Binary Fused Compressive Sensing: 1-Bit Compressive Sensing meets Group Sparsity
This work addresses signal recovery in compressive sensing for applications like imaging or communications, but it is incremental as it builds directly on an existing method.
The paper tackles the problem of recovering sparse piece-wise smooth signals from 1-bit compressive measurements by proposing binary fused compressive sensing (BFCS), which modifies binary iterative hard thresholding (BIHT) to include a total-variation constraint, resulting in more accurate recovery than BIHT.
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.