基于希尔伯特半张量压缩感知的亚采样率采集技术

Sub-Sampling Rate Acquisition Based on Hilbert Semi-Tensor Compressed Sensing

为了解决在无线分布式瞬态压力测试中高采样率带来的数据冗余和无线资源受限间的矛盾,压缩感知方法被提出在编码端实现冗余数据的压缩采样。但每个节点均需存储高维压缩感知观测矩阵,给无线节点的有限资源带来了新的挑战。基于半张量积的压缩感知技术在编码端利用半张量理论突破矩阵乘法维度的限制,显著降低观测矩阵的维度,但会在一定程度上损失信号的有效信息,且降低倍数优先。本文提出基于希尔伯特半张量压缩感知,利用希尔伯特与傅里叶变换的正交空间对冲击波信号进行能量逼近,增强稀疏表达与观测矩阵的不相干性,以此减少半张量积运算带来的观测损失,同时在重构算法中提出一种无先验信息的最优原子选择策略,利用能量正则化对变换后的数据的“能量”进行惩罚,提高原子支撑集选择的准确性。最后,提出变步长更新策略,使得重构算法在更新支撑集的过程中动态调整步长,降低原子选择时间,提高运行效率。通过对多量程实测炮口冲击波信号的仿真结果分析,本文提出的方法相较于奈奎斯特采样可以实现降低采样率,减少数据总量,保障通信的实时性,且相较于传统压缩感知技术,在观测矩阵维度减少到原来的二分之一时仍可以保证解码端的高精度重构,重构误差低于1e-6,且重构时间缩短约87%。此外,本文提出的方法可应用于分布式无线传输系统的高维信号采集,可以解决冗余数据和有限网络资源之间的矛盾。

To address the contradiction between data redundancy and limited wireless resources caused by high sampling rates in wireless distributed transient pressure testing,a compressive sensing method is proposed to realize compressed sampling of redundant data at the encoding end.However,storing high-dimensional compressed sensing observation matrices at each node poses new challenges for the limited resources of wireless nodes.Compressive sensing technology based on the semi-tensor product utilizes semi-tensor theory at the encoding end to overcome the limitation of matrix multiplication dimensions,drastically reducing the dimension of observation matrices.However,some essential signal information may be lost,and the multiple priority may be reduced.This study proposes a compressive sensing method based on the Hilbert semi-tensor,utilizing the orthogonal space of Hilbert and Fourier transform to approximate the energy of shock wave signals,enhancing the incoherence between sparse representation and observation matrices,thus reducing observation loss due to semi-tensor product operations.Furthermore,an optimal atom selection strategy without prior information is proposed in the reconstruction algorithm,penalizing the“energy”of transformed data using energy regularization to improve the accuracy of atom support set selection.Finally,a variable step update strategy is proposed to dynamically adjust the step size when updating the support set in the reconstruction algorithm,reducing the time for atom selection and improving operational efficiency.The analysis of the simulation results of multi-range measured muzzle shock wave signals revealed that the proposed method can achieve a lower sampling rate compared to Nyquist sampling,reducing the total amount of data and ensuring real-time communication.Furthermore,compared to traditional compressive sensing technology,high-precision reconstruction at the decoding end can still be guaranteed,even when the dimension of the observation matrix is reduced by half,with reconstruction errors below 1e-6 and a reduced reconstruction time of approximately 87%.Additionally,the proposed method can be applied to high-dimensional signal acquisition in distributed wireless transmission systems,effectively addressing the contradiction between redundant data and limited network resources.