Multiscale Transforms with Application to Image Processing - Softcover
Book 131 of 180: Signals and Communication Technology
Synopsis
I Introduction to Image Processing.
1 Fundamentals of Digital Image Processing. 1.1 Image Acquisition of Digital Camera. 1.1.1 Introduction. 1.2 Sampling. References.
II Multiscale Transform.
2 Fourier Analysis and Fourier Transform. 2.1 Overview. 2.2 Fourier Series. 2.2.1 Periodic Functions. 2.2.2 Frequency and Amplitude. 2.2.3 Phase. 2.2.4 Fourier Series of Periodic Functions. 2.2.5 Complex form of Fourier Series. 2.3 Fourier Transform. 2.3.1 2D-Fourier Transform. 2.3.2 Properties of Fourier Transform. 2.4 Discrete Fourier Transform. 2.4.1 1D-Discrete Fourier Transform. 2.4.2 Inverse 1D-Discrete Fourier Transform. 2.4.3 2D-Discrete Fourier Transform and 2D-Inverse Discrete Fourier Transform. 2.4.4 Properties of 2D-Discrete Fourier transform. 2.5 Fast Fourier Transform. 2.6 The Discrete Cosine Transform. 2.6.1 1D-Discrete Cosine Transform. 2.6.2 2D-Discrete Cosine Transform. 2.7 Heisenberg Uncertainty Principle. 2.8 Windowed Fourier Transform or Short-Time Fourier Transform. 2.8.1 1D and 2D Short-Time Fourier Transform. 2.8.2 Drawback of Short-Time Fourier Transform. 2.9 Other Spectral Transforms. References
3 Wavelets and Wavelet Transform. 3.1 Overview. 3.2 Wavelets. 3.3 Multiresolution Analysis. 3.4 Wavelet Transform. 3.4.1 The Wavelet Series Expansions. 3.4.2 Discrete Wavelet Transform. 3.4.3 Motivation: From MRA to Discrete Wavelet Transform. 3.4.4 The Quadrature Mirror Filter Conditions. 3.5 The Fast Wavelet Transform. 3.6 Why Use Wavelet. Transforms. 3.7 Two-Dimensional Wavelets. 3.8 2D-discrete Wavelet Transform. 3.9 Continuous Wavelet Transform. 3.9.1 1D Continuous Wavelet Transform. 3.9.2 2D Continuous Wavelet Transform. 3.10 Undecimated Wavelet Transform or Stationary Wavelet Transform. 3.11 Biorthogonal Wavelet Transform. 3.11.1 Linear Independence and Biorthogonality. 3.11.2 Dual MRA. 3.11.3 Discrete Transform for Biorthogonal Wavelets. 3.12 Scarcity of Wavelet Transform. 3.13 Complex Wavelet Transform. 3.14 Dual-Tree Complex Wavelet Transform. 3.15 Quaternion Wavelet and Quaternion Wavelet. Transform. 3.15.1 2D Hilbert Trnasform
3.15.2 Quaternion Algebra. 3.15.3 Quaternion Multiresolution Analysis. References.
4 New Multiscale Constructions. 4.1 Overview. 4.2 Ridgelet Transform. 4.2.1 The Continuous Ridgelet Transform. 4.2.2 Discrete Ridgelet Transform. 4.2.3 The Orthonormal Finite Ridgelet Transform. 4.2.4 The Fast Slant Stack Ridgelet Transform. 4.2.5 Local Ridgelet Transform. 4.2.6 Sparse Representation by Ridgelets. 4.3 Curvelets. 4.3.1 The First Generation Curvelet Transform .4.3.2 Sparse Representation by First Generation Curvelets. 4.3.3 The Second-Generation Curvelet Transform. 4.3.4 Sparse Representation by Second Generation Curvelets. 4.4 Contourlet. 4.5 Contourlet Transform. 4.5.1 Multiscale Decomposition. 4.5.2 Directional Decomposition. 4.5.3 The Discrete Contourlet Transform. 4.6 Shearlet. 4.7 Shearlet Transform. 4.7.1 Continuous Shearlet Transform. 4.7.2 Discrete Shearlet Transform. 4.7.3 Cone-Adapted Continuous Shearlet Transform. 4.7.4 Cone-Adapted Discrete Shearlet Transform. 4.7.5 Compactly Supported Shearlets. 4.7.6 Sparse Representation by Shearlets. References.
III Application of Multiscale transforms to Image Processing
5 Image Restoration. 5.1 Model of image degradation and restoration process. 5.2 Image Quality Assessments Metrics. 5.3 Image Denoising. 5.4 Noise Models. 5.4.1 Additive Noise Model. 5.4.2 Multiplicative Noise Model. 5.5 Types of Noise. 5.5.1 Amplier(Gaussian) Noise. 5.5.2 Rayleigh Noise. 5.5.3 Uniform Noise. 5.5.4 Impulsive(Salt and Pepper) Noise. 5.5.5 Exponential Noise. 5.5.6 Speckle Noise. 5.6 Image Deblurring. 5.6.1 Gaussian Blur. 5.6.2 Motion Blur. 5.6.3 Rectangular Blur. 5.6.4 Defocus Blur. 5.7 Superresolution. 5.8 Classication of Image Restoration Algorithms. 5.8.1 Spatial Filtering.
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