Guide to the MATLAB code for total variation-based
deblurring with FISTA
Amir Beck and Marc Teboulle
August 11, 2008
1 Overview
The MATLAB codes in this package are aimed at solving denoising problems of the form
min
X
{kX − Bk
2
+ 2λTV(X) : l ≤ X
ij
≤ u}, (1.1)
and deblurring problems of the form
min
X
{kA(X) − Bk
2
+ 2λTV(X) : l ≤ X
ij
≤ u}, (1.2)
where
• B ∈ R
m×n
is the observed blurred and noisy image of size m × n.
• A : R
m×n
→ R
m×n
is the linear operator corresponding to a spatially invariant PSF of
the blur operation.
• T V (X) : R
m×n
→ R is a total variation function. Here we consider two possibilities:
the isotropic TV function:
X ∈ R
m×n
, TV
I
(X) =
P
m−1
i=1
P
n−1
j=1
p
(X
i,j
− X
i+1,j
)
2
+ (X
i,j
− X
i,j+1
)
2
+
P
m−1
i=1
|X
i,n
− X
i+1,n
| +
P
n−1
j=1
|X
m,j
− X
m,j+1
|
and the l
1
-based TV function:
X ∈ R
m×n
, TV
l
1
(X) =
P
m−1
i=1
P
n−1
j=1
{|X
i,j
− X
i+1,j
| + |X
i,j
− X
i,j+1
|}
+
P
m−1
i=1
|X
i,n
− X
i+1,n
| +
P
n−1
j=1
|X
m,j
− X
m,j+1
|.
• λ - positive regularization parameter.
The functions are based on the paper
1
评论9