Total Variation Minimization in Compressed Sensing

作者: Felix Krahmer , Christian Kruschel , Michael Sandbichler

DOI: 10.1007/978-3-319-69802-1_11

关键词: GeneralizationAlgorithmGaussianTotal variation minimizationCompressed sensingComputer science

摘要: This chapter gives an overview over recovery guarantees for total variation minimization in compressed sensing different measurement scenarios. In addition to summarizing the results area, we illustrate why approach that is common synthesis sparse signals fails and techniques are necessary. Lastly, discuss a generalization of recent Gaussian measurements subgaussian case.

参考文章(45)
Simon Foucart, Holger Rauhut, A Mathematical Introduction to Compressive Sensing ,(2013)
M. Sandbichler, F. Krahmer, T. Berer, P. Burgholzer, M. Haltmeier, A Novel Compressed Sensing Scheme for Photoacoustic Tomography Siam Journal on Applied Mathematics. ,vol. 75, pp. 2475- 2494 ,(2015) , 10.1137/141001408
Maryia Kabanava, Holger Rauhut, Hui Zhang, Robust analysis $\ell_1$-recovery from Gaussian measurements and total variation minimization arXiv: Information Theory. ,(2014) , 10.1017/S0956792515000236
Roman Vershynin, Estimation in High Dimensions: A Geometric Perspective Sampling Theory, a Renaissance. pp. 3- 66 ,(2015) , 10.1007/978-3-319-19749-4_1
R. Berinde, A. C. Gilbert, P. Indyk, H. Karloff, M. J. Strauss, Combining geometry and combinatorics: A unified approach to sparse signal recovery allerton conference on communication, control, and computing. pp. 798- 805 ,(2008) , 10.1109/ALLERTON.2008.4797639
Richard Baraniuk, Mark Davenport, Ronald DeVore, Michael Wakin, A Simple Proof of the Restricted Isometry Property for Random Matrices Constructive Approximation. ,vol. 28, pp. 253- 263 ,(2008) , 10.1007/S00365-007-9003-X
Deanna Needell, Rachel Ward, Stable Image Reconstruction Using Total Variation Minimization SIAM Journal on Imaging Sciences. ,vol. 6, pp. 1035- 1058 ,(2013) , 10.1137/120868281