Reconstruction of finite-valued sparse signals

Sandra Keiper; Gitta Kutyniok; Dae Gwan Lee; Götz Pfander

doi:10.1117/12.2273893

24 August 2017 Reconstruction of finite-valued sparse signals

Sandra Keiper, Gitta Kutyniok, Dae Gwan Lee, Götz Pfander

Proceedings Volume 10394, Wavelets and Sparsity XVII; 1039415 (2017) https://doi.org/10.1117/12.2273893
Event: SPIE Optical Engineering + Applications, 2017, San Diego, California, United States

Abstract

The need of reconstructing discrete-valued sparse signals from few measurements, that is solving an undetermined system of linear equations, appears frequently in science and engineering. Those signals appear, for example, in error correcting codes as well as massive Multiple-Input Multiple-Output (MIMO) channel and wideband spectrum sensing. A particular example is given by wireless communications, where the transmitted signals are sequences of bits, i.e., with entries in f0; 1g. Whereas classical compressed sensing algorithms do not incorporate the additional knowledge of the discrete nature of the signal, classical lattice decoding approaches do not utilize sparsity constraints. In this talk, we present an approach that incorporates a discrete values prior into basis pursuit. In particular, we address finite-valued sparse signals, i.e., sparse signals with entries in a finite alphabet. We will introduce an equivalent null space characterization and show that phase transition takes place earlier than when using the classical basis pursuit approach. We will further discuss robustness of the algorithm and show that the nonnegative case is very different from the bipolar one. One of our findings is that the positioning of the zero in the alphabet - i.e., whether it is a boundary element or not - is crucial.

Citation Download Citation

Sandra Keiper, Gitta Kutyniok, Dae Gwan Lee, and Götz Pfander "Reconstruction of finite-valued sparse signals", Proc. SPIE 10394, Wavelets and Sparsity XVII, 1039415 (24 August 2017); https://doi.org/10.1117/12.2273893

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