Robust binary fused compressive sensing using adaptive outlier pursuit

We propose a new method, robust binary fused compressive sensing (RoBFCS), to recover sparse piece-wise smooth signals from 1-bit compressive measurements. The proposed method is a modification of our previous binary fused compressive sensing (BFCS) algorithm, which is based on the binary iterative hard thresholding (BIHT) algorithm. As in BIHT, the data term of the objective function is a one-sided norm. Experiments show that the proposed algorithm is able to take advantage of the piece-wise smoothness of the original signal and detect sign flips and correct them, achieving more accurate recovery than BFCS and BIHT.