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This paper proposes a sparse representation of an image using discrete δ-u functions. A δ-u function is defined as the product of a Kronecker delta function and a step function. Based on the sparse representation, we have developed a novel and effective method for reconstructing an image from limited-angle projections. The method first estimates the parameters of the sparse representation from the incomplete projection data, and then directly calculates the image to be reconstructed. Experiments have shown that the proposed method can effectively recover the missing data and reconstruct images more accurately than the total-variation (TV) regularized reconstruction method.