压缩感知光谱测量局部哈达玛矩阵的构造与性能

The construction of partial Hadamard matrix of compressed sensing spectral measurement and its performance

针对压缩感知光谱测量中随机矩阵作为测量矩阵无法获得高质量重建精度问题,提出了一种测量矩阵构造的新方法。介绍了局部哈达玛矩阵的构造方法,以随机测量矩阵为比较对象,通过仿真实验对局部哈达玛矩阵在压缩感知光谱测量中的性能进行分析。实验结果表明,相对于随机矩阵,新型局部哈达玛矩阵下的重建光谱与原始光谱重合度大大提高,在100%采样率时,定量指标MSE为3.2,实现了光谱的精确重建,25%采样率的MSE指标水平已经与随机矩阵100%采样率时相当,局部哈达玛矩阵可以有效的改善光谱重建的精度;光谱重建时间大约缩短到1/3,系统具有更好的信噪比特性。

A new construction method of matrix for spectral measurement based on compressed sensing is proposed. The construction method of partial Hadamard matrix is introduced, and its performance is analyzed using simulation experiments. The result of experiments shows that the new partial Hadamard matrix can improve the reconstruction accuracy of compressed sensing spectral measurement effectively and decrease the reconstruction time to 1/3 compared to random matrix. Moreover, the partial Hadamard matrix makes system have better SNR.