Analysis dictionary learning based on Nesterov´s gradient with application to SAR image despeckling

We focus on the dictionary learning problem for the analysis model. A simple but effective algorithm based on Nesterov´s gradient is proposed. This algorithm assumes that the analysis dictionary contains unit ℓ₂ norm atoms and trains the dictionary iteratively with Nesterov´s gradient. We show that our proposed algorithm is able to learn the dictionary effectively with experiments on synthetic data. We also present examples demonstrating the promising performance of our algorithm in despeckling synthetic aperture radar (SAR) images.