Abstract In this paper, we propose using lq-constrained least-squares to decode n dimensional signals with sparsity level s from m noisy and sign flipped 1-bit quantized measurements. We prove that the solution of the proposed decoder approximates the target signals with the precision δ up to a positive constant with high probability as long as m ≥ O ( s 2 / q − 1 log n δ 2 ) . A weighted primal-dual active set algorithm with continuation is utilized for computing the proposed estimator by combining the data driven majority vote tuning parameter selection rule. Comprehensive numerical simulations indicate that our proposed decoder is robust to noise and sign flips and performs better than state-of-the-art methods.

中文翻译：

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通过 ℓ - 约束最小二乘法在 1 位压缩感知中实现稳健恢复

摘要 在本文中，我们建议使用 lq 约束最小二乘法从 m 个噪声和符号翻转的 1 位量化测量中解码稀疏级别为 s 的 n 维信号。我们证明，只要 m ≥ O (s 2 / q − 1 log n δ 2)，所提出的解码器的解决方案就以高概率将目标信号以精度 δ 逼近为正常数。通过结合数据驱动的多数投票调整参数选择规则，使用具有连续性的加权原始对偶活动集算法来计算建议的估计量。综合数值模拟表明，我们提出的解码器对噪声和符号翻转具有鲁棒性，并且比最先进的方法性能更好。