1-bit compressive sensing with an improved algorithm based on fixed-point continuation

In this paper, 1-bit compressive sensing with improved reconstruction algorithms based on the fixed-point continuation (FPC) method is investigated. By introducing appropriate modifications to the conventional FPC-ℓ2 algorithm, the improved algorithms enjoy several advantages simultaneously. First, the prior knowledge of sparsity level is not required. Second, with a one-sided ℓ1-norm to impose consistency, the performance of the proposed FPC-ℓ1 algorithm offers better performance than the previous FPC-ℓ2 algorithm. Third, by incorporating an adaptive outlier pursuit (AOP) to the FPC-ℓ1 algorithm, the resulting FPC-AOP-ℓ1 algorithm achieves improved robustness against noise. Numerical results are provided to demonstrate the effectiveness and superiority of the proposed algorithm.