Information Theory and Recovery Algorithms for Quantized and Distributed Compressed Sensing

Informationstheorie und Rekonstruktionsalgorithmen für quantisiertes und verteiltes Compressed Sensing

Zusammenfassung

Ein Quellensignal wird durch eine Compressed-Sensing-Messung kodiert. In diesem Projekt sollen informationstheoretische Grenzen und effiziente Algorithmen der Signalrekonstruktion in den folgenden Szenarien untersucht werden: (1) Quantisierung des Quellensignals vor Messungen und / oder Quantisierung der Messungen nach Quellenkodierung; (2) Verrauschen des Quellensignals vor Messungen und / oder der Messungen nach Quellenkodierung. Die beiden oben beschriebenen Szenarien sind eng verwandt, da Quantisierungsfehler als eine Art von Rauschen interpretiert werden können, die entweder das Quellensignal oder das kodierte Signal beeinflussen.

Summary

The project will explore information theory limits and efficient recovery algorithms after signal encoding by distributed compressed sensing in the following scenarios: (1) quantization of the signal prior to measurements and/or quantization of the measurements after source signal encoding; (2) noise on the source prior to measurements and/or on the measurements after source signal encoding. The two situations described above are closely related as quantization error can be interpreted as a type of noise affecting either the source signal or the encoded signal.

Preprints

  1. L. Palzer, R. Timo, G. Kramer, Compression for letter-based fidelity measures, January 2016.

  2. Massimo Fornasier, Johannes Maly, and Valeriya Naumova A-T-LAS_{2,1}: A Multi-Penalty Approach to Compressed Sensing of Low-Rank Matrices with Sparse Decompositions, January 2018

  3. Johannes Maly and Lars Palzer, Analysis of Hard-Thresholding for Distributed Compressed Sensing with One-Bit Measurements, May 2018.

  4. Mark Iwen, Felix Krahmer, Sara Krause-Solberg, and Johannes Maly, On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds, July 2018.

Publications

  1. L. Palzer and R. Timo, A lower bound for the rate-distortion function of spike sources that is asymptotically tight, IEEE Inf. Theory Workshop (ITW), Cambridge, UK, Sep 2016

  2. L. Palzer and R. Timo, Fixed-length compression for letter-based fidelity measures in the finite blocklength regime, IEEE Int. Symp. on Inf. Theory (ISIT), Barcelona, Spain, Jul 2016

  3. L. Palzer and R. Timo, A converse for lossy source coding in the finite blocklength regime, Int. Zurich Sem. on Comm. (IZS), Zurich, Switzerland, Mar 2016

  4. Sara Krause-Solberg and Johannes Maly, tractable approach for one-bit Compressed Sensing on manifolds, Sampling Theory and Applications (SampTA); 2017 International Conference on. IEEE; July 2017

  5. Massimo Fornasier, Johannes Maly, and Valeriya Naumova, Robust Recovery of Low-Rank Matrices using Multi-Penalty Regularization, Neural Information Processing Systems (NIPS) Workshop Optimisation for Machine Learning (OPT2017); December 2017

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