Improving Robustness for Anisotropic Sparse Recovery using Matrix Extensions

Conference: WSA 2018 - 22nd International ITG Workshop on Smart Antennas
03/14/2018 - 03/16/2018 at Bochum, Deutschland

Proceedings: ITG-Fb. 276: WSA 2018

Pages: 7Language: englishTyp: PDF

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Herrmann, Carsten; Lu, Yun; Scheunert, Christian (Technische Universität Dresden, 01062 Dresden, Germany)
Jung, Peter (Communications and Information Theory Group, Technische Universität Berlin, 10587 Berlin, Germany)

Recovery guarantees in compressed sensing (CS) often require upper bounds on the noise level. The robustness with respect to additive errors of unknown power depends on quotient bounds of the measurement matrix. For isotropic random matrices like iid. Gaussian matrices these bounds are known to behave well. In this work we focus instead on explicitly given anisotropic sensing matrices which are more relevant for real world applications. We propose straightforward quotientmodifications of CS decoders using matrix extensions to improve robustness. We reformulate this as a recovery problem under partial off-support knowledge and discuss the implications. Finally, we present numerical results for measurement matrices taken from a particular radar application where our idea of matrix extensions shows substantial performance improvements.