MATLAB User Guide for Plug-and-Play ADMM
Xiran Wang and Stanley Chan
Statistical Signal and Image Processing Lab, Purdue University
https://engineering.purdue.edu/ChanGroup/
Version 1.0
This user guide documents the usage of the MATLAB implementation of Plug-and-Play ADMM.
Acknowledgement of this package should be given to the following reference.
[1] S. H. Chan, X. Wang and O. A. Elgendy, “Plug-and-Play ADMM for image restoration: Fixed
point convergence and applications,” IEEE Trans. Computational Imaging, in Press, Nov. 2016. ArXiv:
https://arxiv.org/abs/1605.01710
1 Introduction
Plug-and-Play ADMM solves the following problem:
b
x = argmin
x
f(x) + λg(x), (Problem (P))
where x ∈ R
n
is the unknown clean image, f (·) is the forward model of the image formation process, g(·) is
a regularization function, and λ > 0 is a regularization parameter. Of interest to this package is the forward
model f(x) =
1
2
kAx−yk
2
, where y ∈ R
m
is the observed image, and A ∈ R
m×n
is the linear transformation
relating x and y.
Plug-and-Play ADMM solves Problem (P) by iteratively solving the a sequence of subproblems:
x
(k+1)
= argmin
x
f(x) +
ρ
k
2
kx −
e
x
(k)
k
2
,
e
x
(k)
def
= v
(k)
− u
(k)
(1)
v
(k+1)
= D
σ
k
(
e
v
(k)
),
e
v
(k)
def
= x
(k+1)
+ u
(k)
(2)
u
(k+1)
= u
(k)
+ (x
(k+1)
− v
(k+1)
) (3)
ρ
k+1
= γ
k
ρ
k
, (4)
In this set of equations, {ρ
k
|k = 1, 2, . . . , k
max
} is a sequence of internal parameters, updated by constants
1
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