In 1996, the JPEG committee began to investigate possibilities for a new still image
compression standard to serve current and future applications. This initiative, which was …

This chapter presents an overview of wavelet-based image coding. We develop the basics
of image coding with a discussion of vector quantization. We motivate the use of transform …

In this chapter, we develop the properties of wavelet systems in terms of the underlying filter
banks associated with them. This is an expansion and elaboration of the material in Chapter …

Historically, the theory of Hilbert spaces originated from David Hilbert's (1862–1943) work
on quadratic forms in infinitely many variables with their applications to integral equations …

In this article we provide an overview of rate-distortion (RD) based optimization techniques
and their practical application to image and video coding. We begin with a short discussion …

This paper discusses the interest of binary partition trees as a region-oriented image
representation. Binary partition trees concentrate in a compact and structured representation …

This paper introduces a new class of bases, called bandelet bases, which decompose the
image along multiscale vectors that are elongated in the direction of a geometric flow. This …

Data compression is one of the main contributing factors in the explosive growth in
information technology. Without it, a number of consumer and commercial products, such as …

In this paper we review some recent interactions between harmonic analysis and data
compression. The story goes back of course to Shannon's R (D) theory in the case of …

Wavelets and wavelet packets have recently emerged as powerful tools for signal
compression. Wavelet and wavelet packet-based compression algorithms based on …