Abstract
Blind deconvolution involves the estimation of a sharp signal or image given only a blurry observation. Because this problem is fundamentally ill-posed, strong priors on both the sharp image and blur kernel are required to regularize the solution space. While this naturally leads to a standard MAP estimation framework, performance is compromised by unknown trade-off parameter settings, optimization heuristics, and convergence issues stemming from non-convexity and/or poor prior selections. To mitigate these problems, several authors have recently proposed substituting a variational Bayesian (VB) strategy that marginalizes over the high-dimensional image space leading to better estimates of the blur kernel. However, the underlying cost function now involves both integrals with no closed-form solution and complex, function-valued arguments, thus losing the transparency of MAP. To elucidate these issues, we demonstrate that the VB methodology can be recast as an unconventional MAP problem with a very particular penalty/prior that couples the image, blur kernel, and noise level in a principled way. This unique penalty has a number of useful characteristics pertaining to relative concavity, local minima avoidance, and scale-invariance that allow us to rigorously explain the success of VB including its existing implementational heuristics and approximations. It also provides strict criteria for choosing the optimal image prior that, perhaps counter-intuitively, need not reflect the statistics of natural scenes. In so doing we challenge the prevailing notion of why VB is successful for blind deconvolution while providing a transparent platform for introducing enhancements and extensions.
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References
Babacan, S.D., Molina, R., Do, M.N., Katsaggelos, A.K.: Bayesian blind deconvolution with general sparse image priors. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part VI. LNCS, vol. 7577, pp. 341–355. Springer, Heidelberg (2012)
Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, Heidelberg (2006)
Chartrand, R., Yin, W.: Iteratively reweighted algorithms for compressive sensing. In: ICASSP (2008)
Cho, S., Lee, S.: Fast motion deblurring. In: ACM SIGGRAPH ASIA (2009)
Fergus, R., Singh, B., Hertzmann, A., Roweis, S.T., Freeman, W.T.: Removing camera shake from a single photograph. In: ACM SIGGRAPH (2006)
Krishnan, D., Tay, T., Fergus, R.: Blind deconvolution using a normalized sparsity measure. In: CVPR (2011)
Krishnan, D., Fergus, R.: Fast image deconvolution using hyper-Laplacian priors. In: NIPS (2009)
Kundur, D., Hatzinakos, D.: Blind image deconvolution. IEEE Signal Process. Mag. 13(3), 43–64 (1996)
Levin, A., Fergus, R., Durand, F., Freeman, W.T.: Deconvolution using natural image priors. Technical report, MIT (2007)
Levin, A., Weiss, Y., Durand, F., Freeman, W.: Understanding and evaluating blind deconvolution algorithms. In: CVPR (2009)
Levin, A., Weiss, Y., Durand, F., Freeman, W.T.: Understanding blind deconvolution algorithms. IEEE Trans. Pattern Anal. Mach. Intell. 33(12), 2354–2367 (2011)
Levin, A., Weiss, Y., Durand, F., Freeman, W.T.: Efficient marginal likelihood optimization in blind deconvolution. In: CVPR (2011)
Miskin, J.W., MacKay, D.J.C.: Ensemble learning for blind image separation and deconvolution. In: Advances in Independent Component Analysis (2000)
Palmer, J.A.: Relatve convexity. Technical report, UCSD (2003)
Palmer, J.A., Wipf, D.P., Kreutz-Delgado, K., Rao, B.D.: Variational EM algorithms for non-Gaussian latent variable models. In: NIPS (2006)
Shan, Q., Jia, J., Agarwala, A.: High-quality motion deblurring from a single image. In: ACM SIGGRAPH (2008)
Xu, L., Jia, J.: Two-phase kernel estimation for robust motion deblurring. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part I. LNCS, vol. 6311, pp. 157–170. Springer, Heidelberg (2010)
Wipf, D.P., Rao, B.D., Nagarajan, S.S.: Latent variable Bayesian models for promoting sparsity. IEEE Tran. Info. Theory 57(9), 6236–6255 (2011)
Wipf, D., Zhang, H.: Revisiting Bayesian blind deconvolution. MSRA Tech Report (March 2013)
Zhang, H., Wipf, D.: Non-uniform blind deblurring with a spatially adaptive prior. MSRA Tech Report (April 2013)
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Wipf, D., Zhang, H. (2013). Analysis of Bayesian Blind Deconvolution. In: Heyden, A., Kahl, F., Olsson, C., Oskarsson, M., Tai, XC. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2013. Lecture Notes in Computer Science, vol 8081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40395-8_4
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DOI: https://doi.org/10.1007/978-3-642-40395-8_4
Publisher Name: Springer, Berlin, Heidelberg
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