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Mathematical Image Processing
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Foreword
1. Introduction
1.1. Related research fields
1.2. Image properties
1.3. Image processing tasks
1.4. Image models
1.5. Image quantization
2. Image transformations
2.1. Fourier transform
2.2. Convolution
3. Statistical Noise Modeling
3.1. Maximum likelihood
3.2. Maximum a-posteriori estimation
4. Variational Image Processing
4.1. Existence and uniqueness of minimizers
4.2. Characterization of minimizers
4.3. First discretize, then optimize
4.4. Variational denoising problem
5. Convex Analysis
5.1. Fenchel conjugate
5.2. Subdifferential
5.3. Primal-dual optimization
5.4. Special case: TV denoising
6. Deconvolution
6.1. van-Cittert iterations
6.2. Deconvolution as inverse problem
6.3. Singular Value Decomposition
6.4. Variational deconvolution
7. Segmentation
7.1. Mumford-Shah model
7.2. Chan-Vese model
8. Referenzen
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