Learning Deep Analysis Dictionaries -- Part II: Convolutional Dictionaries
This work addresses efficient processing of high-dimensional signals for applications like image super-resolution, but it is incremental as it builds on a companion paper by extending to convolutional dictionaries.
The paper tackles the problem of learning convolutional dictionaries for high-dimensional signals like images, introducing Deep Convolutional Analysis Dictionary Model (DeepCAM) and demonstrating that it achieves performance comparable to other methods in single image super-resolution.
In this paper, we introduce a Deep Convolutional Analysis Dictionary Model (DeepCAM) by learning convolutional dictionaries instead of unstructured dictionaries as in the case of deep analysis dictionary model introduced in the companion paper. Convolutional dictionaries are more suitable for processing high-dimensional signals like for example images and have only a small number of free parameters. By exploiting the properties of a convolutional dictionary, we present an efficient convolutional analysis dictionary learning approach. A L-layer DeepCAM consists of L layers of convolutional analysis dictionary and element-wise soft-thresholding pairs and a single layer of convolutional synthesis dictionary. Similar to DeepAM, each convolutional analysis dictionary is composed of a convolutional Information Preserving Analysis Dictionary (IPAD) and a convolutional Clustering Analysis Dictionary (CAD). The IPAD and the CAD are learned using variations of the proposed learning algorithm. We demonstrate that DeepCAM is an effective multilayer convolutional model and, on single image super-resolution, achieves performance comparable with other methods while also showing good generalization capabilities.