Laska, Jason N.Wen, ZaiwenYin, WotaoBaraniuk, Richard G.2018-06-192018-06-192010-11Laska, Jason N., Wen, Zaiwen, Yin, Wotao, et al.. "Trust, But Verify: Fast and Accurate Signal Recovery from 1-bit Compressive Measurements." (2010) <a href="https://hdl.handle.net/1911/102171">https://hdl.handle.net/1911/102171</a>.https://hdl.handle.net/1911/102171The recently emerged compressive sensing (CS) framework aims to acquire signals at reduced sample rates compared to the classical Shannon-Nyquist rate. To date, the CS theory has assumed primarily real-valued measurements; it has recently been demonstrated that accurate and stable signal acquisition is still possible even when each measurement is quantized to just a single bit. This property enables the design of simplified CS acquisition hardware based around a simple sign comparator rather than a more complex analog-to-digital converter; moreover, it ensures robustness to gross non-linearities applied to the measurements. In this paper we introduce a new algorithm --restricted-step shrinkage (RSS) -- to recover sparse signals from 1-bit CS measurements. In contrast to previous algorithms for 1-bit CS, RSS has provable convergence guarantees, is about an order of magnitude faster, and achieves higher average recovery signal-to-noise ratio. RSS is similar in spirit to trust-region methods for non-convex optimization on the unit sphere, which are relatively unexplored in signal processing and hence of independent interest.11 ppengTechnical reportTR10-30