Table of Contents
Advances in Electrical Engineering
Volume 2014 (2014), Article ID 276241, 23 pages
http://dx.doi.org/10.1155/2014/276241
Review Article

Fast Transforms in Image Processing: Compression, Restoration, and Resampling

Department of Physical Electronics, School of Electrical Engineering, Tel Aviv University, 69978 Tel Aviv, Israel

Received 4 March 2014; Accepted 19 May 2014; Published 6 July 2014

Academic Editor: George E. Tsekouras

Copyright © 2014 Leonid P. Yaroslavsky. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Transform image processing methods are methods that work in domains of image transforms, such as Discrete Fourier, Discrete Cosine, Wavelet, and alike. They proved to be very efficient in image compression, in image restoration, in image resampling, and in geometrical transformations and can be traced back to early 1970s. The paper reviews these methods, with emphasis on their comparison and relationships, from the very first steps of transform image compression methods to adaptive and local adaptive filters for image restoration and up to “compressive sensing” methods that gained popularity in last few years. References are made to both first publications of the corresponding results and more recent and more easily available ones. The review has a tutorial character and purpose.