Although hyperspectral images (HSIs) captured by satellites provide much information in spectral regions, some bands are redundant or have large amounts of noise, which are not suitable for image analysis. To address this problem, we introduce a method for reconstructing the HSI with noise reduction and contrast enhancement using a matting model for the first time. The matting model refers to each spectral band of an HSI that can be decomposed into three components, i.e., alpha channel, spectral foreground, and spectral background. First, one spectral band of an HSI with more refined information than most other bands is selected, and is referred to as an alpha channel of the HSI to estimate the hyperspectral foreground and hyperspectral background. Finally, a combination operation is applied to reconstruct the HSI. In addition, the support vector machine (SVM) classifier and three sparsity-based classifiers, i.e., orthogonal matching pursuit (OMP), simultaneous OMP, and OMP based on first-order neighborhood system weighted classifiers, are utilized on the reconstructed HSI and the original HSI to verify the effectiveness of the proposed method. Specifically, using the reconstructed HSI, the average accuracy of the SVM classifier can be improved by as much as 19%.