Parameter Estimation for Blind and Non-Blind Deblurring Using Residual Whiteness Measures

(Abstract, MATLAB code)

Abstract:

Image deblurring (ID) is an ill-posed problem typically addressed by using regularization, or prior knowledge, on the unknown image (and also on the blur operator, in the blind case). ID is often formulated as an optimization problem, where the objective function includes a data term encouraging the estimated image (and blur, in blind ID) to explain well the observed data (typically, the squared norm of a residual) plus a regularizer that penalizes solutions deemed undesirable. The performance of this approach dependes critically (among other things) on the relative weight of the regularizer (the regularization parameter) and on the number of iterations of the algorithm used to address the optimization problem. In this paper, we propose new criteria for adjusting the regularization parameter and/or the number of iterations of ID algorithms. The

rationale is that if the recovered image (and blur, in blind ID) are well estimated, the residual image is spectrally white; contrarily, a poorly deblurred image typically exhibits structured artifacts (e.g., ringing, oversmoothness), yielding residuals that are not spectrally white. The proposed criterion is particularly well suited to a recent blind ID algorithm that uses continuation, i.e., slowly decreases the regularization parameter along the iterations; in this case, choosing this parameter and deciding when to stop are one and the same thing. Our experiments show that the proposed whiteness-based criteria yield improvements in SNR, on average, only 0.15dB below those obtained by (clairvoyantly) stopping the algorithm at the best SNR. We also illustrate the proposed criteria on non-blind ID, reporting results that are competitive with state-of-the-art criteria (such as Monte-Carlobased GSURE and projected SURE), which, however, are not applicable for blind ID.

References:

[1] M. S. C. Almeida and M. A. T. Figueiredo, “Stopping Criteria for Iterative Blind and Non-Blind Image Deblurring Algorithms Based on Residual Whiteness Measures”, IEEE Trans. Image Processing, 2013. (Accepted, Abstract and MATLAB code)

[2] M. S. C. Almeida and M. A. T. Figueiredo, “New stopping criteria for iterative blind image deblurring based on residual whiteness measures”, IEEE Workshop on Statistical Signal Processing – SSP’2011, Nice, France, 2011.

MATLAB Code: six measures of whiteness (.zip)

If you find any bug, please report it to me: M. S. C. Almeida. Thank you!

License:  This code is copyright of Mariana S.C. Almeida and Mário A. T. Figueiredo. Free permission is given for their use for nonprofit research purposes. Any other use is prohibited, unless a license is previously obtained. To obtain a license please contact Mariana S.C. Almeida or Mário A. T. Figureiredo. 

This package is compressed with 7-zip.

ACKNOWLEDGEMENTS: This work was partially supported by Fundação para a Ciência e Tecnologia (FCT), under grants PTDC/EEA-TEL/104515/2008, PEst-OE/EEI/LA0008/2011, PTDC/EEI-PRO/1470/2012, and the fellowship SFRH/BPD/69344/2010.