Recovery of Binary Sparse Signals from Structured Biased Measurements

2020/06/26 by Sandra Keiper, Keiper, Sandra
Computer Science · Engineering · Medicine · #Advanced MRI Techniques and Applications #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2006.14835

openalex publication_date 2020/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 x₀∈ℝ^N as we need to recover a dense signal, more-precisely an N-s-sparse signal x₀∈ℝ^N. We further establish stability with respect to noisy measurements.

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