基于频谱估计的频域稀疏压缩采样信号重构

压缩采样理论突破了采样定理对稀疏信号采样频率的限制，在保证信号重构精度的条件下能够显著降低采样频率，能够在采样过程中对数据进行压缩。在频域稀疏信号的压缩采样中，由于所处理数据长度的有限性，存在频谱泄漏现象，即稀疏表示基失配，从而导致信号重构性能降低。为克服这种表示基失配引起的重构误差，提出一种基于频谱估计的频域稀疏压缩采样信号重构算法。该算法采用root-MUSIC算法对被测信号的表示基进行自适应地构造:用root-MUSIC算法对频率进行估计，用自适应的基向量构造稀疏表示基矩阵。通过实验对该重构算法的可行性进行验证。与传统信号重构算法相比，该重构算法具有更高的信号重构精度。

Spectrum Estimation Based Signal Reconstruction for Frequency Sparse Signal Compressive Sampling

Compressed sampling (CS) theory breaks through the limitation of Shannon sampling theorem for sparse signal sampling. CS can significantly reduce the sampling rate while the reconstruction accuracy can be still guaranteed. CS compresses the samples during the process of sampling. For frequency sparse signal, due to the finite length of samples, the spectrum leakage exists and the leakage leads to the mismatch of the sparse representation basis. The basis mismatch would degrade the performance of signal reconstruction. In order to avoid the reconstruction distortion introduced by the basis mismatch, a signal reconstruction algorithm based on the root multiple signal classification (root-MUSIC) frequency estimation technique is introduced, and the sparse representation matrix is constructed based on the estimated frequency adaptively. Finally, the experimental results verify the feasibility of the proposed algorithm. Compared to the traditional signal reconstruction algorithm, the signal reconstructed by the proposed algorithm exhibits high precision.