Discrete Cosine Transform, Second Edition

Humberto Ochoa-Dominguez, K. R. Rao

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9781351396479
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

Many new DCT-like transforms have been proposed since the first edition of this book. For example, the integer DCT that yields integer transform coefficients, the directional DCT to take advantage of several directions of the image and the steerable DCT. The advent of higher dimensional frames such as UHDTV and 4K-TV demand for small and large transform blocks to encode small or large similar areas respectively in an efficient way. Therefore, a new updated book on DCT, adapted to the modern days, considering the new advances in this area and targeted for students, researchers and the industry is a necessity.

1

Introduction

Transform coding is an integral component of image and video processing applications. The main goal is to map a set of pixel values into a few transform coefficients with certain desired properties. These properties help reconstruct the pixels with the least loss possible. The mapping process, or transform, must fulfill two important features: The coefficients in the transform domain should be decorrelated and the total energy must be conveyed by only a few coefficients with the remaining coefficients carrying insignificant energy.

A number of transformation techniques exist that fulfill the above properties, although their energy packing capabilities vary. The discrete cosine transform (DCT) is widely used because its strong energy packing and decorrelation properties makes it comparable to the Karhunen–Loève transform (KLT), which is an optimal transform in terms of retained transform coefficients and decorrelation because it completely removes the statistical dependence between transformation coefficients.

The disadvantage of the KLT is that its transformation process depends on the input signal and does not have a fast algorithm so that the computational cost is high, especially in areas of transform coding. Sinusoidal transforms, like the discrete cosine transforms and discrete Fourier transforms (DFT) use image-independent transformations. Moreover, fast algorithms and architectures are available for DCT and DFT. However, DCT results in less blocking artifacts due to the even-symmetric extension properties of DCT and it is real, unlike complex computations used in DFT.

The DCT is preferred over the KLT because it is separable, real, orthogonal and has a fast algorithm. There are 8 types of DCT. Nevertheless, th...