Robust 1-bit Compressive Sensing Using Adaptive Outlier Pursuit

In compressive sensing (CS), the goal is to recover signals at reduced sample rate compared to the classic Shannon-Nyquist rate. However, the classic CS theory assumes the measurements to be real-valued and have infinite bit precision. The quantization of CS measurements has been studied recently and it has been shown that accurate and stable signal acquisition is possible even when each measurement is quantized to only one single bit. There are many algorithms proposed for 1-bit compressive sensing and they work well when there is no noise in the measurements, e. g., there are no sign flips, while the performance is worsened when there are a lot of sign flips in the measurements. In this paper, we propose a robust method for recovering signals from 1-bit measurements using adaptive outlier pursuit. This method will detect the positions where sign flips happen and recover the signals using correct measurements. Numerical experiments show the accuracy of sign flips detection and high performance of signal recovery for our algorithms compared with other algorithms.