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Convolutional sparse dictionary learning with smoothed l0 norm and projected gradient descent

Convolutional sparse representation extracts features of given signals. Conventional methods employ Alternating Direction Method of Multipliers (ADMM) to design dictionaries. However, their convergence is slow and computational cost is burden. This paper proposes a faster design method of the dictionaries by using Projected Gradient Descent (PGD) instead of ADMM, where the l0 norm of coefficient vectors is approximated by a smoothed l0 norm function similar to conventional methods. Experimental results demonstrate that the proposed method is faster and less iterations than a conventional method.