中文摘要：

研究局部场电位信号（LocalFieldPotential，LFP）的重构问题。依据传统的采样定理对LFP信号进行采样，将会产生庞大的数据量，为LFP信号的传输、存储及处理带来巨大压力。为降低LFP信号的采样速率，减少有效的采样样本，提出压缩感知的局部场电位信号重构的新方法。利用LFP信号在变换域上的稀疏性，通过随机高斯测量矩阵将LFP信号重构模型转化为压缩感知理论中的稀疏向量重构模型。仿真结果表明，采样速率为奈奎斯特采样速率的一半即可准确重构LFP信号，且正交匹配追踪（OMP）重建算法要优于基追踪（BP）重建算法；当选用离散余弦矩阵（DCT）作为稀疏表示矩阵时，信号在正交匹配追踪和基追踪两种重构算法下都有很高的重构精度。

英文摘要：

The traditional sampling principle will cause massive data which bring about great pressure during the transmission, storage and processing of LFP signal. In order to lower the requirement of LFP signal for sampling rate and reduce the useful samples, a new method based on compressed sensing to reconstruct LFP signal was proposed. Due to the sparsity of LFP signal in transform domain, LFP signal reconstruction model can be converted into sparse vector reconstruction model through Gaussian random matrix. The simulation result turned out to be that the sampling rate is the half of Nyquist rate and the signal can be reconstructed exactly. Also the OMP has a better performance than BP and both reconstruction algorithms perform good recovery accuracy when choosing DCT matrix as the sparse representation base.