Abstract
This article reviews redundant transforms for sparse representation of images. The term “sparse representation” here denotes a way of signal representation by a linear combination of a small number of vectors, sequences or functions. This representation is used for signal modeling and finds a lot of applications such as signal estimation, restoration and feature extraction. In order to obtain a good sparse representation, it is essential to choose a signal transform appropriately. In this article, redundancy is firstly explained as an effective property of transforms for sparse representation. Then, some problem settings of sparse representation are introduced and their solvers are overviewed. Next, redundant transforms are shown to be successfully applied to image restoration problems. Furthermore, desired properties of transforms for image processing are summarized, and then dictionary learning methods are introduced as a design technique of redundant transforms. Finally, trends of related works are summarized as concluding remarks.
