Mathematical Methods of Linear Model Based Image Processing Procedures

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Table of Contents

• 1 Introduction.
• 2 Linear Operators
• 3 Characteristic Input Functions
• 4 General Input Functions - Fourier Transformation
• 5 Laplace-Transformation
  • 5.1 Analysis of linear systems in extended frequency space
  • 5.2 Properties and rules of Laplace transformation
  • 5.3 Laplace transformation of characteristic and any other typical functions
  • 5.4 Mathematical description of the system properties functions
  • 5.5 Inverse transformation method for linear invariant systems
  • 5.6 Inverse transformation of the proper rational function
  • 5.7 Transfer Function
  • 5.8 Transfer characteristic function (Modulation Transfer Function MTF)
  • 5.9 Linear shift invariant system description by the step response function
  • 5.10 Relation between the step response function and weighting function of linear shift invariant system
• 6 Problems (Linear Systems)
• 7 Theory and basic laws of sampling
• 8 Planar imaging as a linear system
• 9 Appendix.
  • 9.1 Theorems, Detailed explanations
    • 9.1.1 Deriving of Fourier Theory, Fourier Series
    • 9.1.2 Description of Fourier series by complex expression
    • 9.1.3 Parzeval theorem
    • 9.1.4 Response function in general case
    • 9.1.5 Deriving of Duhamel Theorem
  • 9.2 Solution of problems
    • 9.2.1 S1.
    • 9.2.2 S2.
    • 9.2.3 S3.
    • 9.2.4 S4.
    • 9.2.5 S5.
    • 9.2.6 S6.
    • 9.2.7 S7.
    • 9.2.8 S8.
    • 9.2.9 S9.
    • 9.2.10 S10.
    • 9.2.11 S11.