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Wavelets and Sparsity

Summer Term 2011

Wavelets and Sparsity

Lecturer: Dr. Simon Setzer,

Office hours: Wednesday, 14:15-15:15

Summer Term 2011

Lectures (3h) with exercises (1h)
(6 credit points)

Time and Location: Tuesday 12-14 c.t. and Friday 14-16 c.t., Building E1.3, Lecture Hall 001

First lecture: Tuesday, April 12, 2011

AnnouncementsDescriptionPrerequisitesLecture NotesAssignmentsExamsLiterature

The last set of slides is now online.

The wavelet transform allows us to represent data in a more suitable "basis". The resulting wavelet coefficients yield interesting ways to analyze and manipulate the data, e.g., compression (JPEG2000), multiscale analysis of seismic data, image denoising and inpainting. A central theme is that the given data is efficiently encoded in only relatively few wavelet coefficents ("sparsity"). We discuss not only the basic theory of the continuous and discrete wavelet transform but also algorithms and applications in image processing.

Undergraduate knowledge in mathematics (e.g. ''Mathematik für Informatiker I-III''). The lectures will be given in English.

Date Topic
12.04. Introduction
15.04. Mathematical preliminaries
19.04. Mathematical preliminaries (cont.) includes Homework 1, due April 26 in class
26.04. Fourier kingdom
29.04. Uncertainty principles includes Homework 2, due May 10 in class fourier_approximation.c, cameraman.pgm
10.05. The windowed Fourier transform
17.05. The continuous wavelet transform includes Homework 3, due May 27 in class
27.05. The discrete wavelet transform includes Homework 4, due June 14 in class FWT_1d.c, IFWT_1d.c,signal256.txt,FWT_1d_solution.c,IFWT_1d_solution.c
07.06. The discrete wavelet transform (cont.) Includes Homework 5, due June 24 in class
11.06. Redundant representations
21.06. Ridgelets and curvelets
01.07. Analysis and synthesis approaches includes Homework 6, due July 8 in class
05.07. Optimization theory for the synthesis approach
15.07. Optimization theory for the synthesis approach (cont.)

Homework will be assigned bi-weekly. To qualify for the exam you need 50% of the points from these assignments.

Please register for the lecture: here.
Remember that you also have to register for the exam in the HISPOS system of the Saarland University

No textbook is required for this course. Examples of books giving background material and further reading are:

  1. Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity
    J.-L. Starck, F. Murtagh and J. M. Fadili, Cambridge University Press, 2010

  2. A wavelet tour of signal processing: the sparse way (second edition)
    S. G. Mallat, Academic Press, 2009

  3. Sparse and Redundant Representations
    M. Elad, Springer, 2010

  4. Ten lectures on wavelets
    I. Daubechies, SIAM, 2006

  5. Wavelets Theory and Application
    A. K. Louis, P. Maaß and A. Rieder, J. Wiley & Sons, Inc., 1997

  6. Fourier Analysis and Applications
    C. Gasquet and P. Witomski, Springer, 1998

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