Recovery of Binary Sparse Signals from Structured Biased Measurements

06/26/2020

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by   Sandra Keiper, et al.

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In this paper we study the reconstruction of binary sparse signals from partial random circulant measurements. We show that the reconstruction via the least-squares algorithm is as good as the reconstruction via the usually used program basis pursuit. We further show that we need as many measurements to recover an s-sparse signal x_0∈ℝ^N as we need to recover a dense signal, more-precisely an N-s-sparse signal x_0∈ℝ^N. We further establish stability with respect to noisy measurements.