ANU College of

Engineering & Computer Science

Blind Image Restoration Muhammad Hanif. Supervisor: Abd-Krim Seghouane

Problem Statement:

Blur and noise are generally undesirable image characteristics that reduce the visibility of image contents in many images analysis applications, i-e., remote sensing, medical , astronomy , photography etc.

.

original Images Observed Images

The main theme of image restoration is to estimate the original scene from its degraded observed version. In most practical imaging situations it is often costly or physically impossible to obtained prior information about the imaging system (blur and noise). In such cases the most practical and accurate approach for the original image estimation is to use blind image restoration/ deconvolution, which require no prior information about imaging scene or blurring process.

Proposed Approach:

Consider an observed image y, described by standard linear observation plus Gaussian noise

model,

(1)

The matrix H represents a 2-D convolution and is assumed block circulant or block Toeplitz with

Toeplitz blocks. The original image x, and the blur H are estimated by successive alternating

minimization of the Kullback Leibler divergence, leads to a hybrid Fourier deconvolution, wavelet

regularization algorithm. To introduce regularization to the problem, the model (1) is enhanced by

using x as an intermediate variable,

Where and represents x in the wavelet domain, which is modelled as GSM.

Successive Minimization of KL Divergence :

a). Let and ,respectively, represents the generating family and model family of

probability densities. The MLE of that maximizes the observed data log-likelihood,

This MLE can be derived by an iterative alternating minimizing scheme, involves two steps

a.1)

a.2)

b). Due to the intermediate complete data assumption, the MLE of (a.2) can be obtained by

iteratively applying two steps,

b.1)

b.2)

ALGORITHM:

Result Comparisons:

a) Semi-Blind Restoration:

b) Blind Image Restoration:

Conclusion:

We present a new method for blind image deconvolution, based on successive alternating

minimization of the Kullback-Leblier divergence. Which leads to a hybrid Fourier deconvolution

and wavelet regularization algorithm. The resulting approach is computationally efficient and has

the advantage of exploiting the strength of the Fourier transform for image deconvolution and the

wavelet transform for image regularization. Comparing to state of the art methods, our approach

produce better results for all kind of blur and noise levels.

Contribution:

•A successive alternating minimization of the Kullback Leibler divergence for blind image restoration (BIR). •A hybrid Fourier deconvolution and wavelet regularization BIR algorithm. •An optimized, high speed BIR algorithm, equally efficient for all kind of blurs.

References: [1] J. M. Bioucas-Dias, “Bayesian wavelet-based image deconvolution: A GEM algorithm exploiting a class of heavy -tailed

priors,” IEEE Transactions on Image Processing, vol. 15, pp. 937–951, 2006.

[2] Q. Shan, J. Jia, and A. Agarwala, “High quality motion deblurring from a single image,” ACM Transactions on Graphics,

vol. 27, pp. 1–10, 2008.

[3] A. K. Seghouane, “A kullbackleibler divergence approach to blind image restoration,” IEEE

Transactions on Image Processing, pp. 2078–2083, 2011.

[4] R. Molina, J. Mateos, and A. K. Katsaggelos, “Blind deconcolution using a variational approach to parameter, image and

blur estimation,” IEEE Transactions on Image Processing, vol. 15, pp. 3715–3727, 2006.

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