Dictionary Learning for Sparse Representations: A Pareto Curve Root Finding Approach

A new dictionary learning method for exact sparse representation is presented in this paper. As the dictionary learning methods often iteratively update the sparse coefficients and dictionary, when the approximation error is small or zero, algorithm convergence will be slow or non-existent. The proposed framework can be used in such a setting by gradually increasing the fidelity of the approximation. This technique has previously been used for the convex sparse representations. It has been extended here to the non-convex dictionary learning problem by allowing the dictionary be modified.