Slice-based Approximate Online Convolutional Dictionary Learning via Convergent Accelerated Inertial Algorithm

Convolutional dictionary learning (CDL) is a widely used technique in computer vision for accurately capturing local features and texture information in signals. However, most existing CDL methods are based on batch processing, which requires computing the entire dataset at once, resulting in a significant memory requirement that limits further development. To address this issue, researchers have turned to online convolutional dictionary learning (OCDL) in recent years. OCDL inputs data as a stream and stores all historical information in a pair of fixed-size history arrays. This approach avoids the problem of increasing memory requirements with the number of samples. However, current OCDL methods encounter two primary issues when handling big datasets or large dictionaries: the high time complexity of updating history arrays or dictionaries and the challenge of selecting hyperparameters linked to the ADMM algorithm. This paper proposes a slice-based approximate OCDL method called SAOCDL to address the aforementioned problems. The algorithm utilizes a sparse approximation model, where historical data samples are approximated as the convolution sum of the best local dictionary of a single sample and the corresponding local sparse codes. The current sample and a pair of fixed-size history arrays that store this approximation are used to update the best local dictionary. The resulting optimization problem is solved in the spatial domain using the proposed convergent inertial proximal-gradient algorithm, which combines dry friction with Hessian-driven damping. Extensive experiments were conducted on various benchmark datasets, and the results demonstrate that the proposed SAOCDL approach is highly competitive in terms of performance, efficiency, and memory with state-of-the-art OCDL and CDL algorithms.