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CompactCourse: Structured Matrices, Multigrid, and Image Processing - Winter16

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Term
Winter 16
Lecturer
Prof. Dr. Marco Donatelli, Como; contact: Univ.-Prof. Dr. Thomas Huckle
Time and Place
Nov. 28 - Dec. 5, 2016; details see below
Audience
all interested students, in particular students of BGCE, TopMath, CSE, Mathematics, and Informatics
Tutorials
-
Exam
n.a.
Semesterwochenstunden / ECTS Credits
1 credit
TUMonline
based on Course from 2014



Contents

News

Schedule

  • Mon, Nov. 28, 16:00-19:00, room MI 03.08.011
  • Tue, Nov. 29, 16:00-19:00, room chemistry TUM.Computational CH63214 (6th floor)
  • Thu, Dec. 01, 16:00-19:00, room chemistry TUM.Computational CH63214 (6th floor)
  • Mon, Dec. 05, 16:00-19:00, room MI 03.08.011

Content

Structured matrices come up naturally in solving stationary or isotropic problems in different disciplines. Examples are the discretization of partial differential equations (involving the Laplace operator, e.g.) or filter operators in image processing.

Structured matrices possess different properties. Typically, the coefficients are constant along diagonals. Structured matrices are also strongly related to the field of Discrete Fourier Transform and convolution operators. For PDE applications, considering structured matrices allows an analytic discussion and design of Multigrid methods for solving the underlying linear system of equations. For image processing, the analysis via structured matrices allows image reconstruction based on regularization methods to recover noisy and perturbed images.

In the lecture, mathematical properties of structured matrices are discussed before applications in Multigrid methods, image processing, and regularization are tackled.


Topics

  • Convolution and structured matrices
  • Ill-posed problems and regularization
  • Multigrid methods for structured matrices
  • Tutorial on image deblurring

Material

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