Fourier Analysis and Medical Image Filtering

Name: Fourier Analysis and Medical Image Filtering
Brand: Cambridge Scholars Publishing
Price: 279.99 EUR
Availability: OnlineOnly

M'hamed Bentourkia(Autor*in)

Cambridge Scholars Publishing

1. Auflage

Erschienen am 9. Januar 2023

660 Seiten

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978-1-5275-8927-8 (ISBN)

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Inhalt

Intro
Table of Contents
About the Author
Preface
Summary
Chapter I
I.1 Brief history of complex numbers
I.2 Definition
I.3 Geometric representation of complex numbers
I.4 Operations on complex numbers
I.5 The polar form of a complex number, or trigonometric representation
I.6 Euler's notation
I.7 The nth roots of a complex number
I.8 Usefulness of complex numbers
I.9 Exercises
Chapter II
II.1 Periodicity
II.2 Parity
II.3 Orthogonality
II.4 Exercises
Chapter III
III.1 Definition of Fourier series
III.2 The conditions of Dirichlet
III.3 The harmonics
III.4 The complex form of FS
III.5 The properties of least squares approximation
III.6 Parseval's theorem
III.7 Symmetry and Fourier series
III.8 Gibbs phenomenon
III.9 Exercises
Chapter IV
IV.1 From the Fourier series to the Fourier transforms
IV.2 Definitions
IV.3 Determination of frequencies
IV.4 Amplitude and phase spectra
IV.5 Fourier transforms and symmetry
IV.6 The Dirac function
IV.7 Properties of Fourier transforms
IV.8 Generalized Fourier transforms
IV.9 Two-dimensional Fourier transforms
IV.10 Properties of 2D Fourier transforms
IV.11 Exercises
Chapter V
V.1 From Fourier transforms to discrete Fourier transforms
V.2 Decomposition of the operations of discrete Fourier transforms
V.3 Symmetry in discrete Fourier transforms
V.4 Interpolation of discrete Fourier transforms
V.5 The periodicity
V.6 Frequency folding
V.7 Nyquist critical frequency
V.8 The two-dimensional DFT
V.9 Exercises
Chapter VI
VI.1 The elements of the fast Fourier transform (FFT)
VI.2 Inverse FFT (IFFT)
VI.3 Two-dimensional FFT
VI.4 Clarifications on the use of the FFT
VI.5 Exercises
Chapter VII
VII.1 Intuitive definitions of convolution
VII.2 Definition and properties of the convolution
VII.3 Correlation
VII.4 Deconvolution
VII.5 Deconvolution by direct methods
VII.6 Deconvolution by the Wiener method
VII.7 Deconvolution with other approaches
VII.8 Examples of convolution with classical kernels
VII.9 Exercises
Chapter VIII
VIII.1 Sampling
VIII.2 The sampling theorem
VIII.3 The cardinal sine function
VIII.4 Theory of function reconstruction from samples
VIII.5 Aliasing and folding, again
VIII.6 Reconstruction of sampled functions
VIII.7 Exercises
Chapter IX
IX.1 Filters and frequency bands
IX.2 The transfer function
IX.3 Examples of current filters
IX.4 Utilization of filters
Bibliography
Matlab Functions
Index

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