The spectral imaging provides important support for ballistic missile early warning by virtue of its abundant spatial and spectral information， and the compressive sensing provides a effective approach for spectral image data collecting and processing. Aiming at the existing compressed perceptual reconstruction mostly adopts the coding method of "spatial domain compressed sampling and inter-spectral traditional compression"， which still exists a certain waste of resources， a compressed perceptual reconstruction method based on tensor decomposition for spectral images is proposed. Taking use of the sparsity of spectral image data in three-dimensional space， a reconstruction model based on Tucker decomposition is built， and the solution algorithm based on orthogonal matching pursuit（OMP） is given. Moreover， an improved OMP algorithm which takes three-dimension tensors as dictionary atoms is proposed by expanding traditional OMP algorithm into three-dimensional space. The experimental results indicate that the proposed method can effectively reduce algorithm complexity and improve the performance of reconstruction.