Analysis of Hard-Thresholding for Distributed Compressed Sensing with One-Bit Measurements

05/09/2018

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by   Johannes Maly, et al.

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A simple hard-thresholding operation is shown to be able to recover L signals x_1,...,x_L ∈R^n that share a common support of size s from m = O(s) one-bit measurements per signal if L >(en/s). This result improves the single signal recovery bounds with m = O(s(en/s)) measurements in the sense that asymptotically fewer measurements per non-zero entry are needed. Numerical evidence supports the theoretical considerations.