A novel predual dictionary learning algorithm

Dictionary learning has been a hot topic fascinating many researchers in recent years. Most of existing methods have a common character that the sequences of learned dictionaries are simpler and simpler regularly by minimizing some cost function. This paper presents a novel predual dictionary learning (PDL) algorithm that updates dictionary via a simple gradient descent method after each inner minimization step of Predual Proximal Point Algorithm (PPPA), which was recently presented by Malgouyres and Zeng (2009) [F. Malgouyres, T. Zeng, A predual proximal point algorithm solving a non negative basis pursuit denoising model, Int. J. Comput. Vision 83 (3) (2009) 294–311]. We prove that the dictionary update strategy of the proposed method is different from the current ones because the learned dictionaries become more and more complex regularly. The experimental results on both synthetic data and real images consistently demonstrate that the proposed approach can efficiently remove the noise while maintaining high image quality and presents advantages over the classical dictionary learning algorithms MOD and K-SVD.

► Our dictionary learning method is motivated by predual proximal point algorithm.
► Predual strategy is applied and dictionary is updated via primal and dual variables.
► Dictionary update procedure is proved to be an iterated refinement process.
► The pathway that our method followed makes it less to be stuck in local minima.
► Results on synthetic data and real images demonstrate strengths of our method.