One-bit Compressive Reconstruction Algorithm with Adaptive Sparsity

The 1-bit compressed sensing technique has received increasing attention. 1-bit signals often have sign flips， and signal reconstruction also requires sparsity a priori information， so how to effectively overcome the dependence of signal reconstruction on sparsity and improve the robustness of reconstruction algorithms to noise is a major challenge in this field. Based on the binary iterative hard thresholding algorithm， adaptive sparsity is introduced to solve the sparsity dependence problem by learning the signal and noise using the magnitude of the residual energy， improving the robustness to noise by pinball loss function and adaptive outlier pursuit，and shortening the operation time by introducing normalization parameters. Numerical simulation experiments show that the reconstruction complexity of the method in this paper is reduced by about 10%， and the reconstruction signal-to-noise ratio of the algorithm in this paper is improved by 2.1 dB under the condition of noiseless signal， and the absolute mean square error （AMSE） is reduced by about 0.3 under the condition of noisy signal. The efficiency of the algorithm is 25% higher than that of the binary hard threshold algorithm based on adaptive outlier pursuit. Compared with current advanced algorithms， it can effectively overcome the dependence of signal reconstruction on sparsity and has good robustness to the noise caused by sign flips.