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

1. Front Matter

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2. Algebraically Approximate and Noisy Realization of Discrete-Time Dynamical Systems

   1. Front Matter

      Pages 1-1

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   2. Introduction

      • Yasumichi Hasegawa

      Pages 3-10

   3. Input/Output Map and Additive Noises

      • Yasumichi Hasegawa

      Pages 11-20

   4. Algebraically Approximate and Noisy Realization of Linear Systems

      • Yasumichi Hasegawa

      Pages 21-51

   5. Algebraically Approximate and Noisy Realization of So-called Linear Systems

      • Yasumichi Hasegawa

      Pages 53-85

   6. Algebraically Approximate and Noisy Realization of Almost Linear Systems

      • Yasumichi Hasegawa

      Pages 87-109

   7. Algebraically Approximate and Noisy Realization of Pseudo Linear Systems

      • Yasumichi Hasegawa

      Pages 111-145

   8. Algebraically Approximate and Noisy Realization of Affine Dynamical Systems

      • Yasumichi Hasegawa

      Pages 147-183

   9. Algebraically Approximate and Noisy Realization of Linear Representation Systems

      • Yasumichi Hasegawa

      Pages 185-212

3. Algebraically Approximate and Noisy Realization of Digital Images

   1. Front Matter

      Pages 213-213

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   2. Algebraically Approximate and Noisy Realization of Two-Dimensional Images

      • Yasumichi Hasegawa

      Pages 215-247

4. Back Matter

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This monograph deals with approximation and noise cancellation of dyn- ical 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 ?ltering theory and system theory and d- ital 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 di?er- tial 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 e?ect, 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 di?erential equations. For our purpose,manyactualexamplesofmodelinformationandnoisereductionwill also be provided. Using the analysis of state space approach, the model reduction problem may have become a major theme of technology after 1966 for emphasizing e?ciency in the ?elds of control, economy, numerical analysis, and others.

• Digital Images
• Discrete-Time Systems
• Dynamic Systems
• Non-Linear Systems
• Two-Dimensional Digital Images
• information
• systems theory
• complexity

From the reviews:

“The volume under review is addressed to advanced students, researchers and engineers specialized in filtering theory, system theory, and digital images analysis. Its content is organized into nine chapters, clustered in two parts. … The volume is completed by references and index.” (Milan Mareš, Zentralblatt MATH, Vol. 1200, 2011)

• Gifu University, Gifu, Japan

  Yasumichi Hasegawa

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