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Topics in Signal Processing
Foundation
1. Algebra
1.2. Sets
1.3. Relations
1.4. Functions
1.5. Integers
1.6. Cardinality
1.7. Sequences
1.8. General Cartesian Product
1.9. Matrices
1.10. Groups
1.11. Enumerative Combinatorics
2. Elementary Real Analysis
2.1. Real Line
2.2. Topology of Real Line
2.3. Sequences and Series
2.4. The Extended Real Line
2.5. Real Valued Functions
2.6. Real Functions
2.7. Differentiable Functions
2.8. Some Important Inequalities
3. Metric Spaces
3.1. Introduction
3.2. Metric Topology
3.3. Boundedness
3.4. Sequences
3.5. Subspace Topology
3.6. Functions and Continuity
3.7. Completeness
3.8. Compactness
3.9. Real Valued Functions
3.10. Discrete Metric Space
3.11. Special Topics
4. Linear Algebra
4.1. Vector Spaces
4.2. Matrices II
4.3. Linear Transformations
4.4. Normed Linear Spaces
4.5. Inner Product Spaces
4.6. Dual Spaces
4.7. The Euclidean Space
4.8. Matrices III
4.9. Eigen Values
4.10. Singular Values
4.11. Important Vector Spaces
4.12. Matrix Norms
4.13. Sequence Spaces
4.14. Affine Sets and Transformations
5. Multivariate Calculus
5.1. Differentiation
5.2. Differentiation in Banach Spaces
6. Geometry
6.1. Algebraic Geometry
7. Probability
7.1. Probability Spaces
7.2. Random Variables
7.3. Univariate Distributions
7.4. Basic Inequalities
7.5. Two Variables
7.6. Expectation
7.7. Random Vectors
7.8. Multivariate Gaussian Distribution
7.9. Subgaussian Distributions
8. Numerical Optimization
8.1. Mathematical Optimization
Convexity
9. Convex Sets and Functions
9.1. Real Vector Spaces
9.2. Convex Sets
9.3. Convex Subsets of
\(\RR^n\)
9.4. Cones
9.5. Cones II
9.6. Cones III
9.7. Generalized Inequalities
9.8. Convex Functions
9.9. Differentiability and Convex Functions
9.10. Function Operations
9.11. Topology of Convex Sets
9.12. Separation Theorems
9.13. Continuity
9.14. Recession Cones
9.15. Directional Derivatives
9.16. Subgradients
9.17. Conjugate Functions
9.18. Smoothness
9.19. Infimal Convolution
10. Convex Optimization
10.1. Convex Optimization
10.2. Projection on Convex Sets
10.3. Directions of Recession
10.4. Basic Duality
10.5. Constrained Optimization I
10.6. Linear Constraints
10.7. Constrained Optimization II
10.8. Lagrange Multipliers
10.9. Lagrangian Duality
10.10. Conjugate Duality
10.11. Linear Programming
10.12. Quadratic Programming
11. Subgradient Methods
11.1. Basic Subgradient Method
12. Proximal Algorithms
12.3. Proximal Mappings and Operators
Signal Processing
13. Signal Theory
14. Detection and Estimation Theory
15. Coding Theory
16. Wavelets
Machine Learning
17. Data Clustering
17.1. Introduction
17.2. Similarity Measures
17.3. Hierarchical Algorithms
17.4. K-Means Clustering
17.5. Graph Algorithms
17.6. Spectral Clustering
17.7. Expectation Maximization
17.8. Evaluation
Sparsity
18. Sparse Signal Models
18.3. Underdetermined Linear Systems
18.4. Sparsity in Orthonormal Bases
18.5. Sparse and Redundant Representations
18.6. Dictionaries
18.7. Compressive Sensing
18.8. Restricted Isometry Property
18.9. Dictionaries II
19. Compressive Sensing
19.1. Sensing Matrices
19.2. Quantization
20. Sparse Approximation with Dictionaries
20.1. Stability of the Sparsest Solution
20.2. Basis Pursuit
20.3. Orthogonal Matching Pursuit
21. Sparse Recovery from Compressive Measurements
21.1. Stability of the Sparsest Solution
21.2. Basis Pursuit
21.3. Orthogonal Matching Pursuit
21.4. Compressive Sampling Matching Pursuit
22. Dictionary Learning
22.1. Introduction
Applications
23. Subspace Clustering
23.5. Motion Segmentation
Epilogue
Notation
Bibliographic Notes
Index
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Subgradient Methods
11.
Subgradient Methods
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