Stacked Bayesian Matching Pursuit for One-Bit Compressed Sensing

We consider a compressed sensing problem to recover a sparse signal vector from a small number of one-bit quantized and noisy measurements. In this system, a probabilistic greedy algorithm, called bayesian matching pursuit (BMP), has been recently proposed in which a new support index is identified for each iteration, via a local optimal strategy based on a Gaussian-approximated maximum a posteriori estimation. Although BMP can outperform the other existing methods as Quantized Compressive Sampling Matched Pursuit (QCoSaMP) and Quantized Iterative Shrinkage-Thresholding Algorithm (QISTA), its accuracy is still far from the optimal, yielding a locally optimal solution. Motivated by this, we propose an advanced greedy algorithm by leveraging the idea of a stack algorithm, which is referred to as stacked BMP (StBMP). The key idea of the proposed algorithm is to store a number of candidate partial paths (i.e., the candidate support sets) in an ordered stack and tries to find the global optimal solution by searching along the best path in the stack. The proposed method can efficiently remove unnecessary paths having lower path metrics, which can provide a lower complexity. Simulation results demonstrate that the proposed StBMP can significantly improve the BMP by keeping a low computational complexity.