Slide 4
Slide 4 text
MOA’15-
Class of problems: motivations
3
x
y H
n × 1
L × 1
m × 1 m × n n × L
Dictionary
Sensing
}
A "
Measurement/degradation
x
y H
n × 1
m × 1 m × n n × L
Dictionary
Sensing
}
x
y H
n × 1
m × 1 m × n n × L
Dictionary
Sensing
}
Inverse problem
Forward model
Prior knowledge
(regularization, constraints)
Many applications in data sciences: signal/image processing,
machine learning, statistics, etc..
x0 typically lives
in a low-dimensional manifold
y 2 Rm
x0
2 Rn
Solve an inverse problem through regularization :
min
x
2Rn F
(
x
)
| {z }
Data fidelity
+
G
(
x
)
| {z }
Regularization, constraints
G promotes objects living in the same manifold as x0.
F and G 2 0
(Rn)