An augmented Lagrangian approach to general dictionary learning for image denoising

This paper presents an augmented Lagrangian (AL) based method for designing of overcomplete dictionaries for sparse representation with general lq-data fidelity term (q ⩽ 2). In the proposed method, the dictionary is updated via a simple gradient descent method after each inner minimization step of the AL scheme. Besides, a modified Iterated Shrinkage/Thresholding Algorithm is employed to accelerate the sparse coding stage of the algorithm. We reveal that the dictionary update strategy of the proposed method is different from most of existing methods because the learned dictionaries become more and more complex regularly. An advantage of the iterated refinement methodology is that it makes the method less dependent on the initial dictionary. Experimental results on real image for Gaussian noise removal (q = 2) and impulse noise removal (q = 1) consistently demonstrate that the proposed approach can efficiently remove the noise while maintaining high image quality.

► An efficient augmented Lagrangian method is proposed for general dictionary learning. ► General dictionary learning problem contains general Lq-data fidelity term. ► 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 Gaussian and impulse noise removal demonstrate our method’s strengths.