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ANHA Series Preface; Preface; The February Fourier Talks (FFT); The Norbert Wiener Center; The Structure of the Volumes; Acknowledgments; Contents; Part XVII Theoretical Harmonic Analysis; Time-Frequency Analysis and Representations of the Discrete Heisenberg Group; 1 Introduction; 2 Direct Integrals; 3 The Rational Case; 4 The Irrational Case; References; Fractional Differentiation: Leibniz Meets Hölder; 1 Introduction; 2 The counterexample; 3 The sharp Kato-Ponce inequalities and preliminaries; 4 The proof of the homogeneous inequality (7); 5 Final remarks; References
Wavelets and Graph C*-Algebras1 Introduction; 2 C-Algebras and Work by Bratteli and Jorgensen and Dutkay and Jorgensen on Representations of ON; 3 Marcolli-Paolucci Wavelets; 4 C*-Algebras Corresponding to Directed Graphs and Higher-Rank Graphs; 4.1 Directed Graphs, Higher-Rank Graphs, and C*-Algebras; 4.2 -Semibranching Function Systems and Representations of C*(); 5 Wavelets on L2(∞, M); 6 Traffic Analysis Wavelets on 2(0) for a Finite Strongly Connected k-Graph , and Wavelets from Spectral Graph Theory; 6.1 Wavelets for Spatial Traffic Analysis
6.2 Wavelets on 2(0) Coming from Spectral Graph TheoryReferences; Part XVIII Image and Signal Processing; Precise State Tracking Using Three-Dimensional Edge Detection; 1 Introduction; 1.1 Previous Work in Tracking; 1.2 Previous Work in Edge Detection; 1.3 Outline and Contributions; 2 The Data; 3 3D Edge Detectors; 3.1 3D Canny Edge Detection; 3.2 3D Wavelet Edge Detection; 3.3 3D Shearlet Edge Detector; 3.4 3D Hybrid Wavelet and Shearlet Edge Detectors; 3.5 Performance of the Edge Detectors; 4 From Edge Detection to Tracking; 5 Experimental Results; 6 Conclusions; References
Approaches for Characterizing Nonlinear Mixtures in Hyperspectral Imagery1 Introduction; 2 Methodology; 2.1 Fully Constrained Least Squares; 2.2 Proposed Method 1: Fully Constrained Least Squares (FCLS) Applied to Single Scattering Albedo Spectra; 2.3 Proposed Method 2: Generalized Kernel Fully Constrained Least Squares; 3 Description of Experiment; 4 Results; 5 Concluding Remarks; References; An Application of Spectral Regularization to Machine Learning and Cancer Classification; 1 Introduction; 1.1 Machine Learning; 1.2 Approach; 1.3 Prior Work; 1.4 Paper Contents; 2 Denoising Theorems
2.1 Statements of Theorems2.1.1 Method 1: Local averaging on a graph; 2.1.2 Method 2: Support vector regression/regularization on a graph; 3 Application: Using Prior Information to Form Graphs; 3.1 Gene Expression; 4 Conclusion; References; Part XIX Quantization; Embedding-Based Representation of Signal Geometry; 1 Introduction; 1.1 Notation; 1.2 Outline; 2 Preserving Distances; 2.1 Randomized Linear Embeddings; 2.2 Embedding Map Design; 2.3 Distance-preserving properties of the map; 2.4 Learning the Embedding Map; 3 Preserving Inner Products, Angles, and Correlations
Wavelets and Graph C*-Algebras1 Introduction; 2 C-Algebras and Work by Bratteli and Jorgensen and Dutkay and Jorgensen on Representations of ON; 3 Marcolli-Paolucci Wavelets; 4 C*-Algebras Corresponding to Directed Graphs and Higher-Rank Graphs; 4.1 Directed Graphs, Higher-Rank Graphs, and C*-Algebras; 4.2 -Semibranching Function Systems and Representations of C*(); 5 Wavelets on L2(∞, M); 6 Traffic Analysis Wavelets on 2(0) for a Finite Strongly Connected k-Graph , and Wavelets from Spectral Graph Theory; 6.1 Wavelets for Spatial Traffic Analysis
6.2 Wavelets on 2(0) Coming from Spectral Graph TheoryReferences; Part XVIII Image and Signal Processing; Precise State Tracking Using Three-Dimensional Edge Detection; 1 Introduction; 1.1 Previous Work in Tracking; 1.2 Previous Work in Edge Detection; 1.3 Outline and Contributions; 2 The Data; 3 3D Edge Detectors; 3.1 3D Canny Edge Detection; 3.2 3D Wavelet Edge Detection; 3.3 3D Shearlet Edge Detector; 3.4 3D Hybrid Wavelet and Shearlet Edge Detectors; 3.5 Performance of the Edge Detectors; 4 From Edge Detection to Tracking; 5 Experimental Results; 6 Conclusions; References
Approaches for Characterizing Nonlinear Mixtures in Hyperspectral Imagery1 Introduction; 2 Methodology; 2.1 Fully Constrained Least Squares; 2.2 Proposed Method 1: Fully Constrained Least Squares (FCLS) Applied to Single Scattering Albedo Spectra; 2.3 Proposed Method 2: Generalized Kernel Fully Constrained Least Squares; 3 Description of Experiment; 4 Results; 5 Concluding Remarks; References; An Application of Spectral Regularization to Machine Learning and Cancer Classification; 1 Introduction; 1.1 Machine Learning; 1.2 Approach; 1.3 Prior Work; 1.4 Paper Contents; 2 Denoising Theorems
2.1 Statements of Theorems2.1.1 Method 1: Local averaging on a graph; 2.1.2 Method 2: Support vector regression/regularization on a graph; 3 Application: Using Prior Information to Form Graphs; 3.1 Gene Expression; 4 Conclusion; References; Part XIX Quantization; Embedding-Based Representation of Signal Geometry; 1 Introduction; 1.1 Notation; 1.2 Outline; 2 Preserving Distances; 2.1 Randomized Linear Embeddings; 2.2 Embedding Map Design; 2.3 Distance-preserving properties of the map; 2.4 Learning the Embedding Map; 3 Preserving Inner Products, Angles, and Correlations