Sparse representation is widely used in signal processing. The best representation is based on the adaptive dictionary that trained from the processing data. This paper proposes a new complex valued dictionary learning method which turns the dictionary learning into an optimization problem and performs the optimization on the dictionary atoms and coding alternately. An online training method with memory is used in the optimization on the dictionary atoms, and an insurance of alternated direction method of multipliers is solved in the optimization on the coding. The proposed algorithm is proved to be of high efficiency, minimizing the training time while converging to the optimized value. The presented method is also robust to the noise in the training set.