Graph Spectral Image Processing

4Graph Spectral Image and Video Compression

Hilmi E. EGILMEZ¹, Yung-Hsuan CHAO¹ and Antonio ORTEGA²

¹Qualcomm Technologies Inc., San Diego, USA

²University of Southern California, Los Angeles, USA

4.1. Introduction

Transforms are integral parts of many state-of-the-art compression systems and standards, and are used to provide compact spectral representations for signals to be compressed. This chapter presents methods for building graph Fourier transforms (GFTs)¹ for image and video compression. A key insight developed in this chapter is that classical transforms, such as the discrete sine/cosine transform (DST/DCT) or the Karhunen–Loeve transform (KLT), can be interpreted from a graph perspective. Thus, the ideas presented in this chapter can be viewed as extensions of these conventional techniques, where changes to some of the underlying assumptions are made. We consider two sets of techniques for designing graphs, from which the associated GFTs are derived:

• – Graph learning oriented GFT (GL-GFT) approaches aim to find graphs that best fit a collection of image/video block data. Similar to the KLT, these methods are data driven, but unlike the KLT they learn the graph (rather than the transform) and introduce regularization parameters as part of the learning.
• – Block-adaptive GFT (BA-GFT) approaches are based on adaptively updating graph weights according to important features (such as texture and discontinuities) in an image/video block. A typical approach to design these ...