Abstract
This chapter gives an overview over recovery guarantees for total variation minimization in compressed sensing for different measurement scenarios. In addition to summarizing the results in the area, we illustrate why an approach that is common for synthesis sparse signals fails and different techniques are necessary. Lastly, we discuss a generalization of recent results for Gaussian measurements to the subgaussian case.
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Acknowledgments
FK and MS acknowledge support by the Hausdorff Institute for Mathematics (HIM), where part of this work was completed in the context of the HIM trimester program “Mathematics of Signal Processing”; FK and CK acknowledge support by the German Science Foundation in the context of the Emmy Noether Junior Research Group “Randomized Sensing and Quantization of Signals and Images” (KR 4512/1-1) and by the German Ministry of Research and Education in the context of the joint research initiative ZeMat. MS has been supported by the Austrian Science Fund (FWF) under Grant no. Y760 and the DFG SFB/TRR 109 “Discretization in Geometry and Dynamics.”
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Krahmer, F., Kruschel, C., Sandbichler, M. (2017). Total Variation Minimization in Compressed Sensing. In: Boche, H., Caire, G., Calderbank, R., März, M., Kutyniok, G., Mathar, R. (eds) Compressed Sensing and its Applications. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-69802-1_11
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DOI: https://doi.org/10.1007/978-3-319-69802-1_11
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