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In recent years, considerable efforts have been made in the research of sparse representation for signals over overcomplete dictionaries. The dictionaries can be either pre-specified transforms or designed by learning from a set of training signals. In the paper, the dictionary learning problem was extended into a quadratic programming framework. A projected gradient with line search method was presented for solving this large-scale box-constrained quadratic program. The non-negative dictionary learned using this method was applied to image de-noising. Experimental results demonstrated that this learning-based method had better performance than the wavelet-based, the variation-based and the K-SVD methods. [ABSTRACT FROM AUTHOR]