Adaptive Outlier Pursuit

1-bit Compressive Sensing

1-bit compressive sensing was firstly introduced and studied by Boufounos and Baraniuk in 2008, and the framework is as follows:

where A(cdot) is a mapping from $mathbf{R}^N$ to the Boolean cube $mathcal{B}^M:={-1,1}^M$ . We have to recover signals $xin sum_K^*:={xin S^{N-1}:|x|_0leq K}$ where $S^{N-1}:={xinmathbf{R}^N:|x|_2=1}$ is the unit hyper-sphere of dimension . See more details about 1-bit compressive sensing, please go to http://dsp.rice.edu/1bitCS.