.     Multiwavelets and their Applications (invited and sponsored by the Alleghany Section of the MAA, Meadville, Pennsylvania, June 1997).

3.     An Introduction to Fractal Functions and Fractal Surfaces and Their Connection to Wavelet Theory (invited and sponsored by the MAA, San Francisco, California, January 1995).

 

 

MEMBERSHIPS AND  OTHER  SCHOLARLY  ACTIVITIES:

·       Member of Phi Mu Epsilon (National Honorary Mathematics Fraternity) and Sigma Pi Sigma (Physics Honor Society)

·       Invited member of IAG (International Association of Geodesy) Special Study Group IAG-SSG 4.195, Fractal Geometry in Geodesy

·       Invited external member of Board of Examiners, Indian Institute of Technology, Kanpur, India, for PhD dissertation entitled A Study of Coalescence and Spline Fractal Interpolation Functions.

·       Refereed for     

-       Constructive Approximation

-       Journal of Approximation Theory

-       Journal of Mathematical Analysis and Applications

-       The American Mathematical Monthly

-       SIAM J. Matrix Analysis

-       SIAM J. Numerical Analysis

-       SIAM J. Applied Dynamical Systems

-       European Journal of Applied Mathematics

-       Transactions of the American Mathematical Society

-       Applied and Computational Harmonic Analysis

-       International Journal of Mathematics and Mathematical Sciences

-       Chinese Journal of Mathematics

-       Advances in Computational Mathematics

-       Fractals

-       Journal of Applied Mathematics

-       Real Analysis Exchange

-       Mathematics of Computation

-       IEEE Signal Processing Letters

-       IEEE Transactions on Signal Processing

-       IEEE Proceedings on Imaging

-       Computers & Graphics

·       Reviewer for Mathematical Reviews

·       Conference and Scientific Committees

-       Summer School on New Trends and Directions in Harmonic Analysis, Approximation Theory, and Image Analysis, Inzell, Germany, September 2007.

-       Special Session on Frames and Wavelets in Harmonic Analysis, Geometry and Applications, Annual Meeting of the AMS in New Orleans, Louisiana, January 2007.

-       Special Session on Frames and Operator Theory in Analysis and Signal Processing, Annual Meeting of the AMS in San Antonio, Texas, January 2006.

-       Second International Conference on Applied and Abstract Analysis, Qui Nhon, Vietnam, June 2005.

-       First International Summer School on Harmonic, Wavelet and p-adic Analysis, Qui Nhon, Vietnam, June 2005.

-       Invited Special Session on Design and Applications of Multidimensional Wavelets and MRAs, Wavelets XI, SPIE International Symposium on Optical Science and Technology, SPIE 50th Annual Meeting, San Diego, California, July/August 2005.

-       Special Session on Designing Frames and Wavelets: From Theory to Digitization, Sixth Joint Meeting of the America Mathematical Society and the Sociedad Matemática Méxicana, Houston, Texas, May 2004.

-       International Conference on Abstract and Applied Analysis 2002, A satellite conference of the International Congress of Mathematicians (ICM) 2002, Hanoi, Vietnam, August 2002.

-       Special Session on (Multi)wavelets and Numerical PDEs, Western Sectional Meeting of the AMS, University of New Mexico, Albuquerque, New Mexico, November 1997.

-       International Conference on Multiwavelets: Theory and Applications, Sam Houston State University, Huntsville, Texas, March 1997.

 

 

INVITED PRESENTATIONS AT NATIONAL AND  INTERNATIONAL CONFERENCES  AND  WORKSHOPS:

·       NeuWave Imaging Workshop, Technische Universität München, April 2008.

·       7. Workshop Approximationstheorie, Universität Erlangen – Nürnberg,  February 2007.

·       Wavelets XII, SPIE Conference, San Diego, U.S.A., August 2007.

·       Mini-Workshop on Geometric Measure Theorretic Approaches to Potentials on Fractals and Manifolds, Oberwolfach Research Institute, Oberwolfach, Germany, April 2007.

·       
47. Workshop on Approximationstheorie, Universität Erlangen – Nürnberg, February 2007.

·       Workshop on Operator Methods in Fractal Analysis, Wavelets, and Dynamical Systems, Banff, Canada, December 2006.

·       IMA/MCIM Industrial Problems Seminar, Mathematical Problems associated with a Class of Nondestructive Evaluations, IMA, Minneapolis, Minnesota, March 2006.

·       Workshop on Harmonic Analysis and Fractal Geometry, Louisiana State University, Baton Rouge, Louisiana, February 2006.

·       Workshop on New Mathematics and Algorithms for 3-D Image Analysis, Institute of Mathematics and its Applications (IMA), University of Minnesota, Minneapolis, Minnesota, January 2006.

·       International Conference on Fractals in Engineering V, Tours, France, June 2005.

·       First International Summer School on Harmonic, Wavelet, and p-adic Analysis, Qui Nhon University, Qui Nhon, Vietnam (two one-hour lectures), June 2005.

·       Second International Conference on Abstract and Applied Analysis, ICAAA 2005, Qui Nhon, Vietnam (plenary lecture), June 2005.

·       Special Session on The Radon Transform and Inverse Problems, Annual Meeting of the AMS, Atlanta, Georgia, January 2005.

·       Workshop on Functional and Harmonic Analyses of Wavelets and Frames, Institute of Mathematical Sciences, National University of Singapore, Singapore, August 2004

·       Workshop on New Mathematics and Algorithms for 3D Image Analysis, Louisiana State University, Baton Rouge, Louisiana, September, 2003.

·       Special Session on Wavelets, Frames, and Tomography, Southeastern Sectional Meeting of the AMS, Baton Rouge, Louisiana, March 2003.

·       International Conference on Abstract and Applied Analysis, a satellite conference of the International Congress of Mathematics, Hanoi, Vietnam, August 2002.

·       Special Session on (Multi)wavelets and Numerical PDEs, Western Regional Meeting of the AMS, Albuquerque, New Mexico, November 1997.

·       International Conference on Fractals in Engineering III, Arcachon, France, June 1997.

·       Seventh International Workshop in Analysis and its Applications, University of Maine, Orono, Maine, June 1997.

·       Minisymposium on Wavelets and their Applications, SIAM Annual Meeting, Kansas City, Missouri, July 1996.

·       Special Session on Numerical Solutions of Nonlinear Partial Differential Equations, Second Meeting of the AMS and the Sociedad Matemática Méxicana, Guanajuato, México, November 1995.

·       Special Session on Wavelets and Applications, International Conference on Applied Science and Computations, Eastern Illinois University, Charleston, Illinois, October 1995.

·       Third US National Congress of Computational Mechanics, Dallas, Texas, June 1995.

·       Special Session on New Trends in Generalized Functions, Southeastern Regional Meeting of the AMS, Orlando, Florida, March 1995.

·       31st Annual Symposium of the Society of Engineering Science, Texas A & M University, College Station, Texas, October 1994.

·       NATO Advanced Research Workshop, Shape in Picture, Driebergen, The Netherlands, September 1992.

·       Sixth International Workshop on Analysis and it Applications, University of Maine, Orono, Maine, June 1992.

 

 

INVITED COLLOQUIA AND SEMINAR TALKS:

·       Technical University Munich, Germany

·       University of North Texas, Denton, Texas

·       Texas A & M University, College Station, Texas (several occasions).

·       University of Houston, Houston, Texas (several occasions).

·       Tuboscope Pipeline Service, Houston, Texas (several occasions).

·       Iowa State University, Ames, Iowa.

·       University of St. Thomas, St. Paul, Minnesota (several occasions).

·       Rice University, Houston, Texas.

·       Center of Approximation Theory, Texas A & M University, College Station, Texas (several occasions).

·       Vanderbilt University (several occasions).

·       New Mexico Institute of Mining and Technology, Socorro, New Mexico.

·       Sandia National Laboratories, Albuquerque, New Mexico.

·       Sam Houston State University (several occasions).

·       University of Central Florida, Orlando, Florida.

·       Arnold Engineering and Development Center (AEDC), Tullahoma, Tennessee.

·       Bradley University, Peoria, Illinois.

·       University of Tennessee Space Institute, Tullahoma, Tennessee.

·       University of Louisville, Louisville, Kentucky.

·       Georgia Institute of Technology, Atlanta, Georgia (several occasions).

·       State University of West Georgia, Carrollton, Georgia.

·       LaGrange College, LaGrange, Georgia.

·       North Harris College, Houston, Texas (several occasions).

 

 

TEACHING  EXPERIENCE:

 

    U.S.A.

·       Finite and Discrete Mathematics

·       Univariate and Multivariate Calculus

·       Vector Calculus

·       Ordinary and Partial Differential Equations

·       Real and Complex Analysis

·       Probability Theory

·       Numerical Analysis

·       Fractal Geometry

·       Numerical Methods for Ordinary and Partial Differential Equations

·       Mathematical Physics

·       Physics I and II