Blind Image Deconvolution

Abstract
The objective of this project is to realize an algorithm for a blind restoration of image by using the Total Variation regularization. Blind image restoration is the process of estimating both the true image and the blur from the degraded image characteristics, using partial information about the imaging system.

The problem
The general blind deconvolution problem refers to the task of separating two convoluted signals, when both the signals are either unknown or partially known. Unfortunately, in many practical situations, the blur is often unknown, and little information is available about the true image. Therefore, the true image must be identified directly from the observation by using partial or no information about the blurring process and the true image.

The solution (or the basic approach)
One of the most successful regularization approaches is the TV regularization method, which can effectively recover edges of the image.

x = s*h

The idea is to think about this problem as an optimization problem
with the following cost function:

The TV norm is displayed in the project report.
lambda is the regularization weight.

Results and Conclusions

In one dimension:

s is the original image
h is the original kernal
s recon is the reconstrated image
h recon is the reconstrated kernal
x is the observation

In two dimensions:

S is the original image
H is the original kernal
S RECON  is the reconstrated image
H RECON is the reconstrated kernal
X is the observation

We can see that in one dimension the results are very good,
but in tow dimension the results are not well.
We think that the prior of the kernal in this algorithm is not
appropriate to complicated images.

Acknowledgment
We are grateful to our project supervisor Michael Bronstein for his help and guidance throughout this work. We are also grateful to the this lab teem for his support in this project.
We are also grateful to the Ollendorff Minerva Center Fund for supporting this project.