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.