基于变换域的压缩感知快速重构算法

压缩感知是信号处理领域热门研究课题，其应用前提为原信号是稀疏或可压缩的。时域非稀疏信号可以变换为频域稀疏信号，但变换后的信号和传感矩阵表示形式为复数，增加了重构复杂度。为了降低复杂度，提高信号重构效率，提出一种基于实变换的重构算法，该算法将复数形式的稀疏信号和传感矩阵的实部和虚部分离后再参与重构。与传统重构算法相比，该算法改善了重构信号的均方误差，明显缩短了重构时间，极大提高了信号重构效率。

Fast Reconstruction Algorithm Based on Transformation Domain for Compressed Sensing

Compressed Sensing is a hot research theory in the field of signal processing in recent years.Its application precondition is that the original signal is sparse or compressible.Time domain non-sparse signals can be transformed into frequency domain sparse signals，but the transformed signal and sensor matrix are expressed in the complex number increasing the complexity of reconstruction.In order to reduce complexity and improve the efficiency of signal reconstruction， a reconstruction algorithm based on real transformation is proposed.The algorithm separates the real and imaginary parts of complex sparse signal and sensor matrix，then participating in the reconstruction operation.Experiments show that compared with the traditional reconstruction algorithms， the proposed algorithm improves the mean square error of reconstructed signal，shortens the reconstruction time and greatly improves the efficiency of signal reconstruction.