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variant of the superresolution alignment with Whittaker- Tikhonov regularisation and large regularisation parameter γ=0.3 is used for the displacement estimation, followed by the actual MSE/PSNR computation with TV regularisation and γ= 0.03. The latter method gives in a few cases a slightly lower PSNR than the ground-truth displacement, but otherwise approximates the previous scenario well. It is evident that the variation of PSNR measures is reduced to about half with respect to the measurements with bicubic interpolation, both in terms of the amplitude between maximal and minimal PSNR and the standard deviation. With an amplitude of 1.2dB it is close to the variation of the shift-free subset of 0.7dB as reported in Section II. VI. SUMMARY AND OUTLOOK In this paper we have studied the reliability of MSE/PSNR measurements for the quality assessment of blind deconvo- lution results, where the necessity arises to compare images that may be shifted relative to each other by non-integer displacements. An experimental study of simple alignment procedures with bilinear and bicubic interpolation showed that it introduces substantial deviations into the discrepancy measures in question. Comparisons of blind deconvolution methods should therefore not be based on such procedures. As an attempt to overcome this difficulty, we have designed a superresolution-based error measurement procedure that can substantially reduce the variations in MSE/PSNR estimates induced by the alignment step, leaving error margins that are closer to the uncertainty in shift-free cases. In future work, these tests will have to be extended to more test cases. The applicability of the proposed procedure to other error measures such as MSSIM [17] or perceptual similaritymeasures [13]will be studied.Further analysiswill bedevoted to theobservedvariationoferrormeasuresamong the shift-free reconstructed images. It will also be of interest to include the PSF into the displacement estimation. Furthermore, the proposed approach will be used for comparisons between blind deconvolution methods. Taking into account the results from the present contribution and TABLE III STATISTICS OF DISPLACEMENT MISESTIMATIONSδx,δy AND PSNR FOR 256 RECONSTRUCTED IMAGES WITH SUPERRESOLUTION-BASED ALIGNMENT WITH TV REGULARISATION, (A) USING EXACT DISPLACEMENTS, (B) ESTIMATING DISPLACEMENTS BY MSE MINIMISATION WITH TV REGULARISATION, (C) ESTIMATING DISPLACEMENTS BY MSE MINIMISATION WITH WHITTAKER-TIKHONOV REGULARISATION. Setting (a) (b) (c) max|δx| 0.09 0.09 std.dev. δx 0.037 0.033 max|δy| 0.08 0.08 std.dev. δy 0.031 0.036 min PSNR 29.38 29.40 29.40 max PSNR 30.47 30.63 30.46 (max−min) PSNR 1.09 1.23 1.06 mean PSNR 29.93 29.98 29.92 std.dev. PSNR 0.240 0.263 0.236 the envisioned more extensive studies will help to assess the significance of method differences in such work. REFERENCES [1] M.S.C.AlmeidaandL.B.Almeida, “Blindandsemi-blinddeblurring of natural images,” IEEE Transactions on Image Processing, vol. 19, no. 1, pp. 36–52, 2010. [2] L. Bar, N. Sochen, and N. Kiryati, “Variational pairing of image segmentationandblind restoration,” inComputerVision–ECCV2004, Part II, ser.LectureNotes inComputerScience,T.PajdlaandJ.Matas, Eds. Berlin: Springer, 2004, vol. 3022, pp. 166–177. [3] T. F. Chan and C. K. Wong, “Total variation blind deconvolution,” IEEE Transactions on Image Processing, vol. 7, pp. 370–375, 1998. [4] T. F. Chan, A. M. Yip, and F. E. Park, “Simultaneous total variation image inpainting and blind deconvolution,” International Journal of Imaging Systems and Technology, vol. 15, no. 1, pp. 92–102, 2005. [5] R. Fergus, B. Singh, A. Hertzmann, S. T. Roweis, and W. T. Free- man, “Removing camera shake from a single photograph,” in Proc. SIGGRAPH 2006, New York, NY, July 2006, pp. 787–794. [6] V. Katkovnik, D. Paliy, K. Egiazarian, and J. Astola, “Frequency domain blind deconvolution in multiframe imaging using anisotropic spatially-adaptive denoising,” in 14th European Signal Processing Conference (EUSIPCO 2006). Florence, Italy: EURASIP, 2006. [7] R. Ko¨hler, M. Hirsch, B. Mohler, B. Scho¨lkopf, and S. Harmeling, “Recording and playback of camera shake: Benchmarking blind de- convolution with a real-world database,” in Computer Vision – ECCV 2012, Part VII, ser. Lecture Notes inComputer Science, A. Fitzgibbon, S. Lazebnik, P. Perona, Y. Sato, and C. Schmid, Eds. Berlin: Springer, 2012, vol. 7578, pp. 27–40. [8] A. Levin, Y. Weiss, F. Durand, and W. T. Freeman, “Understanding and evaluating blind deconvolution algorithms,” in IEEE Conference on Computer Vision and Pattern Recognition, 2009, pp. 1964–1971. [9] ——, “Efficient marginal likelihood optimization in blind deconvolu- tion,” in IEEE Conference on Computer Vision and Pattern Recogni- tion, 2011, pp. 2657–2664. [10] D. Li, R. M. Mersereau, and S. Simske, “Blind image deconvolution through support vector regression,” IEEE Transactions on Neural Networks, vol. 18, no. 3, pp. 931–935, 2007. [11] G. Liu, S. Chang, and Y. Ma, “Blind image deblurring using spectral properties of convolution operators,” IEEE Transactions on Image Processing, vol. 23, no. 12, pp. 5047–5056, 2014. [12] P. Moser and M. Welk, “Robust blind deconvolution using convolution spectra of images,” in 1st OAGM-ARW Joint Workshop: Vision Meets Robotics, K. Niel, P. M. Roth, and M. Vincze, Eds. Wels, Austria: O¨sterreichische Computer-Gesellschaft, 2016, pp. 69–78. [13] R. Reisenhofer, S. Bosse, G. Kutyniok, and T. Wiegand, “A Haar wavelet-based perceptual similarity index,” arXiv.org, Tech. Rep. cs:1607.06140, 2016. [14] K. Schelten, S. Nowozin, J. Jancsary, C. Rother, and S. Roth, “Inter- leaved regression tree field cascades for blind image deconvolution,” in IEEE Winter Conference on Applications of Computer Vision, 2015, pp. 494–501. [15] J. Tian and K.-K. Ma, “A survey on super-resolution imaging,” Signal, Image and Video Processing, vol. 5, pp. 329–342, 2011. [16] C. R. Vogel and M. E. Oman, “Fast, robust total variation-based reconstruction of noisy, blurred images,” IEEE Transactions on Image Processing, vol. 7, pp. 813–824, 1998. [17] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600–612, 2004. [18] M. Welk, “A robust variational model for positive image deconvolu- tion,” Signal, Image and Video Processing, vol. 10, no. 2, pp. 369–378, 2016. [19] M. Welk, J. Weickert, and G. Steidl, “A four-pixel scheme for singular differential equations,” in Scale Space and PDE Methods in Computer Vision, ser. Lecture Notes in Computer Science, R. Kimmel, N. Sochen, and J. Weickert, Eds. Berlin: Springer, 2005, vol. 3459, pp. 585–597. [20] L. Xu, S. Zheng, and J. Jia, “Unnatural L0 sparse representation for natural image deblurring,” in IEEE Conference on Computer Vision and Pattern Recognition, 2013, pp. 1107–1114. [21] Y.-L. You and M. Kaveh, “Anisotropic blind image restoration,” in Proc. 1996 IEEE International Conference on Image Processing, vol. 2, Lausanne, Switzerland, Sept. 1996, pp. 461–464. 139