BannerHauptseite TUMHauptseite LehrstuhlMathematik SchriftzugHauptseite LehrstuhlHauptseite Fakultät

Advanced Seminar Course: Compressive Sensing

Organization

Date Time Topics Room
24.05.19
13:00 - 18:00
Algorithms for l1 Minimization (Wester)
Success of Sparse Recovery (Junge)
Dudley's Inequality (Callies)
Atomic Norm as Convex Regularizer (Freytag)
02.06.011
14.06.19
13:00 - 18:00
Thresholding & Greedy Algorithms (Xu)
Random Sampling in Bounded Orthonormal Systems (Decker)
RIP for Special Matrices (Ay)
02.06.011
28.06.19
13:00 - 18:00
Gelfand Widths of lp-Balls (Pieroth)
Instance Optimality and Quotient Property (Loncar)
Lossless Expanders in Compressive Sensing (Callies)
02.06.011

Topics

  Topic Literature  
1.
Algorithms for l1 Minimization [1]Ch.15, [2]
DS
2.
Thresholding & Greedy Algorithms [1]Ch.6.3-6.4, [3], [4]
DS
3.
Small-Ball Method [5]
DS
4.
Instance Optimality and Quotient Property [1]Ch.11, [6]
5.
Random Sampling in Bounded Orthonormal Systems [1]Ch.12, [7]
DS
6.
Lossless Expanders in Compressive Sensing [1]Ch.13, [8]
7.
Success of Sparse Recovery [9]
8.
Gelfand Widths of lp-Balls [1]Ch.10, [10]
9.
Atomic Norm as Convex Regularizer [11]
DS
10.
RIP for Special Matrices [12]
11.
Sparse Reconstruction from Fourier Measurements [13]Ch.1-3

Literature

[1]    S. Foucart, H. Rauhut, A Mathematical Introduction to Compressive Sensing, Applied and Numerical Harmonic Analysis, Birkhäuser, (2013)

[2]    D. L. Donoho and Y. Tsaig, Fast solution of l1 minimization problems when the solution may be sparse, IEEE Trans. Inform. Theory, 54, pp. 4789–4812, (2008)

[3]    D. Needell and J. A. Tropp, CoSaMP: Iterative signal recovery from incomplete andinaccurate samples, Appl. Comput. Harmon.Anal., vol. 26, no. 3, pp. 301–321, (2009)

[4]    T. Blumensath, M. Davies, Iterative hard thresholding for compressed sensing. Appl. Comput.Harmon. Anal.27(3), 265–274 (2009)

[5]    G. Lecúe and S. Mendelson. Sparse recovery under weak moment assumptions. Technical report, CNRS, Ecole Polytechnique and Technion, (2014)

[6]    P. Wojtaszczyk, Stability and instance optimality for Gaussian measurements in compressed sensing. Found. Comput. Math.10, 1–13 (2010)

[7]    H. Rauhut, Random sampling of sparse trigonometric polynomials. Appl. Comput. Harmon.Anal.22(1), 16–42 (2007)

[8]    R. Berinde, A. Gilbert, P. Indyk, H. Karloff, M. Strauss, Combining geometry and combinatorics: A unified approach to sparse signal recovery. InProc. of 46th Annual Allerton Conference on Communication, Control, and Computing, pp. 798–805, (2008)

[9]    D. L. Donoho, Neighborly polytopes andsparse solution of underdetermined linear equations, Dept. Stat., Stanford Univ.,Stanford, CA, Tech. Rep., (2004)

[10]    S. Foucart, A. Pajor, H. Rauhut, T. Ullrich, The Gelfand widths of lp-balls for 0 < p ≤ 1, J. Complex. 26(6), 629–640 (2010)

[11]    Chandrasekaran, V., Recht, B., Parrilo, P.A. et al. The Convex Geometry of Linear Inverse Problems, Found Comput Math (2012)

[12]    F. Krahmer, S. Mendelson and H. Rauhut. Suprema of Chaos Processes and the Restricted Isometry Property, Comm. Pure Appl. Math., 67(11):1877-1904, (2014)

[13]    Rudelson, M. and Vershynin, R. On sparse reconstruction from Fourier and Gaussian measurements,Comm. Pure Appl. Math.,61, 1025–1045. (2008)

Contact

  Person E-Mail Büro
  Felix Krahmer  felix.krahmeremattum.de   02.10.039
  Tim Fuchs   tim.fuchsematma.tum.de 02.10.052

nach oben