"Compressed sensing" (also known as "compressive sensing", "compressive sampling" or "sparse sampling") is a modern signal processing technique. Compressed sensing exploits an intrinsic low-dimensional structure of real world signals. On the one hand this low-dimensional structure allows for a nearly losless compression. On the other hand, by exploiting this structure, one can achieve significant performance gains compared to existing methods. The applications of CS range from radar and image processing to gene analysis.
Tentative Outline:
- Introduction: model-based signal processing, sparsity, degrees of freedom, sampling theorems
- The Sparse Linear Model: CS measurement matrices, fundamental performance limits, NP-hardness of ell0 norm minimziation
- Recovery based on convex relaxation: convex optimization, LASSO, basis pursuit
- Recovery based on greedy algorithms: Matching Pursuit and variants, Iterative Thresholding
- Recovery based on Approximate Message Passing (AMP)
- Nonlinear CS: logistic regression, one-bit compressed sensing
- Applications of CS: Graphical Model Selection, Dictionary Learning, Sparse Signal Reconstruction
first class: Monday, 3.3.2014, 1.00 - 3.00 pm, SEM 389, room no. CG0118
The lecture is roughly based on the textbooks
- "A Mathematical Introduction to Compressive Sensing" by Simon Foucart and Holger Rauhut, Birkhäuser 2013
- "Statistics for High-Dimensional Data - Methods, Theory and Applications" by Peter Bühlmann and Sara van de Geer, Springer 2011
- "A Wavelet Tour of Signal Processing - The Sparse Way" by Stephane Mallat, Elsevier 2009