Fast image deconvolution using Hyper-Laplacian Prior
Dilip Krishnan Rob Fergus
New york University
Presented by Zhengming Xing

Outline
• Introduction
• Algorithm
• Experiment result

introduction
• Hyper-Laplacian Prior p ( x )
 exp(
 k | x |

) ( typically with 0 .
5
  
0 .
8 )
• speed

algorithm
For non-blind deconvolution problem
Given y (the blurred image), and k( blur kernel), x(original image). Assume Gaussian noise.
p ( x | y , k )
 p ( y | x , k ) p ( x )
Hyper-Laplacain prior
Minimize
 log p ( x | y , k )

Optimize problem recall
Half quadratic penalty method, introduce auxiliary variable.And consider the one special case.
j

2 .
f
1

[ 1

1 ] , f
2

[ 1

1 ]
T
F i j x

( x
 f j
) i

Recall:
Solve sub-problem
• Fixed w

Recall:
Solve sub-problem
Fixed X
Lookup table: pre-compute solution for different
Analytic solution: for particular value of


,


Recall:
Take derivative
 
1 / 2
 
2 / 3
Compare the different root and find the global minimum

Summary of the algorithm

Summary of the algorithm

Experiment description
• Grey scale real world image, blurred by camera shaked kernels and add Gaussian noise. The kernels are minor perturbed.
• Measured with the SNR
10 log
10
(
|| x
ˆ 
||
 x
ˆ 
( x
ˆ
) x ||
2
||
2
)

result

result

result