## Multidimensional Discrete Unitary Transforms: Representation: Partitioning, and AlgorithmsThis 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. |

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### Contents

Basic Concepts and Notation | 1 |

Discrete Transform Tensor Representations | 33 |

Discrete Transform Paired Representations | 91 |

Multiple Paired Unitary Transforms | 147 |

Analysis and effective computing procedures | 221 |

Fast 2D Discrete Unitary Transforms | 295 |

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2-D DFT 2-D discrete 2ero 2r x 2r-point 8-point A.M. Grigoryan A'-point DFT algorithm for calculating algorithm for computing arbitrary basis functions coefficients complex consider construction corresponding cyclic convolution cyclic groups decomposition defined deuote DHdT DHFT dimensional directional signal-images discrete cosine transform discrete Fourier transform discrete Hartley transform domain elements equal example fast algorithms fast Fourier transform Figure formula frequency fundamental period given Haar Hadamard transform hexagonal lattice IEEE IEEE Trans image enhancement image f image processing image reconstruction image-signal integer inverse irreducible covering linear multidimensional multiplications required number of multiplications number of operations one-dimensional operations of multiplication orthogonal transforms paired algorithm paired functions paired representation paired transform partition polyuomial samples shown in Fig si2e Signal Processing splitting set subsets tensor algorithm tensor representation Theorem two-dimensional discrete two-dimensional sequence unitary transforms uot difficult values vector XN,N

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Page 471 - Ji, MK Sundareshan, and H. RoeHrig, "Adaptive image contrast enhancement based on human visual properties.