Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Analog to digital conversion
- 3 Elements of rate-distortion theory
- 4 Scalar quantization with memory
- 5 Transform coding
- 6 Filter banks and wavelet filtering
- 7 Speech coding: techniques and standards
- 8 Image coding standards
- 9 Video-coding standards
- 10 Audio-coding standards
- A Lossless-coding techniques
- References
- Index
5 - Transform coding
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Analog to digital conversion
- 3 Elements of rate-distortion theory
- 4 Scalar quantization with memory
- 5 Transform coding
- 6 Filter banks and wavelet filtering
- 7 Speech coding: techniques and standards
- 8 Image coding standards
- 9 Video-coding standards
- 10 Audio-coding standards
- A Lossless-coding techniques
- References
- Index
Summary
Transform coding (Jayant and Noll 1984) is the second approach to exploiting redundancy (source memory) by using scalar quantization with linear preprocessing. The source samples xi are collected into a vector of dimension N that is linearly transformed into a vector of N transform coefficients y = (y1, y2, …, yN). Such a linear transform can be described as a multiplication of the input vector x = (x1, x2, …, xN) by a transform matrix T of size N × N. The value N is referred to as the order of the transform. The obtained coefficients yi, i = 1, 2, …, N, are then quantized. Scalar quantization of transform coefficients is rather efficient but, in principle, they can be vector quantized with lower average distortions. Notice that if scalar quantization is used, then each coefficient can be quantized by a different quantizer. In the decoder the inverse transform described by the matrix T−1 is applied to the vector of approximating values ŷ = (ŷ1, ŷ2, …, ŷN). A block diagram of transform coding is shown in Fig. 5.1. This kind of lossy coding was introduced in 1956 by Kramer and Mathews (1956), and analyzed and popularized in 1962–3 by Huang and Schultheiss (1963). This method has been developed for coding of images and video, where the Discrete Cosine Transform (DCT) is most commonly used because of its good performance.
- Type
- Chapter
- Information
- Compression for Multimedia , pp. 91 - 109Publisher: Cambridge University PressPrint publication year: 2009