2023 Volume 17 Issue 2 Pages 116-125
In this article, convolutional dictionary learning (CDL) and its evolution as an effective and systematic data-driven sparse modeling for high-dimensional signals, especially image data, are outlined. With the development of measurement technology, it has become possible to acquire a large amount of diverse data. At the same time, demands for high-performance signal estimation and prediction are increasing. In order to meet such demands, a generative model is necessary for the effective representation of the data of interest. This article describes A CDL method that applies filter-bank theory is described as an example of a signal generation model that can easily reflect domain knowledge. The theory allows us to construct convolutional networks that preserve unitarity and filter kernel symmetry by combining several primitive local operations such as Givens rotation, shift, and butterfly operations. The significance of the convolutional dictionary is demonstrated through an example of CDL and an example of image approximation using learned dictionaries.
