Robust Reconstruction of Block Sparse Signals from Adaptively One‐Bit Measurements

Though various theoretical results and algorithms have been proposed in one‐bit Compressed sensing (1‐bit CS), there are few studies on more structured signals, such as block sparse signals. We address the problem of recovering block sparse signals from one‐bit measurements. We first propose two recovery schemes, one based on second‐order cone programming and the other based on hard thresholding, for common non‐adaptively thresholded one‐bit measurements. Note that the worst‐case error in recovering sparse signals from non‐adaptively thresholded one‐bit measurements is bounded below by a polynomial of oversampling factor. To break the limit, we introduce a recursive strategy that allows the thresholds in quantization to be adaptive to previous measurements at each iteration. Using the scheme, we propose two iterative algorithms and show that corresponding recovery errors are both exponential functions of the oversampling factor. Several simulations are conducted to reveal the superiority of our methods to existing approaches.