Paper:
Non-Uniform Camera Shake Removal Using a Spatially-Adaptive Sparse Penalty
Typical blur from camera shake often deviates from the standard uniform convolutional assumption, in part because of problematic rotations which create greater blurring away from some unknown center point. Consequently, successful blind deconvolution for removing shake artifacts requires the estimation of a spatiallyvarying or non-uniform blur operator. Using ideas from Bayesian inference and convex analysis, this paper derives a simple non-uniform blind deblurring algorithm with a spatially-adaptive image penalty. Through an implicit normalization process, this penalty automatically adjust its shape based on the estimated degree of local blur and image structure such that regions with large blur or few prominent edges are discounted. Remaining regions with modest blur and revealing edges therefore dominate on average without explicitly incorporating structureselection heuristics. The algorithm can be implemented using an optimization strategy that is virtually tuning-parameter free and simpler than existing methods, and likely can be applied in other settings such as dictionary learning. Detailed theoretical analysis and empirical comparisons on real images serve as validation.

Review:
The paper addresses the problem of single image blind 
      deconvolution with non-uniform blur caused by camera shake. The authors 
      propose a two step procedure: first to estimate the motion blur and second 
      the recovery of the sought-after latent image through non-blind 
      deconvolution. This procedure is common practice in blind deconvolution. 
      The main contribution made here is the derivation of a Bayesian inference 
      strategy for motion blur estimation. In a number of experiments the 
      authors demonstrate the validity of their approach and compare its 
      performance against other state-of-the-art methods. The mathematical 
      derivation appears sound and the proposed scheme is claimed to exhibit a 
      number of favourable properties. Although these details are discussed in 
      some detail in the second half of Section 4, no empirical evidence is 
      given, which would strengthen the argumentation and verify the claims 
      made. The authors also miss to make connections to other recent approaches 
      that advocate a similar line of reasoning, in particular [15] and the 
      missing reference: S.D.Babacan, et al., "Bayesian Blind 
      Deconvolution with General Sparse Image Priors", ECCV 2012 In 
      addition, the authors miss another relevant reference, namely 
      R.Kohler, et al., "Recording and playback of camera shake: 
      Benchmarking blind deconvolution with a real-world database." ECCV 2012. 
      that would allow them to benchmark their approach against other 
      state-of-the-art single image blind deblurring methods for both uniform 
      and non-uniform blur. Besides, a number of questions remain unanswered 
      (see below) in the presented exposition, that lower the overall quality of 
      the paper. The paper is clearly structured and well written. 
      Section 4 would benefit from a division in smaller subsections as it feels 
      a bit lengthy for my tasting. Unfortunately, some important details are 
      missing (e.g. which algorithm is used for the final non-blind 
      deconvolution, see also comments below), which impair the overall clarity 
      of the paper. The theoretical foundation of the proposed approach 
      build on previous work [19,26], however its application to the problem of 
      single image blind deconvolution seems novel. Although the 
      presented algorithm seems to deliver comparable results to 
      state-of-the-art algorithms, the provided insights are very limited. It 
      remains unclear in which situations/cases the proposed method works better 
      and why. It also fails to make connections to other recent relevant work 
      (see above) and place its contribution into context, which lowers its 
      significance considerably. Further comments: * What method is 
      employed for the final non-blind deconvolution? * It is stated, that 
      the approach is "parameter-free". Is this also true for the kernel size? 
      * It is mentioned in Section 4, that initialization with a large 
      $\lambda$ and its subsequent evolution render the deconvolution process 
      more stable. It would be interesting to see a plot that shows the 
      evolution of $\lambda$ in the course of the motion blur estimation 
      process. * What basis (i.e. $B$ in Eq.(8)) is chosen for the 
      experiments with non-uniform blur? Is $w^\bar_i$ evaluated for every 
      pixel? If not, how are the evaluation locations chosen? * From the 
      main paper it is not clear that a coarse-to-fine scheme is employed. Great 
      if this could be made clearer. * What are typical run-times for the 
      proposed method? * Large blur is challenging even for state-of-the-art 
      methods. How does performance scale with kernels size? * The ringing 
      artifacts in Whyte's result in Fig.4 are stemming primarily from the final 
      non-blind deconvolution (see his talk slides). It would be more fair to 
      use the one published on the accompanying project webpage 
      (http://www.di.ens.fr/willow/research/deblurring/). * The correct 
      reference for the efficient filter flow framework mentioned in Section 2 
      is M.Hirsch, et al., "Efficient filter flow for space-variant 
      multiframe blind deconvolution." CVPR 2010. * What are the limitations 
      of the proposed approach?