Fall, 2010 Teaching


           MWF                                      T/Th


9       MATH 673/AMSC 673    Margetis 
        STAT 705    Kedem
                                               9:30     MATH 602   Schafer
                                                        AMSC/CMSC 660 O'Leary 

10      MATH 630    Warner
        MATH 648E   Boyle 
                    (Symbolic dynamics)
        STAT 798    Slud



11      MATH 744    Rosenberg                    11     MATH 600   Tamvakis
        AMSC 660/CMSC 660    Wolfe                      MATH 642   Jakobson
        AMSC 666/CMSC 666 von Petersdorff             



12      MATH 668B   Wentworth (Complex Geom)
        STAT 600    Koralov

                                               12:30    MATH 730   Novikov
                                                        MATH 718D  Laskowski
                                                        MATH 740   Goldman
                                                        STAT 698   Freidlin


1       MATH 712    Kueker
        Num. PDE    Levermore



2        STAT 740    Smith                     2:00     MATH 670/AMSC 670   Antman (AND Mon, 4pm)
                                                        MATH 632   Fitzpatrick




                                               3:30     MATH 648L/MAIT 679L*   Benedetto
                                                                (Wavelet theory and Applications)


                                               5:00     STAT 700    Kagan

                                               5:15-6:30 AMSC 663/CMSC 663   Balan/Tiglio(team)
   * = Description follows

                        MATH 648L : WAVELET THEORY AND APPLICATIONS
                                   Fall Semester - 2010
 
Instructor: John J. Benedetto
Time: Tuesday and Thursday, 3:30 - 4:45
Place: MATH 0304

Prerequisites: MATH 630 OR permission of instructor. 
              
Book: Wavelet Notes (supplied by the instructor), as well as portions of the 
     following books:
          - Harmonic Analysis and Applications (by the instructor),
          - Ten Lectures on Wavelets (by Ingrid Daubechies),
          - A Wavelet Tour of Signal Processing (by Stephane Mallat),
          - Wavelets (by Yves Meyer).

Grading: The grade will be determined by regular homework assignments, classroom 
     participation, and an end of semester project.
...............................................................................

                                    Course Outline

1. Introduction
        - Real analysis and Hilbert spaces
        - History and background of wavelet theory
        - The role of the classical sampling theorem 

2. Wavelet theory
        - The Haar system
        - Quadrature mirror filters
        - Multiresolution analysis (MRA)
        - MRA wavelet orthonormal bases

3. Waveletpackets
        - The Walsh system
        - Waveletpacket theorems and algorithms

4. Multidimensional wavelet theory
        - MRA wavelet orthonormal bases
        - Non-MRA wavelet orthonormal bases

5. Frames
        - Frames of translates
        - Wavelet, Gabor, and Fourier frames
        - Generalized frame multiresolution analysis

6. Wavelet theory on locally compact Abelian groups G
        - Harmonic analysis on G
        - G containing compact open subgroups
        - p-adic wavelet theory

7. Selected applications of wavelet theory
        - Wavelet auditory modelling
        - Image processing

8. The uncertainty principle in wavelet and Gabor theory


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