Binary Fused Compressive Sensing: 1-Bit Compressive Sensing meets Group Sparsity

We propose a new method, binary fused compressive sensing (BFCS), to recover sparse piece-wise smooth signals from 1-bit compressive measurements. The proposed algorithm is a modification of the previous binary iterative hard thresholding (BIHT) algorithm, where, in addition to the sparsity constraint, the total-variation of the recovered signal is upper constrained. As in BIHT, the data term of the objective function is an one-sided l1 (or l2) norm. Experiments on the recovery of sparse piecewise smooth signals show that the proposed algorithm is able to take advantage of the piece-wise smoothness of the original signal, achieving more accurate recovery than BIHT.