Topics in Signal Processing
Overview
Foundation
1. Set Theory
1.1. Sets
1.2. Relations
1.3. Functions
1.4. Cardinality
1.5. Sequences
1.6. General Cartesian Product
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. Matrices I
4.2. Vector Spaces
4.3. Matrices II
4.4. Linear Transformations
4.5. Normed Linear Spaces
4.6. Inner Product Spaces
4.7. Dual Spaces
4.8. The Euclidean Space
4.9. Matrices III
4.10. Eigen Values
4.11. Singular Values
4.12. Important Vector Spaces
4.13. Matrix Norms
4.14. Sequence Spaces
4.15. Affine Sets and Transformations
5. Multivariate Calculus
5.1. Differentiation
5.2. Differentiation in Banach Spaces
6. Probability
6.1. Random Variables
6.2. Univariate Distributions
6.3. Basic Inequalities
6.4. Two Variables
6.5. Expectation
6.6. Random Vectors
6.7. Multivariate Gaussian Distribution
6.8. Subgaussian Distributions
7. Numerical Optimization
7.1. Mathematical Optimization
Convexity
8. Convex Sets and Functions
8.1. Real Vector Spaces
8.2. Convex Sets
8.3. Convex Subsets of
\(\RR^n\)
8.4. Cones
8.5. Cones II
8.6. Cones III
8.7. Generalized Inequalities
8.8. Convex Functions
8.9. Differentiability and Convex Functions
8.10. Function Operations
8.11. Topology of Convex Sets
8.12. Separation Theorems
8.13. Continuity
8.14. Recession Cones
8.15. Directional Derivatives
8.16. Subgradients
8.17. Conjugate Functions
8.18. Smoothness
8.19. Infimal Convolution
9. Convex Optimization
9.1. Convex Optimization
9.2. Projection on Convex Sets
9.3. Directions of Recession
9.4. Basic Duality
9.5. Constrained Optimization I
9.6. Linear Constraints
9.7. Constrained Optimization II
9.8. Lagrange Multipliers
9.9. Lagrangian Duality
9.10. Conjugate Duality
9.11. Linear Programming
9.12. Quadratic Programming
10. Subgradient Methods
10.1. Basic Subgradient Method
11. Proximal Algorithms
11.3. Proximal Mappings and Operators
Sparsity
12. Sparse Signal Models
12.3. Underdetermined Linear Systems
12.4. Sparsity in Orthonormal Bases
12.5. Sparse and Redundant Representations
12.6. Dictionaries
12.7. Compressive Sensing
12.8. Restricted Isometry Property
12.9. Dictionaries II
13. Compressive Sensing
13.1. Sensing Matrices
14. Sparse Approximation with Dictionaries
14.1. Stability of the Sparsest Solution
14.2. Basis Pursuit
14.3. Orthogonal Matching Pursuit
15. Sparse Recovery from Compressive Measurements
15.1. Stability of the Sparsest Solution
15.2. Basis Pursuit
15.3. Orthogonal Matching Pursuit
15.4. Compressive Sampling Matching Pursuit
16. Dictionary Learning
16.1. Introduction
Epilogue
Notation
Bibliographic Notes
Index
repository
open issue
Index
Index
A
|
B
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C
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D
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E
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F
|
G
|
H
|
I
|
L
|
M
|
N
|
O
|
P
|
Q
|
R
|
S
|
T
|
U
A
Accumulation point
Analysis matrix
Approximate Subdifferential
Approximate subgradient
Atom
B
Babel function
Baire space
Banach space
Barrier cone
barrier vector
Basic feasible solution
Biconjugate
Bolzano-Weierstrass property
Boundary
Boundary point
Bounded function
Boundedness
metric space
C
Cantor set
Cardinal number
Cardinality of the continuum
Cartesian product
Chain
Choice function
Closed ball
Closed convex function
Closed function
extended real valued
Closed set
Closure
Closure point
Co-meager set
Coherence
arbitrary matrices
Compact metric space
Compact set
Complete metric space
Compressed sensing
Compressive sampling
Compressive sensing
embedding
explanation
Concave function
Cone
Conic combination
Conic hull
Conjugate function
Connected subset
Connectedness
Contour
Convergence
metric space
Convex combination
Convex cone
Convex function
closure
effective domain
extended value extension
improper
proper
strict
Convex hull
Convex set
dimension
Countable set
D
Deleted neighborhood
Dense set
Derived set
Descent direction
Diameter
Dictionary
incoherent
spark
Differentiability
proper function
Directional derivative
Distance
point and set
set and set
Dual cone
E
Effective domain
Enumeration
Epigraph
Equivalence class
Equivalence relation
Equivalent metrics
Equivalent norms
Equivalent sets
Extended real valued function
closed function
contour
epigraph
graph
hypograph
limit inferior
limit superior
proper function
strict epigraph
sublevel set
superlevel set
Extended value extension
Extreme point
F
Family of sets
index set
intersection
pairwise disjoint
union
Feasible direction
Finite set
Frontier
Frontier point
Function
bijective
composition
composition (total)
domain
equality
extension
graph
identity
injective
inverse
inverse (total)
partial
range
restriction
set image
set inverse image
surjective
total
value
G
Gauge function
Global maximum
Global minimum
Grassmannian frame
H
Halfspace
lower and closed
upper and closed
Hyperplane
horizontal
nonvertical
vertical
Hypograph
I
Improper function
Incoherent dictionary
Indicator function
,
[1]
Infinite cardinal number
Infinite set
Interior
Interior point
Isolated point
L
Limit inferior
extended real valued
Limit superior
extended real valued
Line
vertical
Line segment
Linear transformation
bounded
Local extreme value
Locally bounded function
Lower semicontinuity
extended real valued
Lower semicontinuous hull
M
Matrix
spark
Max crossing problem
Maximin problem
Meager set
Measurement space
Metric
induced by norm
Metric space
Cauchy sequence
completion
convergence
finite product
from a norm
open cover
sequence
Metric subspace
Min common problem
Minimax problem
Min common/max crossing framework
Mutual coherence
N
Natural numbers
segment
Non-meager set
Norm
Norm cone
Norm topology
Normal cone
normal vector
Normed linear space
bounded set
continuity
convergence
unit ball
Normed space
Nowhere dense set
Null space property
O
Open ball
Open set
Ordered pair
P
Partial order
lower bound
maximal element
minimal element
upper bound
Partially ordered set
Pointed cone
Polar cone
Polyhedral cone
Power set
Proper cone
Proper function
Proximity
Q
Quasi convex function
Quasi incoherent dictionary
R
Ray
Real valued function
partial order
Relation
binary
composition
functional
injective
intersection
many-to-many
many-to-one
one-to-many
one-to-one
serial
surjective
union
S
Saddle point
minimax
Self dual cone
Semicontinuity
extended real valued
Sequence
eventual satisfaction
Set
complement
disjoint
empty
equality
operations
singleton
symmetric difference
Set of real valued functions
Set partition
Set valued function
composition
domain
inverse
range
selection
set image
single valued
Sign vector
complex
Signal
$K$-term approximation
compressible
mask
restriction
Signal space
Simplex
k-simplex
midpoint
Stationary point
Strict epigraph
Strict global maximum
Strict global minimum
Strongly equivalent metrics
Subdictionary
Subdifferentiability
domain
Subdifferential
Subgradient
Sublevel set
Subsequence
Subset
proper
Subset equivalence
Superlevel set
Support function
Synthesis matrix
T
Tangent cone
Tangent direction
Topology
Total order
Totally bounded metric space
Totally ordered set
Two ortho basis
U
Uncountable set
Upper semicontinuity
extended real valued