Learning multiscale sparse representations for image and video restoration

This paper presents a framework for learning multiscale sparse representations of color images and video with overcomplete dictionaries. A single-scale K-SVD algorithm was introduced in [M. Aharon, M. Elad, and A. M. Bruckstein, IEEE Trans. Signal Process., 54 (2006), pp. 4311-4322], formulating sparse dictionary learning for grayscale image representation as an optimization problem, efficiently solved via orthogonal matching pursuit (OMP) and singular value decomposition (SVD). Following this work, we propose a multiscale learned representation, obtained by using an efficient quadtree decomposition of the learned dictionary and overlapping image patches. The proposed framework provides an alternative to predefined dictionaries such as wavelets and is shown to lead to state-of-the-art results in a number of image and video enhancement and restoration applications. This paper describes the proposed framework and accompanies it by numerous examples demonstrating its strength. © 2008 Society for Industrial and applied Mathematics.

Full Text

Duke Authors

Cited Authors

  • Mairal, J; Sapiro, G; Elad, M

Published Date

  • 2008

Published In

Volume / Issue

  • 7 / 1

Start / End Page

  • 214 - 241

International Standard Serial Number (ISSN)

  • 1540-3459

Digital Object Identifier (DOI)

  • 10.1137/070697653

Citation Source

  • SciVal