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In recent years, research on dictionary design for sparse representation (SR) has changed from pre-defined to training. A Hierarchical K-means Clustering (HKC) dictionary training algorithm is proposed in this paper. The algorithm presents a framework for SR for a class of images. HKC used K-means clustering to generate atoms which is one to one corresponding to hyperplanes for approximating hyperspherical cap. Compared with conventional algorithms, this algorithm is more flexible and efficiency. Finally, experimental results show that this algorithm can be used for compressive sensing and denoising.