Exploiting Two-Dimensional Group Sparsity in 1-Bit Compressive Sensing
This work addresses signal recovery in compressive sensing for applications like imaging, but it is incremental as it modifies an existing algorithm.
The paper tackles the problem of recovering 2D sparse piece-wise signals from 1-bit measurements by proposing a new method called two-dimensional fused binary compressive sensing (2DFBCS), which achieves more accurate recovery than the previous 2DBIHT algorithm, with 2DFBCS using MTV and ℓ₂ penalty performing best in experiments.
We propose a new approach, {\it two-dimensional fused binary compressive sensing} (2DFBCS) to recover 2D sparse piece-wise signals from 1-bit measurements, exploiting 2D group sparsity for 1-bit compressive sensing recovery. The proposed method is a modified 2D version of the previous {\it binary iterative hard thresholding} (2DBIHT) algorithm, where the objective function includes a 2D one-sided $\ell_1$ (or $\ell_2$) penalty function encouraging agreement with the observed data, an indicator function of $K$-sparsity, and a total variation (TV) or modified TV (MTV) constraint. The subgradient of the 2D one-sided $\ell_1$ (or $\ell_2$) penalty and the projection onto the $K$-sparsity and TV or MTV constraint can be computed efficiently, allowing the appliaction of algorithms of the {\it forward-backward splitting} (a.k.a. {\it iterative shrinkage-thresholding}) family. Experiments on the recovery of 2D sparse piece-wise smooth signals show that the proposed approach is able to take advantage of the piece-wise smoothness of the original signal, achieving more accurate recovery than 2DBIHT. More specifically, 2DFBCS with the MTV and the $\ell_2$ penalty performs best amongst the algorithms tested.