In this paper, we propose a novel algorithm for fast single image super-resolution based on self-example learning and sparse representation. We propose an efficient implementation based on the K-singular value decomposition (SVD) algorithm, where we replace the exact SVD computation with a much faster approximation, and we employ the straightforward orthogonal matching pursuit algorithm, which is more suitable for our proposed self-example-learning-based sparse reconstruction with far fewer

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... als. The patches used for dictionary learning are efficiently sampled from the low-resolution input image itself using our proposed sample mean square error strategy, without an external training set containing a large collection of highresolution images. Moreover, the ℓ 0 -optimization-based criterion, which is much faster than ℓ 1 -optimization-based relaxation, is applied to both the dictionary learning and reconstruction phases. Compared with other super-resolution reconstruction methods, our low dimensional dictionary is a more compact representation of patch pairs and it is capable of learning global and local information jointly, thereby reducing the computational cost substantially. Our algorithm can generate high-resolution images that have similar quality to other methods but with a greater than hundredfold increase in the computational efficiency. Index Terms-Approximate K-singular value decomposition, sample mean square error, self-example, single image superresolution, sparse representation.