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Point spread function estimation for blind image deblurring problems based on framelet transform

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Abstract

One of the most important issues in image processing is the approximation of the image that has been lost due to the blurring process. These types of matters are divided into non-blind and blind problems. The second type of problem is more complex in terms of calculations than the first problem due to the unknown of original image and point spread function estimation. In the present paper, an algorithm based on coarse-to-fine iterative by \(l_{0}-\alpha l_{1}\) regularization and framelet transform is introduced to approximate the spread function estimation. Framelet transfer improves the restored kernel due to the decomposition of the kernel to different frequencies. Also, in the proposed model, a fraction gradient operator is used instead of the ordinary gradient operator. The proposed method is investigated on different kinds of images such as text, face and natural. The output of the proposed method reflects the effectiveness of the proposed algorithm in restoring images from blind problems.

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Notes

  1. See: http://vllab.ucmerced.edu/wlai24/cvpr16_deblur_study/ and https://jspan.github.io/projects/text-deblurring/index.html.

  2. See:https://webdav.tuebingen.mpg.de/pixel/benchmark4camerashake/.

References

  1. Hu, D., Tan, J., Zhang, L., Ge, X.: Image deblurring based on enhanced salient edge selection. Vis. Comput. (2021). https://doi.org/10.1007/s00371-021-02329-6

    Article  Google Scholar 

  2. Feng, Q., Fei, H., Wencheng, W.: Blind image deblurring with reinforced use of edges. Vis. Comput. 35(6), 1081–1090 (2019)

    Article  Google Scholar 

  3. Khan, A., Yin, H.: Arbitrarily shaped point spread function (PSF) estimation for single image blind deblurring. Vis. Comput. 37(7), 1661–1671 (2021)

    Article  Google Scholar 

  4. Hansen, P.C., Nagy, J.G., Oleary, D.P.: Deblurring Images: Matrices, Spectra, and Filtering. Society for Industrial and Applied Mathematics, Philadelphia (2006)

    Book  Google Scholar 

  5. Christiansen, M., Hanke, M.: Deblurring methods using antireflective boundary conditions. SIAM J. Sci. Comput. 30(2), 855–872 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Campisi, P., Egiazarian, K. (eds.): Blind Image Deconvolution: Theory and Applications. CRC Press, Boca Raton (2017)

    MATH  Google Scholar 

  7. Liu, G., Huang, T.Z., Liu, J., Lv, X.-G.: Total variation with overlapping group sparsity for image deblurrinag under impulse noise. PLoS ONE 10(4), e0122562 (2015)

    Article  Google Scholar 

  8. Parvaz, R.: Color image restoration with impulse noise based on fractional-order total variation and framelet (2021). arXiv preprint arXiv:2110.15170

  9. Rajagopalan, A.N., Chellappa, R. (eds.): Motion Deblurring: Algorithms and Systems. Cambridge University Press, Cambridge (2014)

    Google Scholar 

  10. Cho, S., Lee, S.: Fast motion deblurring. In: ACM SIGGRAPH Asia 2009 papers, pp. 1–8 (2009)

  11. Whyte, O., Sivic, J., Zisserman, A.: Deblurring shaken and partially saturated images. Int. J. Comput. Vis. 110(2), 185–201 (2014)

    Article  Google Scholar 

  12. Pan, J., Hu, Z., Su, Z., Yang, M.-H.: \( l_0 \)-regularized intensity and gradient prior for deblurring text images and beyond. IEEE Trans. Pattern Anal. Mach. Intell. 39(2), 342–355 (2016)

    Article  Google Scholar 

  13. Cai, J.-F., Osher, S., Shen, Z.: Linearized Bregman iterations for frame-based image deblurring. SIAM J. Imaging Sci. 2(1), 226–252 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Liu, J., Lou, Y., Ni, G., Zeng, T.: An image sharpening operator combined with framelet for image deblurring. Inverse Probl. 36(4), 045015 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  15. Levin, A., Weiss, Y., Durand, Fredo, F., William, T.: Understanding and evaluating blind deconvolution algorithms. In: 2009 IEEE Conference on Computer Vision and Pattern Recognition, pp. 1964–1971. IEEE (2009)

  16. Liu, J., Ni, A., Ni, G.: A nonconvex \(l_1(l_1-l-2)\) model for image restoration with impulse noise. J. Comput. Appl. Math. 378, 112934 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  17. Lou, Y., Yan, M.: Fast \(L_1-L_2\) minimization via a proximal operator. J. Sci. Comput. 74(2), 767–785 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yang, X.-J.: General Fractional Derivatives: Theory, Methods and Applications. CRC Press, Boca Raton (2019)

    Book  MATH  Google Scholar 

  19. Guo, L., Zhao, X.-L., Gu, X.-M., Zhao, Y.-L., Zheng, Y.-B., Huang, T.-Z.: Three-dimensional fractional total variation regularized tensor optimized model for image deblurring. Appl. Math. Comput. 404, 126224 (2021)

    MathSciNet  MATH  Google Scholar 

  20. Fairag, F., Al-Mahdi, A., Ahmad, S.: Two-level method for the total fractional-order variation model in image deblurring problem. Numer. Algorithms 85(3), 931–950 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  21. Shi, M., Han, T., Liu, S.: Total variation image restoration using hyper-Laplacian prior with overlapping group sparsity. Signal Process. 126, 65–76 (2016)

    Article  Google Scholar 

  22. Dong, J., Pan, J., Ren, J., Lin, L., Tang, J., Yang, M.-H.: Learning spatially variant linear representation models for joint filtering. IEEE Trans. Pattern Anal. Mach. Intell. 01, 1 (2021)

    Google Scholar 

  23. Yuan, Q., Li, J., Zhang, L., Wu, Z., Liu, G.: Blind motion deblurring with cycle generative adversarial networks. Vis. Comput. 36(8), 1591–1601 (2020)

    Article  Google Scholar 

  24. Dong, J., Roth, S., Schiele, B.: DWDN: deep wiener deconvolution network for non-blind image deblurring. IEEE Trans. Pattern Anal. Mach. Intell. 01, 1 (2021)

    Google Scholar 

  25. Shan, Q., Jia, J., Agarwala, A.: High-quality motion deblurring from a single image. ACM Trans. Graph. TOG 27(3), 1–10 (2008)

    Article  Google Scholar 

  26. Pan, J., Hu, Z., Su, Z., Yang, M.-H.: Deblurring text images via L0-regularized intensity and gradient prior. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2901–2908 (2014)

  27. Li, J., Lu, W.: Blind image motion deblurring with L0-regularized priors. J. Vis. Commun. Image Represent. 40, 14–23 (2016)

    Article  Google Scholar 

  28. Zhang, F., Lu, W., Liu, H., Xue, F.: Natural image deblurring based on \(l_0\)-regularization and kernel shape optimization. Multimedia Tools Appl. 77(20), 26239–26257 (2018)

    Article  Google Scholar 

  29. Zhao, C., Wang, Y., Jiao, H., Yin, J., Li, X.: \( L_p \)-Norm-based sparse regularization model for license plate deblurring. IEEE Access 8, 22072–22081 (2020)

    Article  Google Scholar 

  30. Estatico, C., Gratton, S., Lenti, F., Titley-Peloquin, D.: A conjugate gradient like method for p-norm minimization in functional spaces. Numer. Math. 137(4), 895–922 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  31. Repetti, A., Pham, M.Q., Duval, L., Chouzenoux, E., Pesquet, J.-C.: Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed \({\ell _1}/{\ell _2} \) Regularization. IEEE Signal Process. Lett. 22(5), 539–543 (2014)

    Article  Google Scholar 

  32. Lou, Y., Osher, S., Xin, J.: Computational aspects of constrained \(L_1-L_2\) minimization for compressive sensing. In: Modelling, Computation and Optimization in Information Systems and Management Sciences, pp. 169–180. Springer, Cham (2015)

  33. Ron, A., Shen, Z.: Affine systems in \(L_2(R^d)\): the analysis of the analysis operator. J. Funct. Anal. 148(2), 408–447 (1997)

    Article  MathSciNet  Google Scholar 

  34. Chai, A., Shen, Z.: Deconvolution: a wavelet frame approach. Numer. Math. 106(4), 529–587 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  35. Daubechies, I., Han, B., Ron, A., Shen, Z.: Framelets: MRA-based constructions of wavelet frames. Appl. Comput. Harmonic Anal. 14(1), 1–46 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  36. Mainardi, F.: Fractional calculus: theory and applications. Mathematics 6, 145 (2018)

    Article  MATH  Google Scholar 

  37. Cafagna, D.: Fractional calculus: a mathematical tool from the past for present engineers [Past and present]. IEEE Ind. Electron. Mag. 1(2), 35–40 (2007)

    Article  Google Scholar 

  38. Sridevi, G., Srinivas Kumar, S.: Image inpainting based on fractional-order nonlinear diffusion for image reconstruction. Circuits Syst. Signal Process. 38(8), 3802–3817 (2019)

    Article  Google Scholar 

  39. Xu, L., Lu, C., Xu, Y., Jia, J.: Image smoothing via L 0 gradient minimization. In: Proceedings of the 2011 SIGGRAPH Asia conference, pp. 1–12 (2011)

  40. Cai, J.-F., Osher, S., Shen, Z.: Split Bregman methods and frame based image restoration. Multiscale Model. Simul. 8(2), 337–369 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  41. Goldstein, T., Osher, Stanley: The split Bregman method for L1-regularized problems. SIAM J. Imaging Sci. 2(2), 323–343 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  42. Beck, A.: First-Order Methods in Optimization. Society for Industrial and Applied Mathematics, Philadelphia (2017)

    Book  MATH  Google Scholar 

  43. Liu, R., Jia, J.: Reducing boundary artifacts in image deconvolution. In: 2008 15th IEEE International Conference on Image Processing, pp. 505–508. IEEE (2008)

  44. Wang, Z., Li, Q.: Information content weighting for perceptual image quality assessment. IEEE Trans. Image Process. 20(5), 1185–1198 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  45. Wang, Z., Simoncelli, E.P., Bovik, A.C.: Multiscale structural similarity for image quality assessment. In: The Thrity-Seventh Asilomar Conference on Signals, Systems and Computers, 2003, vol. 2, pp. 1398–1402. IEEE (2003)

  46. Zhang, L., Zhang, L., Mou, X., Zhang, D.: FSIM: A feature similarity index for image quality assessment. IEEE Trans. Image Process. 20(8), 2378–2386 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  47. Wen, F., Ying, R., Liu, Y., Liu, P., Truong, T.-K.: A simple local minimal intensity prior and an improved algorithm for blind image deblurring. IEEE Trans. Circuits Syst. Video Technol. 31, 2923–2937 (2020)

    Article  Google Scholar 

  48. Völcker, A.: The influence of scanning mobile apps on consumer behavior regarding cosmetic products. Master’s thesis, Handelshøyskolen BI (2021)

  49. Lai, W.-S., Huang, J.-B., Hu, Z., Ahuja, N., Yang, M.-H.: A comparative study for single image blind deblurring. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1701–1709 (2016)

  50. Xu, L., Jia, J.: Two-phase kernel estimation for robust motion deblurring. In: European Conference on Computer Vision, pp. 157–170. Springer, Berlin, Heidelberg (2010)

  51. Krishnan, D., Tay, T., Fergus, R.: Blind deconvolution using a normalized sparsity measure. In: CVPR 2011, pp. 233–240. IEEE (2011)

  52. Xu, L., Zheng, S., Jia, J.: Unnatural l0 sparse representation for natural image deblurring. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1107–1114 (2013)

  53. Pan, J., Sun, D., Pfister, H., Yang, M.-H.: Blind image deblurring using dark channel prior. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1628–1636 (2016)

  54. He, K., Sun, J., Tang, X.: Single image haze removal using dark channel prior. IEEE Trans. Pattern Anal. Mach. Intell. 33(12), 2341–2353 (2010)

    Google Scholar 

  55. Hu, Z., Cho, S., Wang, J., Yang, M.-H.: Deblurring low-light images with light streaks. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3382–3389 (2014)

  56. Zhou, C., Teng, M., Han, J., Xu, C., Shi, B.: DeLiEve-Net: deblurring low-light images with light streaks and local events. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 1155–1164 (2021)

  57. Köhler, R., Hirsch, M., Mohler, B., Schölkopf, B., Harmeling, S.: Recording and playback of camera shake: benchmarking blind deconvolution with a real-world database. In: European Conference on Computer Vision, pp. 27–40. Springer, Berlin, Heidelberg (2012)

  58. Hirsch, M., Schuler, C.J., Harmeling, S., Schölkopf, B.: Fast removal of non-uniform camera shake. In: 2011 International Conference on Computer Vision, pp. 463–470. IEEE (2011)

  59. Fergus, R., Singh, B., Hertzmann, A., Roweis, S.T., Freeman, W.T.: Removing camera shake from a single photograph. In: ACM SIGGRAPH 2006 Papers, pp. 787–794 (2006)

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I would like to thank the referees and the editor for their valuable comments to improve the manuscript.

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  1. Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, 56199-11367, Iran

    Reza Parvaz

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Parvaz, R. Point spread function estimation for blind image deblurring problems based on framelet transform. Vis Comput 39, 2653–2669 (2023). https://doi.org/10.1007/s00371-022-02484-4

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