Algebraically Approximate and Noisy Realization of Discrete-time Systems and Digital Images

by Hasegawa, Yasumichi

• ISBN13: 9783642032165
• ISBN10: 3642032168
• Format: Hardcover
• Copyright: 2009-10-01
• Publisher: Springer Verlag

Summary

This monograph deals with approximation and noise cancellation of dynamical systems which include linear and nonlinear input/output relationships. It also deal with approximation and noise cancellation of two dimensional arrays. It will be of special interest to researchers, engineers and graduate students who have specialized in filtering theory and system theory and digital images. This monograph is composed of two parts. Part I and Part II will deal with approximation and noise cancellation of dynamical systems or digital images respectively. From noiseless or noisy data, reduction will be made. A method which reduces model information or noise was proposed in the reference vol. 376 in LNCIS [Hasegawa, 2008]. Using this method will allow model description to be treated as noise reduction or model reduction without having to bother, for example, with solving many partial differential equations. This monograph will propose a new and easy method which produces the same results as the method treated in the reference. As proof of its advantageous effect, this monograph provides a new law in the sense of numerical experiments. The new and easy method is executed using the algebraic calculations without solving partial differential equations. For our purpose, many actual examples of model information and noise reduction will also be provided.

Table of Contents

Algebraically Approximate and Noisy Realization of Discrete-Time Dynamical Systems
Introduction	p. 3
Input/Output Map and Additive Noises	p. 11
Input Response Maps (Input/Output Maps with Causality)	p. 11
Analysis for Algebraically Approximate and Noisy Realization	p. 13
Measurement Data with Noise	p. 14
Analyses for Approximate and Noisy Data	p. 14
Algebraically Constrained Least Square Method	p. 17
Algebraic CLS Method and Analytic CLS Method	p. 19
Historical Notes and Concluding Remarks	p. 19
Algebraically Approximate and Noisy Realization of Linear Systems	p. 21
Basic Facts Regarding Linear Systems	p. 21
Finite Dimensional Linear Systems	p. 23
Partial Realization Theory of Linear Systems	p. 25
Algebraically Approximate Realization of Linear Systems	p. 26
Algebraically Noisy Realization of Linear Systems	p. 36
Comparative Table of the Algebraic CLS and AIC Method	p. 48
Historical Notes and Concluding Remarks	p. 49
Algebraically Approximate and Noisy Realization of So-called Linear Systems	p. 53
Basic Facts about So-called Linear Systems	p. 54
Finite Dimensional So-called Linear Systems	p. 55
Partial Realization of So-called Linear Systems	p. 58
Real-Time Partial Realization of Almost Linear Systems	p. 60
Algebraically Approximate Realization of So-called Linear Systems	p. 61
Algebraically Noisy Realization of So-called Linear Systems	p. 72
Historical Notes and Concluding Remarks	p. 83
Algebraically Approximate and Noisy Realization of Almost Linear Systems	p. 87
Basic Facts of Almost Linear Systems	p. 88
Finite Dimensional Almost Linear Systems	p. 89
Algebraically Approximate Realization of Almost Linear Systems	p. 90
Algebraically Noisy Realization of Almost Linear Systems	p. 99
Historical Notes and Concluding Remarks	p. 108
Algebraically Approximate and Noisy Realization of Pseudo Linear Systems	p. 111
Basic Facts about Pseudo Linear Systems	p. 111
Finite Dimensional Pseudo Linear Systems	p. 113
Partial Realization of Pseudo Linear Systems	p. 116
Real-Time Partial Realization of Pseudo Linear Systems	p. 118
Algebraically Approximate Realization of Pseudo Linear Systems	p. 120
Algebraically Noisy Realization of Pseudo Linear Systems	p. 131
Historical Notes and Concluding Remarks	p. 144
Algebraically Approximate and Noisy Realization of AfTine Dynamical Systems	p. 147
Basic Facts about Affine Dynamical Systems	p. 148
Finite Dimensional Affine Dynamical Systems	p. 150
Partial Realization Theory of Affine Dynamical Systems	p. 153
Algebraically Approximate Realization of Affine Dynamical Systems	p. 155
Algebraically Noisy Realization of Affine Dynamical Systems	p. 170
Historical Notes and Concluding Remarks	p. 182
Algebraically Approximate and Noisy Realization of Linear Representation Systems	p. 185
Basic Facts about Linear Representation Systems	p. 186
Finite Dimensional Linear Representation Systems	p. 187
Partial Realization Theory of Linear Representation Systems	p. 190
Algebraically Approximate Realization of Linear Representation Systems	p. 191
Algebraically Noisy Realization of Linear Representation Systems	p. 201
Historical Notes and Concluding Remarks	p. 211
Algebraically Approximate and Noisy Realization of Digital Images
Algebraically Approximate and Noisy Realization of Two-Dimensional Images	p. 215
Commutative Linear Representation Systems	p. 216
Finite-Dimensional Commutative Linear Representation Systems	p. 218
Partial Realization Theory of Two-Dimensional Images	p. 223
Measurement Data with Approximate and Noisy Error	p. 226
Analyses for Approximate and Noisy Data	p. 227
Non-linear Integer Programming for Digital Images	p. 228
Algebraically Approximate Realization of Two-Dimensional Images	p. 229
Algebraically Noisy Realization of Two-Dimensional Images	p. 237
Historical Notes and Concluding Remarks	p. 246
References	p. 249
Index	p. 253
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