自适应稀疏度的1 bit压缩重构算法

One-bit Compressive Reconstruction Algorithm with Adaptive Sparsity

1 bit压缩感知技术日益受到关注。1 bit信号往往有符号跳变,同时信号重构还需要稀疏度先验信息,如何有效地克服信号重构对稀疏度的依赖性,提高重构算法对噪声的鲁棒性,这是该领域面临的重大挑战。本文在二进制迭代硬阈值算法基础上,引入自适应稀疏度,利用残差能量的大小,通过对信号和噪声的学习,解决稀疏度依赖问题,通过引入弹球损失和自适应异常值追踪提高对噪声的鲁棒性,通过引入归一化参数,缩短运算时间。数值仿真实验表明,本文算法重构复杂度降低10%左右,在信号无噪声条件下重构信噪比提高2.1 dB,在有噪声条件下绝对均方误差(AMSE)降低约0.3。算法运行效率比基于自适应异常值追踪的二进制硬阈值算法提升了25%。与当前先进算法相比,能有效地克服信号重构对稀疏度的依赖性,对符号跳变引起的噪声具有很好的鲁棒性。

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-tonoise 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.