Efficient Online Convolutional Dictionary Learning Using Approximate Sparse Components

Most available convolutional dictionary learning (CDL) methods use a batch-learning strategy, which consists of alternating optimization of the dictionary and the sparse representations using a training dataset. The computational efficiency of CDL can be improved using an online-learning approach, where the dictionary is optimized incrementally following a sparse approximation of each training sample. However, the existing online CDL (OCDL) methods are still computationally costly when learning large dictionaries. In this paper, we propose an OCDL approach that incorporates decomposed sparse approximations instead of the training samples and substantially improves the computational costs of the existing CDL methods. The resulting optimization problem is addressed using the alternating direction method of multipliers (ADMM).