Block-Sparse Signal Recovery From Binary Measurements

We address the issue of block-sparse signal recovery from binary measurements of random projections. While a variety of recovery algorithms for sparse signals have been proposed in the context of 1-bit compressed sensing, there remains a gap in the recovery of more structured signals. We propose a convex programming approach tailored to the class of block-sparse signals, as well as an iterative method based on the binary iterative hard thresholding algorithm. We motivate the respective recovery schemes, and demonstrate their effectiveness and superior performance to previously established methods in a series of numerical experiments.