一种基于盲运算的1比特压缩感知重建算法

为了解决1比特压缩感知中符号匹配追踪算法(matching sign pursuit)在稀疏度未知的情况下不能自适应重构信号的问题,提出了向前/向后迭代符号匹配追踪算法(forward-backward matching sign pursuit, FBMSP).该算法以逐步逼近理论为核心,通过逐步扩大支撑集来扩大搜索范围,把相邻两次迭代的差值作为终止条件,在MSP算法模型下进行盲运算,以实现信号的重构.数值试验表明:在控制迭代系数=8,=1的情况下,FBMSP算法比传统的符号匹配追踪算法重构精度提高了3 dB,运算时间减少了40%. 

1 Bit Compressed Sensing Reconstruction Algorithm Based on Blind Operation

To solve the problem that the matching sign pursuit (MSP) algorithm can not adaptively reconstruct signals when the sparsity is unknown, we proposed a forward-backward matching sign pursuit (FBMSP) algorithm. Based on successive approximation theory, by gradually expanding the support set to expand search scope, FBMSP algorithm takes a difference between adjacent iterations as a termination criterion and conducts blind operations to reconstruct the signals under the model of the MSP algorithm. The numerical experiments show that compared with the traditional MSP algorithm, the precision of FBMSP is increased by 3 dB, and the calculation time is reduced by 40% when the control iterative coefficient =8 and =1.