自适应阈值的1-bit压缩感知算法
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摘要
针对二进制迭代硬阈值(BIHT)算法中固定的量化阈值在一定程度上限制了该算法重构性能的问题,提出了一种基于自适应阈值的二进制迭代硬阈值(AT-BIHT)算法,用于实现可压缩信号的1-bit压缩感知(CS)采集与重构。该算法采用基于自适应阈值的二进制量化器替代了BIHT算法中的符号函数,根据已获得的重构信号为当前测量值的1-bit量化选择合适的量化阈值;在继承BIHT算法优点的基础上,有效提高了重构性能。仿真实验表明,对于随机稀疏信号和实际心电信号,AT-BIHT算法的重建性能均高于BIHT算法。
In the binary iteration hard thresholding(BIHT) algorithm, the threshold of the binary quantization is fixed as zero, which limits its reconstruction performance in some degree. Facing this problem, an adaptive thresholding-based binary iteration hard thresholding(AT-BIHT) algorithm is designed to realize sampling and reconstruction of 1-bit compressed sensing(CS) for compressible signals. This algorithm uses the adaptive thresholding-based binary quantizer instead of the symbolic function in BIHT. It selects the quantization threshold for the 1-bit quantization of the current measurement value adaptively, based on reconstructed signal already obtained. It not only inherits the advantages of BIHT, but also improves the reconstruction performance efficiently. Simulation results on both random sparse signals and real electrocardiographs show that AT-BIHT can achieve higher reconstruction performance than BIHT.
In the binary iteration hard thresholding(BIHT) algorithm, the threshold of the binary quantization is fixed as zero, which limits its reconstruction performance in some degree. Facing this problem, an adaptive thresholding-based binary iteration hard thresholding(AT-BIHT) algorithm is designed to realize sampling and reconstruction of 1-bit compressed sensing(CS) for compressible signals. This algorithm uses the adaptive thresholding-based binary quantizer instead of the symbolic function in BIHT. It selects the quantization threshold for the 1-bit quantization of the current measurement value adaptively, based on reconstructed signal already obtained. It not only inherits the advantages of BIHT, but also improves the reconstruction performance efficiently. Simulation results on both random sparse signals and real electrocardiographs show that AT-BIHT can achieve higher reconstruction performance than BIHT.
引文
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[2]Jacques L.Error decay of(almost)consistent signal estimations from quantized Gaussian random projections[J].IEEE Transactions on Information Theory,2014,62(8):4696-4709
[3]Boufounos P T,Jacques L,Krahmer F,et al.Compressed Sensing and Its Applications[M].Berlin:Springer International Publishing,2015.193-237
[4]Wang H T,Ghosh S,Leon-Salas W D.Compressive sensing recovery from non-ideally quantized measurements[C].In:Proceedings of the IEEE International Symposium on Circuits and Systems,Beijing,China,2013.1368-1371
[5]Laska J N,Boufounos P T,Davenport M A,et al.Democracy in action:quantization,saturation,and compressive sensing[J].Applied and Computational Harmonic A-nalysis,2011,31(3):429-443
[6]Boufounos P T,Baraniuk R G.1-bit compressive sensing[C].In:Proceedings of the Conference on Information Sciences and Systems,Princeton,USA,2008.16-21
[7]Cai X,Zhang Z,Zhang H,et al.Soft consistency reconstruction:a robust 1-bit compressive sensing algorithm[C].In:Proceedings of the IEEE International Conference on Communications,Sydney,Australia,2014.4530-4535
[8]Li F,Fang J,Li H,et al.Robust one-bit Bayesian compressed sensing with sign-flip errors[J].IEEE Signal Processing Letters,2014,22(7):857-861
[9]Laska J N,Baraniuk R G.Regime change:bit-depth versus measurement-rate in compressive sensing[J].IEEETransactions on Signal Processing,2012,60(7):3496-3505
[10]Huang X,Xia Y,Shi L,et al.Mixed one-bit compressive sensing with applications to overexposure correction for CT reconstruction[EB/OL].ar Xiv:1701.00694v1,2017
[11]Jacques L,Laska J N,Boufounos P T,et al.Robust 1-bit compressive sensing via binary stable embeddings of sparse vectors[J].IEEE Transactions on Information Theory,2013,59(4):2082-2102
[12]Yan M,Yang Y,Osher S.Robust 1-bit compressive sensing using adaptive outlier pursuit[J].IEEE Transactions on Signal Processing,2012,60(7):3868-3875
[13]Huang X,Shi L,Yan M,et al.Pinball loss minimization for one-bit compressive sensing[J].Mathematics,2015,1-11
[14]Kamilov U S,Bourquard A,Amini A,et al.One-bit measurements with adaptive thresholds[J].IEEE Signal Processing Letters,2012,19(10):607-610
[15]Fang J,Shen Y,Yang L,et al.Adaptive one-bit quantization for compressed sensing[J].Signal Processing,2016,125(C):145-155
[16]Moody B,Mark G.The impact of the MIT-BIH Arrhythmia database[J].IEEE Engineering in Medicine and Biology Magazine,2001,20(3):45-50