Department of Mathematics

Numerical Analysis Seminar: Sparse and Redundant Representations

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Prof. Philipp Grohs
HG G 5
Do 15:15 - 16:55
First Lecture
Prof. Philipp Grohs
Seminar for Applied Mathematics
Prerequisites Lineare Algebra, Numerische Mathematik 1
In the past decade, the idea to use sparsity as a prior in underconstrained optimization problems has been widely used with impressive results for a number of problems in data processing such as image denoising, feature classification or dimensionality reduction, to name only a few examples. An area of particular recent attention is Compressive Sensing which falls into the aforementioned class of methods.

Here, sparsity means that our data possesses a sparse representation with respect to a given dictionary. The latter can be fixed (Fourier, wavelets, Gabor, curvelets, ...) or learned from the data at hand.

The goal of this seminar is to give a comprehensive overview of recent developments in the field. This includes theoretical analysis as well as algorithms and implementation in MATLAB.

More concretely we will work through the book [1] which is excellently suited for a seminar. 

Each student will give a talk on one chapter in the book. The goal of the seminar is to learn the current state of research in the field. It can also serve as an ideal preparation for subsequent Bachelor or Master studies.

Literature [1] M. Elad. Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. Springer (2010). A related MATLAB package is available at

[2] A. Bruckstein, D. Donoho and M. Elad. From sparse solutions of systems of equations to sparse modeling of signals and images, SIAM Review, 51(1):34-81, (2009).


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