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- Simon Foucart, Holger Rauhut
- Applied and Numerical Harmonic Analysis
- 2013

- Holger Rauhut
- 2009

These notes give a mathematical introduction to compressive sensing focusing on recovery using `1-minimization and structured random matrices. An emphasis is put on techniques for proving probabilistic estimates for condition numbers of structured random matrices. Estimates of this type are key to providing conditions that ensure exact or approximate… (More)

- Holger Rauhut, Karin Schnass, Pierre Vandergheynst
- IEEE Transactions on Information Theory
- 2008

This paper extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a deterministic dictionary, has small restricted isometry constants. Thus, signals that are sparse with respect to the… (More)

- Yonina C. Eldar, Holger Rauhut
- IEEE Transactions on Information Theory
- 2010

This paper considers recovery of jointly sparse multichannel signals from incomplete measurements. Several approaches have been developed to recover the unknown sparse vectors from the given observations, including thresholding, simultaneous orthogonal matching pursuit (SOMP), and convex relaxation based on a mixed matrix norm. Typically, worst case… (More)

- Massimo Fornasier, Holger Rauhut, Rachel Ward
- SIAM Journal on Optimization
- 2011

We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements. The algorithm is designed for the simultaneous promotion of both a minimal nuclear norm and an approximatively low-rank solution. Under the assumption that the linear measurements fulfill… (More)

- Massimo Fornasier, Holger Rauhut
- SIAM J. Numerical Analysis
- 2008

Vector valued data appearing in concrete applications often possess sparse expansions with respect to a preassigned frame for each vector component individually. Additionally, different components may also exhibit common sparsity patterns. Recently, there were introduced sparsity measures that take into account such joint sparsity patterns, promoting… (More)

- Georg Tauböck, Franz Hlawatsch, Daniel Eiwen, Holger Rauhut
- IEEE Journal of Selected Topics in Signal…
- 2010

We consider the application of <i>compressed sensing</i> (CS) to the estimation of doubly selective channels within pulse-shaping multicarrier systems (which include orthogonal frequency-division multiplexing (OFDM) systems as a special case). By exploiting sparsity in the delay-Doppler domain, CS-based channel estimation allows for an increase in spectral… (More)

- Stefan Kunis, Holger Rauhut
- Foundations of Computational Mathematics
- 2008

We investigate the problem of reconstructing sparse multivariate trigonometric polynomials from few randomly taken samples by Basis Pursuit and greedy algorithms such as Orthogonal Matching Pursuit (OMP) and Thresholding. While recovery by Basis Pursuit has recently been studied by several authors, we provide theoretical results on the success probability… (More)

- Felix Krahmer, Shahar Mendelson, Holger Rauhut
- ArXiv
- 2012

We present a new bound for suprema of a special type of chaos processes indexed by a set of matrices, which is based on a chaining method. As applications we show significantly improved estimates for the restricted isometry constants of partial random circulant matrices and time-frequency structured random matrices. In both cases the required condition on… (More)

- Holger Rauhut, Justin K. Romberg, Joel A. Tropp
- ArXiv
- 2010

In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to succeed when the restricted isometry constants of the sampling matrix are small. Many potential applications of… (More)