One-bit block sparse signal recovery via nonconvex ℓ2/ℓp(0<p<1) -minimization

Jieqiong Chen, Yi Gao, Jianxi Li, Jianjun Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

One-bit compressed sensing (1-bit CS) shows that a sparse signal can exactly be recovered from extremely quantized linear measurements which just catch their signs. While in many applications, real-world signals also exhibit additional structures aside from standard sparsity, such as block-sparsity. We proposed a nonconvex ℓ2 / ℓp (0 < p < 1) -minimization model. Using the best approximation, covering number, and packing number, we obtain a weak condition to reconstruct block-sparse signals with high probability. And the lower bound of the required number of measurements is lower than some existing 1-bit CS methods. At last, we propose a block adaptive binary iteration thresholding algorithm to recover ℓ2 / ℓp effectively block sparse signals. The algorithm can be used without knowing the sparsity of the underlying signal. Several simulations are conducted to reveal the superiority of our methods to existing approaches, which expose the advantage of 1-bit CS in the reconstruction of block-sparse signals.

Original languageEnglish
Article number063020
JournalJournal of Electronic Imaging
Volume31
Issue number6
DOIs
Publication statusPublished - 1 Nov 2022

Keywords

  • block-sparse signal
  • covering number
  • nonconvex ℓ / ℓ-minimization
  • one-bit compressed sensing
  • thresholding algorithm

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