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E-raamat: Transform and Data Compression Handbook

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Using data compression as a common theme to unify the chapters into a single account, computer engineers from Europe and North America explore different discrete transforms and their ever-expanding applications in the general area of signal processing. They cover the Karhunen-LoFvem, the discrete Fourier, comparametric, discrete cosine and sine, and lapped transforms and wavelet-based image and fractal-based image and video compression and the compression of wavelet transform coefficients. The material should interest researchers and engineers in any field that requires data compression. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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 DVD, videophone, digital camera, MP3, video-streaming and wireless PCS, would have been virtually impossible. Transforming the data to a frequency or other domain enables even more efficient compression. By illustrating this intimate link, The Transform and Data Compression Handbook serves as a much-needed handbook for a wide range of researchers and engineers.

The authors describe various discrete transforms and their applications in different disciplines. They cover techniques, such as adaptive quantization and entropy coding, that result in significant reduction in bit rates when applied to the transform coefficients. With clear and concise presentations of the ideas and concepts, as well as detailed descriptions of the algorithms, the authors provide important insight into the applications and their limitations. Data compression is an essential step towards the efficient storage and transmission of information. The Transform and Data Compression Handbook provides a wealth of information regarding different discrete transforms and demonstrates their power and practicality in data compression.
Karhunen-Loeve Transform
1(36)
Introduction
1(1)
Data Decorrelation
2(9)
Calculation of the KLT
9(2)
Performance of Transforms
11(6)
Information Theory
11(2)
Quantization
13(1)
Truncation Error
13(2)
Block Size
15(2)
Examples
17(13)
Calculation of KLT
17(1)
Quantization and Encoding
18(4)
Generalization
22(2)
Markov-1 Solution
24(1)
Medical Imaging
25(3)
Color Images
28(2)
Summary
30(7)
References
34(3)
The Discrete Fourier Transform
37(42)
Introduction
37(2)
The DFT Matrix
39(1)
An Example
40(1)
DFT Frequency Analysis
41(4)
Selected Properties of the DFT
45(4)
Symmetry Properties
47(2)
Real-Valued DFT-Based Transforms
49(6)
The Fast Fourier Transform
55(3)
The DFT in Coding Applications
58(2)
The DFT and Filter Banks
60(8)
Cosine-Modulated Filter Banks
63(3)
Complex DFT-Based Filter Banks
66(2)
Conclusion
68(4)
FFT Web sites
72(7)
References
74(5)
Comparametric Transforms for Transmitting Eye Tap Video with Picture Transfer Protocol (PTP)
79(38)
Introduction: Wearable Cybernetics
79(2)
Historical Overview of WearComp
80(1)
Eye Tap Video
80(1)
The Edgertonian Image Sequence
81(2)
The Edgertonian versus Nyquist Thinking
81(1)
Frames versus Rows, Columns, and Pixels
82(1)
Picture Transfer Protocol (PTP)
83(1)
Best Case Imaging and Fear of Functionality
84(4)
Comparametric Image Sequence Analysis
88(6)
Camera, Eye, or Head Motion: Common Assumptions and Terminology
91(1)
VideoOrbits
92(2)
Framework: Comparameter Estimation and Optical Flow
94(5)
Fear-Based Methods
94(1)
Featureless Methods Based on Generalized Cross-Correlation
95(1)
Featureless Methods Based on Spatio-Temporal Derivatives
96(3)
Multiscale Projective Flow Comparameter Estimation
99(7)
Four Point Method for Relating Approximate Model to Exact Model
101(1)
Overview of the New Projective Flow Algorithm
102(1)
Multiscale Repetitive Implementation
103(1)
Exploiting Commutativity for Parameter Estimation
104(2)
Performance/Applications
106(3)
A Paradigm Reversal in Resolution Enhancement
106(1)
Increasing Resolution in the ``Pixel Sense''
107(2)
Summary
109(2)
Acknowledgements
111(6)
References
112(5)
Discrete Cosine and Sine Transforms
117(80)
Introduction
117(1)
The Family of DCTs and DSTs
118(4)
Definitions of DCTs and DSTs
118(1)
Mathematical Properties
119(2)
Relations to the KLT
121(1)
A Unified Fast Computation of DCTs and DSTs
122(24)
Definitions of Even-Odd Matrices
123(1)
DCT-11/DST-11 and DCT-III/DST-III Computation
124(5)
DCT-I and DST-I Computation
129(2)
DCT-IV/DST-IV Computation
131(3)
Implementation of the Unified Fast Computation of DCTs and DSTs
134(12)
The 2-D DCT/DST Universal Computational Structure
146(15)
The Fast Direct 2-D DCT/DST Computation
146(6)
Implementation of the Direct 2-D DCT/DST Computation
152(9)
DCT and Data Compression
161(30)
DCT-Based Image Compression/Decompression
162(4)
Data Structure for Compression/Decompression
166(2)
Setting the Quantization Table
168(2)
Standard Huffman Coding/Decoding Tables
170(2)
Compression of One Sub-Image Block
172(7)
Decompression of One Sub-Image Block
179(5)
Image Compression/Decompression
184(2)
Compression of Color Images
186(2)
Results of Image Compression
188(3)
Summary
191(6)
References
192(5)
Lapped Transforms for Image Compression
197(70)
Introduction
197(7)
Notation
198(1)
Brief History
198(1)
Block Transforms
199(1)
Factorization of Discrete Transforms
200(1)
Discrete MIMO Linear Systems
201(2)
Block Transform as a MIMO System
203(1)
Lapped Transforms
204(6)
Orthogonal Lapped Transforms
204(6)
Nonorthogonal Lapped Transforms
210(1)
LTs as MIMO Systems
210(3)
Factorization of Lapped Transforms
213(2)
Hierarchical Connection of LTs: An Introduction
215(7)
Time-Frequency Diagram
215(2)
Tree-Structured Hierarchical Lapped Transforms
217(2)
Variable-Length LTs
219(3)
Practical Symmetric LTs
222(11)
The Lapped Orthogonal Transform: LOT
222(1)
The Lapped Bi-Orthogonal Transform: LBT
223(3)
The Generalized LOT: GenLOT
226(4)
The General Factorization: GLBT
230(3)
The Fast Lapped Transforms: FLT
233(3)
Modulated LTs
236(4)
Finite-Length Signals
240(6)
Overall Transform
241(2)
Recovering Distorted Samples
243(1)
Symmetric Extensions
244(2)
Design Issues for Compression
246(2)
Transform-Based Image Compression Systems
248(5)
JPEG
249(1)
Embedded Zerotree Coding
250(2)
Other Coders
252(1)
Performance Analysis
253(5)
JPEG
253(2)
Embedded Zerotree Coding
255(3)
Conclusions
258(9)
References
260(7)
Wavelet-Based Image Compression
267(46)
Introduction
267(1)
Dyadic Wavelet Transform
268(6)
Two-Channel Perfect-Reconstruction Filter Bank
270(2)
Dyadic Wavelet Transform, Multiresolution Representation
272(1)
Wavelet Smoothness
273(1)
Wavelet-Based Image Compression
274(39)
Lossy Compression
274(4)
EZW Algorithm
278(7)
SPIHT Algorithm
285(9)
WDR Algorithm
294(5)
ASWDR Algorithm
299(6)
Lossless Compression
305(1)
Color Images
305(1)
Other Compression Algorithms
306(1)
Ringing Artifacts and Postprocessing Algorithms
306(1)
References
306(7)
Fractal-Based Image and Video Compression
313(34)
Introduction
313(1)
Basic Properties of Fractals and Image Compression
314(2)
Contractive Affine Transforms, Iterated Function Systems, and Image Generation
316(2)
Image Compression Directly Based on the IFS Theory
318(3)
Image Compression Based on IFS Library
321(1)
Image Compression Based on Partitioned IFS
322(4)
Image Partitions
323(1)
Distortion Measure
323(1)
A Class of Discrete Image Transformations
324(1)
Encoding and Decoding Procedures
325(1)
Experimental Results
326(1)
Image Coding Using Quadtree Partitioned IFS (QPIFS)
326(7)
RMS Tolerance Selection
328(1)
A Compact Storage Scheme
329(2)
Experimental Results
331(2)
Image Coding by Exploiting Scalability of Fractals
333(3)
Image Spatial Sub-Sampling
334(1)
Decoding to a Larger Image
334(1)
Experimental Results
334(2)
Video Sequence Compression using Quadtree PIFS
336(5)
Definitions of Types of Range Blocks
336(2)
Encoding and Decoding Processes
338(2)
Storage Requirements
340(1)
Experimental Results
340(1)
Discussion
341(1)
Other Fractal-Based Image Compression Techniques
341(2)
Segmentation-Based Coding Using Fractal Dimension
341(1)
Yardstick Coding
342(1)
Conclusion
343(4)
References
343(4)
Compression of Wavelet Transform Coefficients
347(32)
Introduction
347(6)
Embedded Coefficient Coding
353(4)
Statistical Context Modeling of Embedded Bit Stream
357(2)
Context Dilution Problem
359(1)
Context Formation
360(2)
Context Quantization
362(3)
Optimization of Context Quantization
365(2)
Dynamic Programming for Minimum Conditional Entropy
367(2)
Fast Algorithms for High-Order Context Modeling
369(4)
Context Formation via Convolution
370(1)
Shared Modeling Context for Signs and Textures
371(2)
Experimental Results
373(1)
Lossy Case
373(1)
Lossless Case
374(1)
Summary
374(5)
References
375(4)
Index 379


Kamisetty Ramam Rao, Patrick C. Yip