We propose a new method, {\it 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 {\it 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 $\ell_1$ (or $\ell_2$) norm.
Experiments on the recovery of sparse piece-wise 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.