(Ebook) Multidimensional Discrete Unitary Transforms Representation Partitioning and Algorithms 1st Edition by Artyom M Grigoryan, Sos S Agaian ISBN 1482276321 9780429179815

(Ebook) Multidimensional Discrete Unitary Transforms Representation Partitioning and Algorithms 1st Edition by Artyom M Grigoryan, Sos S Agaian ISBN 1482276321 9780429179815

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ISBN 10: 1482276321 
ISBN 13: 9780429179815
Author: Artyom M Grigoryan, Sos S Agaian

This reference presents a more efficient, flexible, and manageable approach to unitary transform calculation and examines novel concepts in the design, classification, and management of fast algorithms for different transforms in one-, two-, and multidimensional cases. Illustrating methods to construct new unitary transforms for best algorithm selection and development in real-world applications, the book contains a wide range of examples to compare the efficacy of different algorithms in a variety of one-, two-, and three-dimensional cases. Multidimensional Discrete Unitary Transforms builds progressively from simple representative cases to higher levels of generalization.

(Ebook) Multidimensional Discrete Unitary Transforms Representation Partitioning and Algorithms 1st Table of contents:

1 Basic Concepts and Notation
1.1 New approach to image processing
1.2 Sets and set-theoretic operations
1.3 Groups
1.4 Covering and partition
1.5 Sequences
1.6 Matrices
1.7 Transformation

I Tensor Representation of Multidimensional Signals

2 Discrete Transform Tensor Representations
2.1 Covering with cyclic groups
2.2.1 Directional signal-images
2.2.2 n-dimensional representation
2.3 Shifted Fourier transform tensor presentation
2.5 2-D sine transform tensor representation
2.6 2-D Hartley transform tensor representation
2.7 2-D Hadamard transform tensor representation
Bibliography

3 Discrete Transform Paired Representations
3.1 Concept of the paired representation
3.2 Concept of the paired representation
3.2.2 Case N=Lr ( La prime number, r>1)
3.2.3 Case Nis a non-prime number
3.3 2-D DHdT paired representation
3.4 2-D DCT paired representation
3.5 2-D DST paired representation
3.6 2-D DHT paired representation
3.7 Representations for transforms with arbitrary fundamental period
3.8 2-D DFT on hexagonal lattices
3.8.1 Paired representation
3.8.2 Another 2-D DHFT
3.9 Piecewise 2-D DFT representation
Bibliography

4 Multiple Paired Unitary Transforms
4.1 Paired functions for the Fourier transform
4.2 Properties of paired functions
4.3 2-D unitary L-paired transforms
4.4 Paired functions and frequency-time wavelets
4.4.1 Fir tree of the paired transform
4.4.2 Basis construction
4.4.3 Atomic decomposition
4.4.4 The Haar and 2-paired transforms
4.5 Decomposition by directional signal-images
4.6 Non-classic discrete unitary Fourier transforms
4.6.1 1-D unitary transforms
4.6.2 2-D unitary transforms
4.7 MATLAB programs
4.7.1 Code to calculate the image-signals
4.7.2 Code to generate the paired functions
Bibliography

II Analysis and effective computing procedures

5 Fast 1-D Transforms
5.1 Basic statutes
5.1.1 Fourier transformation
5.1.2 Model of a signal
5.1.3 Sampling theorem
5.1.4 Fast algorithm
5.2 Problem formulation
5.2.1 Partitions revealing transforms
5.2.2 General algorithm
5.3 Discrete Fourier transforms
5.4 Discrete Hadamard transform
5.5 Discrete cosine transform
5.5.1 Sine transform
5.6 Discrete Hartley transforms
5.6.1 Traditional DHT
5.6.2 Odd-time DHT
5.7 Complexity and comparison
5.7.1 Programs
Bibliography

6 Fast 2-D Discrete Unitary Transforms
6.1 General algorithm
6.2 Tensor algorithm for unitary transforms
6.2.1 Case when N>1 is a prime
6.2.2 Case N=Lr ( L is a prime, r>1 )
6.2.3 Case N=L1L2L1>1,L2>1
6.2.4 Case N is arbitrary
6.2.5 Case N1≠N2
6.3 Effective algorithms for the 2-D DFT
6.3.1 Case Nis a prime
6.3.2 Case N=2r
6.3.3 Case N=Lr
6.3.4 Case N=L1L2
6.3.5 Modified algorithms of the 2-D DFT
6.3.6 Case 2r×2r
6.3.7 Case Lr×Lr
6.4 Method of the polynomial transforms
6.5 Realization of the tensor algorithm
6.6.1 Tensor algorithm of the 2-D DHFT
6.7 Tensor algorithm of the 2-D DCT
6.7.1 Modified algorithms of the 2-D DCT
6.8 Tensor algorithm for the 2-D DHT
6.8.1 General algorithm
6.8.2 Case when Nis a prime
6.8.3 Case N=Lr
6.8.4 Improvement algorithm for the 2-D DHT
6.9 Tensor algorithm of the 2-D DHdT
6.10.3 n-dimensional DHT
Bibliography

7 Paired Algorithms
7.1 The algorithm of paired transforms
7.2 Method of the 2-D paired transforms
7.2.1 Fast algorithms of the 2-D DFT
7.3 Paired algorithm for the 2-D DHT and DCT
7.3.1 Paired algorithms of the 2-D DHdT
7.4 Paired algorithm for 2-D hexagonal DFT
7.5 Comparison of the proposed algorithms
Bibliography

III Applications of Paired Transformations

8 Fourier Transform, Geometrical Interpretation, and Convolution
8.1 Operations over two-dimensional images
8.1.1 Local operations over images
8.1.2 Global operations on images
8.3 Paired image-signals and cyclic convolution
Bibliography

9 Image Enhancement by Paired Transforms
9.1 Transforms with frequency ordered systems
9.1.1 General transform-based image enhancement algorithm
9.1.2 Performance measure of enhancement
9.1.3 Experimental results
9.1.4 Zonal transform-based enhancement methods
9.2 Tensor method of enhancement
Bibliography

10 Image Reconstruction from Projections by Paired Transforms
10.1 Organization of the reconstruction problem
10.1.1 The Radon transformation
10.1.2 The Hounsfield principle
10.2 Discrete model formulation
10.3 Solution of the discrete model
10.3.1 Vector representation
10.3.2 Tensor representation on the 3-D torus
10.3.3 Paired representation
10.3.4 Minimum number of projections
10.4.1 Method of reconstruction
10.4.2 Solution of the convolution equation

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Tags: Artyom M Grigoryan, Sos S Agaian, Discrete Unitary, Partitioning, Algorithms