In the field of visible image SR, a sparse representation based algorithm6 has shown good performance. However, for the aforementioned reasons, it is not suitable to be directly used for hyperspectral images. On the other hand, a pixel curve based sparse method has been proven effective for describing hyperspectral images and has shown good performances in spectral unmixing and classification applications, but few for SR. In this paper, the sparse representation based SR method6 is specially investigated for hyperspectral images and a redundant dictionary based hyperspectral image SR restoration algorithm is proposed. According to the specific characteristics of the hyperspectral images, the pixel curve (formed by the pixels located on the same coordinate point through the bands) instead of the pixel patch is considered as an atom of the dictionary. During the process of dictionary training, a pair of high resolution (HR) and low resolution (LR) corresponding training sets are created by pixel curves from HR hyperspectral images and their simulated degraded images. Then the dictionary pair is jointly trained from the set of pixel curves with the constraint that when a pixel curve from the HR hyperspectral image and its degraded image is decomposed according to the HR and LR dictionary pair, respectively, we can get the same sparse coefficients. In the process of SR restoration, each pixel curve from the LR hyperspectral image will first be decomposed according to the LR dictionary of the dictionary pair to obtain a set of sparse coefficients, then the corresponding HR curve is reconstructed by the LR coefficients and the HR dictionary. When all the curves are SR reconstructed, all the bands of the estimated HR image are optimized by a maximum a prior (MAP) based algorithm to further improve the quality. In this algorithm, the hyperspectral images are sparsely decomposed as a whole for each pixel on the spectral dimension. In this way, the pixel curves are regarded as a unit during the entire process; spectral features that are often described by the curves are effectively preserved. The pixel curve based sparse representation is more suitable for hyperspectral images in order to make better use of its high spectral correlations. At the same time, as the number of bands (corresponding to number of values in a pixel curve) is often larger than the number of pixels in the traditional image patches, the total computation is also saved. The experimental results are compared with the following related algorithms including bilinear interpolation, MAP based SR, and the traditional pixel patch based sparse SR method. The proposed algorithm is superior in both objective and subjective results.