Hierarchical Compressed Sensing

Eisert J, Flinth A, Groß B, Roth I, Wunder G (2022)

Publication Type: Book chapter / Article in edited volumes

Publication year: 2022

Publisher: Birkhauser

Series: Applied and Numerical Harmonic Analysis

Pages Range: 1-35

Abstract

Compressed sensing is a paradigm within signal processing that provides the means for recovering structured signals from linear measurements in a highly efficient manner. Originally devised for the recovery of sparse signals, it has become clear that a similar methodology would also carry over to a wealth of other classes of structured signals. In this work, we provide an overview over the theory of compressed sensing for a particularly rich family of such signals, namely those of hierarchically structured signals. Examples of such signals are constituted by blocked vectors, with only few non-vanishing sparse blocks. We present recovery algorithms based on efficient hierarchical hard thresholding. The algorithms are guaranteed to converge, in a stable fashion with respect to both measurement noise and model mismatches, to the correct solution provided the measurement map acts isometrically restricted to the signal class. We then provide a series of results establishing the required condition for large classes of measurement ensembles. Building upon this machinery, we sketch practical applications of this framework in machine-type communications and quantum tomography.

Involved external institutions

Chalmers University of Technology / Chalmers tekniska högskola

Sweden (SE) Freie Universität Berlin

Germany (DE) Technology Innovation Institute (TII) / معهد الابتكار التكنولوجي

United Arab Emirates (AE)

How to cite

APA:

Eisert, J., Flinth, A., Groß, B., Roth, I., & Wunder, G. (2022). Hierarchical Compressed Sensing. In (pp. 1-35). Birkhauser.

MLA:

Eisert, Jens, et al. "Hierarchical Compressed Sensing." Birkhauser, 2022. 1-35.

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