Discrete Cosine Transform 2nd Edition by Humberto Ochoa Dominguez, K R Rao 1138304727 9781138304727

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ISBN-10 :  1138304727 

ISBN-13 :  9781138304727

Author:  Humberto Ochoa-Dominguez, K. R. Rao 

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.

Discrete Cosine Transform 2nd Table of contents:

Chapter 1: Introduction
Applications
Chapter 2: The Karhunen-Loève Transform
Introduction
The Karhunen-Loève Transform for a 1D Random Field
Eigenvalues and Eigenvectors of R
Application of KLT to Data Compression
KLT for a 2D Random Field
Applications
Summary
Problems
Projects
Chapter 3: The Discrete Cosine Transform
Introduction
The Fourier Cosine Transform
Properties of the FCT
Definitions
The Unitarity of DCTs
Scaling in Time
Shift in Time
The Difference Property
The Convolution Property
Relation to the KLT
DCT-I
Fast Algorithms
DCT via FFT
Direct Computation by Sparse Matrix Factorizations
Decimation-in-Time (DIT) and Decimation-in-Frequency (DIF) Algorithms
The DIT Algorithm
The DIF Algorithm
The DCT via the Walsh-Hadamard Transform (WHT)
The DCT via the Discrete Hartley Transform (DHT)
Other Fast Algorithms
Prime Factor Algorithm (PFA)
A Fast Recursive Algorithm
DCT-II Realization via Planar Rotations
Applications
Summary
Problems
Projects
Chapter 4: The Discrete Sine Transform
Introduction
The Fourier Sine Transform
Properties of the FST
The Discrete Sine Transform
The Discrete Fourier Transform of a Skewed Sequence
The Discrete Sine Transform via the DFT
Fast Algorithms
The Fast DST-I via the SST Algorithm
Sparse Matrix Factorization of the DST-I
The Split-Radix Algorithm for DST-I
Applications
Summary
Problems
Projects
Chapter 5: The Modified Discrete Cosine Transform
Introduction
Definitions
MDCT as the Shifted Discrete Fourier Transform
Properties of the MDCT
Evenly Stacked MDCT
MDCT Block Transform
Symmetry Properties of MDCT Block Transform
Matrix Representation of the MDCT
Oddly Stacked MDCT
MDCT Block Transform
Symmetry Properties of MDCT Block Transform
Matrix Representation of the MDCT
Applications
Summary
Problems
Projects
Chapter 6: The Integer Discrete Cosine Transform
Introduction
Integer DCT Matrix
The ICT by Direct Scaling
H264 4×4 and 8×8 ICT Matrices
WMV9 4×4 and 8×8 ICT Matrices
AVS1 China 8×8 ICT Matrix
H265 4×4, 8×8, 16×16 and 32×32 ICT Matrices
AVS2 China 4×4, 8×8, 16×16 and 32×32 ICT Matrices
Versatile Video Coding (VVC)
The ICT by Kernel Component Replacement
Fast Algorithm
The Lifting Matrix and the Lifting Step
The Integer DCT-II by Lifting Matrix
Low-Complexity ICT (LCICT)
Square Wave Transform
Round-off Approximation of IntDCT
The Tchebichef Polynomials
Orthogonality
Discrete Tchebichef Polynomials
Orthogonality
Even Symmetry
The Discrete Tchebichef Transform
4×4 and 8×8 Discrete Tchebichef Transforms
Integer Discrete Tchebichef Transform
Metrics to Evaluate a Transform
Mean-Square Error
Coding Gain
Transform Efficiency
Variance Distribution
Energy Packing Efficiency (EPE)
Residual Correlation
Implementations
Applications
Summary
Problems
Projects
Chapter 7: The Directional Discrete Cosine Transform
Introduction
The Directional DCT
The Basis Images for DDCT Mode 3
The Steerable DCT
Basic Graph Theory
Adjacency Matrix
Laplacian Matrix
The Normalized Adjacency and Normalized Laplacian Matrices
Spectrum of the Laplacian Matrix
Kronecker Product
Cartesian Product of Two Graphs
Steerable DCT Definition
Rotation Angle Optimization
Applications
Summary
Problems
Projects
Chapter 8: Transform Mirroring and Rotation
Sequence Mirroring Properties for Discrete Orthogonal Transforms Consisting of the Even and Odd Symmetric Row Vectors
Two-Dimensional Extension
Rotation by 90 Degrees
Rotation by 180 Degrees
Rotation by 270 Degrees
Image Mirroring and Rotation in the Wavelet Domain
Perfect Reconstruction
Two-Dimensional Extension
Horizontal and Vertical Mirroring
Rotation by 90 Degrees
Rotation by 180 Degrees
Rotation by 270 Degrees

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Tags: Discrete Cosine, Humberto Ochoa Dominguez, K R Rao