Hyperspectral remote sensing provides the possibility of direct detection of material information; however, coarse spatial resolution can restrict the scope of its application. The super-resolution (SR) technique can overcome this problem, but the separate application of SR reconstruction to each spectral band is computationally intensive. We proposed an approach that combines empirical mode decomposition (EMD), single-image SR reconstruction using compressed sensing (CS), and principal component analysis (PCA). EMD was used to extract details from within the images, whereas PCA was implemented to reduce the spectral dimensions of the hyperspectral image cube and to retain meaningful spectral information. The CS-based single-image SR reconstruction involved the use of both the K-SVD algorithm for learning and obtaining an over-complete dictionary, and the orthogonal matching pursuit algorithm for the image reconstruction. Experimental results obtained using an EO-1 hyperion image were used to validate the proposed approach.