Light field cameras simultaneously capture light intensity and direction information of a scene from a single shot which has potentially very broad applications in the reconstruction of three-dimensional scenes and their focus from previously captured images. However, compared with ordinary cameras, the images captured by light field cameras are not sufficiently sharp, i.e., the spatial resolution of the image is low. In this study, we propose a super-resolution reconstruction algorithm of light field images based on sparse representation. The algorithm used the redundant information from multiview light field images of a scene to reconstruct a high-resolution image. First, the middle image of the multiview light field images was selected as the low-resolution image to be reconstructed. The images from the other views and their down-sampled versions were used as samples for training, wherein the sparse K-singular value decomposition (SVD) method was used to obtain a pair of dictionaries for both high- and low-resolution representations. Finally, an improved Gaussian Laplace method was used to extract features of the low-resolution light field image in the image reconstruction process. Experimental results show that the improved method is capable of recovering more image detail and greatly reduces the time required for dictionary training.