Algebraically Approximate and Noisy Realization of Discrete-Time Systems and Digital Images (eBook)

Title Page 2
Preface 5
Contents 8
Part I Algebraically Approximate and Noisy Realization of Discrete-Time Dynamical Systems 11
Introduction 12
Input/Output Map and Additive Noises 20
Input Response Maps (Input/Output Maps with Causality) 20
Analysis for Algebraically Approximate and Noisy Realization 22
Measurement Data with Noise 23
Analyses for Approximate and Noisy Data 23
Algebraically Constrained Least Square Method 26
Algebraic CLS Method and Analytic CLS Method 28
Historical Notes and Concluding Remarks 28
Algebraically Approximate and Noisy Realization of Linear Systems 30
Basic Facts Regarding Linear Systems 30
Finite Dimensional Linear Systems 32
Partial Realization Theory of Linear Systems 34
Algebraically Approximate Realization of Linear Systems 35
Algebraically Noisy Realization of Linear Systems 45
Comparative Table of the Algebraic CLS and AIC Method 57
Historical Notes and Concluding Remarks 58
Algebraically Approximate and Noisy Realization of So-called Linear Systems 61
Basic Facts about So-called Linear Systems 62
Finite Dimensional So-called Linear Systems 63
Partial Realization of So-called Linear Systems 66
Real-Time Partial Realization of Almost Linear Systems 68
Algebraically Approximate Realization of So-called Linear Systems 69
Algebraically Noisy Realization of So-called Linear Systems 80
Historical Notes and Concluding Remarks 91
Algebraically Approximate and Noisy Realization of Almost Linear Systems 94
Basic Facts of Almost Linear Systems 95
Finite Dimensional Almost Linear Systems 96
Algebraically Approximate Realization of Almost Linear Systems 97
Algebraically Noisy Realization of Almost Linear Systems 106
Historical Notes and Concluding Remarks 115
Algebraically Approximate and Noisy Realization of Pseudo Linear Systems 117
Basic Facts about Pseudo Linear Systems 117
Finite Dimensional Pseudo Linear Systems 119
Partial Realization of Pseudo Linear Systems 122
Real-Time Partial Realization of Pseudo Linear Systems 124
Algebraically Approximate Realization of Pseudo Linear Systems 126
Algebraically Noisy Realization of Pseudo Linear Systems 137
Historical Notes and Concluding Remarks 150
Algebraically Approximate and Noisy Realization of Affine Dynamical Systems 152
Basic Facts about Affine Dynamical Systems 153
Finite Dimensional Affine Dynamical Systems 155
Partial Realization Theory of Affine Dynamical Systems 158
Algebraically Approximate Realization of Affine Dynamical Systems 160
Algebraically Noisy Realization of Affine Dynamical Systems 175
Historical Notes and Concluding Remarks 187
Algebraically Approximate and Noisy Realization of Linear Representation Systems 189
Basic Facts about Linear Representation Systems 190
Finite Dimensional Linear Representation Systems 191
Partial Realization Theory of Linear Representation Systems 194
Algebraically Approximate Realization of Linear Representation Systems 195
Algebraically Noisy Realization of Linear Representation Systems 205
Historical Notes and Concluding Remarks 215
Part II Algebraically Approximate and Noisy Realization of Digital Images 217
Algebraically Approximate and Noisy Realization of Two-Dimensional Images 218
Commutative Linear Representation Systems 219
Finite-Dimensional Commutative Linear Representation Systems 221
Partial Realization Theory of Two-Dimensional Images 226
Measurement Data with Approximate and Noisy Error 229
Analyses for Approximate and Noisy Data 230
Non-linear Integer Programming for Digital Images 231
Algebraically Approximate Realization of Two-Dimensional Images 232
Algebraically Noisy Realization of Two-Dimensional Images 240
Historical Notes and Concluding Remarks 249
References 251
Index 254