基于空间外差光谱特性, 针对传统傅里叶变换算法在光谱复原中的局限性, 引入现代谱估计的多重信号分类MUSIC算法进行空间外差信号光谱复原, 采用自回归传递函数准则(CAT)对影响谱估计效果的信号空间维数值进行估计.测试结果显示CAT准则直接定维值与最佳结果存在偏差, 将CAT准则直接定维值减数值3作为改进后的新准则重新应用于实测数据光谱复原.改进的CAT准则与MUSIC算法配合能够很好地适用于空间外差干涉数据, 光谱复原效果优于直接傅里叶变换结果.以光谱角度匹配和均方误差作为改进CAT准则的MUSIC算法谱估计效果评价指标, 与理想光谱相比, MUSIC算法对钾盐双谱峰信号处理后复原光谱相似度达到0.764, 均方误差为0.040, 对氖灯多谱峰信号和处理结果分别为0.806和0.046.复色光结果分别为0.988和0.089.采用改进的CAT准则进行自适应定维的MUSIC算法对空间外差光谱复原具有一定优势, 提高了功率谱复原效果.

To overcome the limitations of traditional Fourier transform algorithm in spectral restoration, a modern spectral estimation method, multiple signal classification (MUSIC) algorithm, is introduced to recover spatial heterodyne signals based on the characteristics of spatial heterodyne spectroscopy. Criterion Autoregressive Transfer function (CAT) criterion is used to estimate the spatial dimension. The results show that there is a deviation between direct fixed dimension value by CAT criterion and the optimal one, while the direct fixed dimension value minus 3 can be regarded as a new improved criterion for spectral restoration. When applied to the spatial heterodyne interference data, the spectral restoration results of this improved CAT criterion as well as its related MUSIC algorithm is better than those of direct Fourier transform. Spectral Angel Mapper (SAM) and Mean-Squared Error (MSE) are used as the performance evaluation indexes. Compared with the ideal spectrum, SAM of MUSIC algorithm restoration spectra is 0.764 and MSE is 0.040 for potassium bimodal peak signal processing. For the multi-spectrum peak signal processing of Ne lamp, SAM is 0.806 and MSE is 0.046. The results of polychromatic light are 0.988 and 0.089, respectively. Indicating that this adaptively dimensioned MUSIC algorithm with improved CAT criterion has advantages to the spatial heterodyne spectral restoration and improves the power spectrum restoration effect.