Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

access icon free Image super-resolution reconstruction using the high-order derivative interpolation associated with fractional filter functions

© The Institution of Engineering and Technology
Received 16/10/2015, Accepted 17/06/2016, Revised 27/05/2016, Published 20/06/2016

In this stydy, the authors present a single image super-resolution (SISR) reconstruction based on high-order derivative interpolation (HDI) in the fractional Fourier transform (FRFT) domain. First, the HDI formula is derived using a simple technique, which is based on the relationship between the fractional band-limited signal and the traditional band-limited signal. This interpolation formula contains the derivative information of the image and the FRFT domain filter functions (FDFF). Moreover, the advantages of the FDFF are also analysed. Second, the new SISR reconstruction is presented via the HDI. The main advantage is that the presented method involves the derivatives of an image in the resizing process. Moreover, the authors take advantage of the FDFF to resize the image. Furthermore, three evaluation criteria and some simulations are presented to validate the effectiveness of the proposed method. Last, the proposed method is applied to colour image processing. For a colour image case, the RGB colour space is chosen for super-resolution reconstruction. In addition to peak signal-to-noise ratio, the authors have also used the correlation to assess the quality of the reconstruction. Compared with many methods, extensive experimental results validate that the proposed method can obtain the better-edge characteristic, less blur and less aliasing.

Inspec keywords: interpolation; Fourier transforms; image colour analysis; image resolution; image reconstruction; filtering theory

Other keywords: single image super-resolution reconstruction; peak signal-to-noise ratio; FRFT domain filter functions; SISR reconstruction; reconstruction quality assessment; traditional band-limited signal; high-order derivative interpolation; RGB colour space; HDI; colour image processing; resizing process; fractional band-limited signal; fractional filter functions; fractional Fourier transform domain

Subjects: Integral transforms in numerical analysis; Integral transforms in numerical analysis; Interpolation and function approximation (numerical analysis); Interpolation and function approximation (numerical analysis); Filtering methods in signal processing; Computer vision and image processing techniques; Optical, image and video signal processing

References

    1. 1)
      • 37. Hore, A., Ziou, D., Deschenes, F.: ‘A new image scaling algorithm based on the sampling theorem of Papoulis and application to color images’. IEEE Fourth Int. Conf. on Image and Graphics, 2007, pp. 39–44.
    2. 2)
      • 42. Zhang, F., Tao, R., Wang, Y.: ‘Multi-channel sampling theorems for band-limited signals with fractional Fourier transform’, Sci. China Ser. E – Tech. Sci., 2008, 51, (6), pp. 790–802.
    3. 3)
      • 25. Celik, T.: ‘Image resolution enhancement using dual-tree complex wavelet transform’, IEEE Geosci. Remote Sens. Lett., 2010, 7, (3), pp. 554–557.
    4. 4)
      • 50. Xia, X.: ‘On bandlimited signals with fractional Fourier transform’, IEEE Signal Process. Lett., 1996, 3, (3), pp. 72–74.
    5. 5)
      • 22. Bose, N.K., Lertrattanapanich, S., Chappali, M.B.: ‘Superresolution with second generation wavelets’, Signal Process. Image Commun., 2004, 19, pp. 387–391.
    6. 6)
      • 4. Wang, J., Zhu, S.: ‘Resolution-invariant coding for continuous image super-resolution’, Neurocomputing, 2012, 82, pp. 21–28.
    7. 7)
      • 48. Wang, Z., Bovik, A.C., Sheikh, H.R., et al: ‘Image quality assessment: from error visibility to structural similarity’, IEEE Trans. Image Process., 2004, 13, (4), pp. 1–14.
    8. 8)
      • 9. Gonzalez, R.C., Woods, R.E.: ‘Digital image processing’ (Addison-Wesley, Reading, MA, 1992).
    9. 9)
      • 53. Munoz, A., Blu, T., Unser, M.: ‘Least-squares image resizing using finite differences’, IEEE Trans. Image Process., 2001, 10, (9), pp. 1365–1378.
    10. 10)
      • 41. Pei, S.C., Ding, J.J.: ‘Relations between fractional operations and time-frequency distributions, and their applications’, IEEE Trans. Signal Process., 2001, 49, (8), pp. 1638–1655.
    11. 11)
      • 15. Gerchberg, R.W.: ‘Super-resolution through error energy reduction’, J. Mod. Opt., 1974, 21, (9), pp. 709–720.
    12. 12)
      • 36. Kadyrov, A., Petrou, M.: ‘The trace transform and its applications’, IEEE Trans. Pattern Anal. Mach. Intell., 2001, 23, (8), pp. 811–828.
    13. 13)
      • 12. Li, X., Orchard, M.T.: ‘New edge directed interpolation’, IEEE Trans. Image Process., 2001, 10, (10), pp. 1521–1527.
    14. 14)
      • 39. Almeida, L.B.: ‘The fractional Fourier transform and time-frequency representations’, IEEE Trans. Signal Process., 1994, 42, (11), pp. 3084–3091.
    15. 15)
      • 20. Kinebuchi, K., Muresan, D.D., Parks, T.W.: ‘Image interpolation using wavelet-based hidden Markov trees’. IEEE Proc. Int. Conf. on Acoustics, Speech, and Signal Processing, 2001, pp. 7–11.
    16. 16)
      • 13. Li, M., Nguyen, T.Q.: ‘Markov random field model-based edge-directed image interpolation’, IEEE Trans. Image Process., 2008, 17, (7), pp. 1121–1128.
    17. 17)
      • 27. Ma, X., Luong, H.Q., Philips, W., et al: ‘Sparse representation and position prior based face hallucination upon classified over-complete dictionaries’, Signal Process., 2012, 92, pp. 2066–2074.
    18. 18)
      • 6. Yang, J., Wang, Z., Lin, Z., et al: ‘Coupled dictionary training for image super-resolution’, IEEE Trans. Image Process., 2012, 21, (8), pp. 3467–3478.
    19. 19)
      • 18. Champagnat, F., Besnerais, G.L.: ‘A Fourier interpretation of super-resolution techniques’. Proc. IEEE Int. Conf. on Image Processing, Italy, 2005, vol. 1, pp. 865–868.
    20. 20)
      • 1. Nasrollahi, K., Moeslund, T.B.: ‘Super-resolution: a comprehensive survey’, Mach. Vis. Appl., 2014, 25, pp. 1423–1468.
    21. 21)
      • 31. Freeman, W.T., Jones, T.R., Pasztor, E.C.: ‘Example-based super-resolution’, IEEE Comput. Graph. Appl., 2002, 22, pp. 56–65.
    22. 22)
      • 3. Kulkarni, N., Nagesh, P., Gowda, R., et al: ‘Understanding compressive sensing and sparse representation-based superresolution’, IEEE Trans. Circuits Syst. Video Technol., 2012, 22, (5), pp. 778–789.
    23. 23)
      • 29. Li, B., Chang, H., Shan, S., et al: ‘Aligning coupled manifolds for face hallucination’, IEEE Signal Process. Lett., 2009, 16, pp. 957–960.
    24. 24)
      • 46. Kim, J.K., Park, J.M., Song, K.S., et al: ‘Adaptive mammographic image enhancement using first derivative and local statistics’, IEEE Trans. Med. Imaging, 1997, 16, (5), pp. 495–502.
    25. 25)
      • 33. Gao, X.B., Zhang, K.B., Tao, D.C.: ‘Image super-resolution with sparse neighbor embedding’, IEEE Trans. Image Process., 2012, 21, (7), pp. 3194–3205.
    26. 26)
      • 51. Parker, J.A., Kenyon, R.V., Troxel, D.E.: ‘Comparison of interpolation methods for image resampling’, IEEE Trans. Med. Imaging, 1983, 2, pp. 31–39.
    27. 27)
      • 11. Lehmann, T.M., Goonner, C., Spitzer, K.: ‘Survey: interpolation methods in medical image processing’, IEEE Trans. Med. Imaging, 1999, 18, (11), pp. 1049–1075.
    28. 28)
      • 52. Thevenaz, P., Blu, T., Unser, M.: ‘Image interpolation and resampling’, in Bankman, I.N (Eds): ‘Handbook of medical imaging’ (Academic Press, 2000), pp. 393–420.
    29. 29)
      • 43. Wei, D., Ran, Q., Li, Y.: ‘Generalized sampling expansion for bandlimited signals associated with the fractional Fourier transform’, IEEE Signal Process. Lett., 2010, 17, (6), pp. 595–598.
    30. 30)
      • 30. Gao, X., Zhang, K., Tao, D., et al: ‘Joint learning for single-image super-resolution via a coupled constraint’, IEEE Trans. Image Process., 2012, 21, pp. 469–480.
    31. 31)
      • 17. Tsai, R., Huang, T.: ‘Multiframe image restoration and registration’, in Tsai, R.Y., Huang, T.S. (Eds.): ‘Advances in computer vision and image processing’ (JAI Press Inc., Stamford, 1984), vol. 1, pp. 317–339.
    32. 32)
      • 5. Yang, S., Wang, M., Chen, Y., et al: ‘Single-image superresolution reconstruction via learned geometric dictionaries and clustered sparse coding’, IEEE Trans. Image Process., 2012, 21, (9), pp. 4016–4028.
    33. 33)
      • 24. Sen, P., Darabi, S.: ‘Compressive image super-resolution’. Proc. 43rd IEEE Asilomar Conf. on Signals, Systems and Computers, USA, 2009, pp. 1235–1242.
    34. 34)
      • 10. Hou, H.S., Andrews, H.C.: ‘Cubic splines for image interpolation and digital filtering’, IEEE Trans. Acoust. Speech Signal Process., 1978, ASSP 26, pp. 508–517.
    35. 35)
      • 45. Wei, D., Ran, Q., Li, Y.: ‘Multichannel sampling and reconstruction of bandlimited signals in the linear canonical transform domain’, IET Signal Process., 2011, 5, (8), pp. 717–727.
    36. 36)
      • 32. Yang, J.C., Wright, J., Huang, T.S., et al: ‘Image super-resolution via sparse representation’, IEEE Trans. Image Process., 2010, 19, (11), pp. 2861–2873.
    37. 37)
      • 16. Santis, P.D., Gori, F.: ‘On an iterative method for super-resolution’, J. Mod. Opt., 1975, 22, (8), pp. 691–695.
    38. 38)
      • 54. Fornberg, B.: ‘Numerical differentiation of analytic functions’, ACM Trans. Math. Softw., 1981, 7, (4), pp. 512–526.
    39. 39)
      • 2. Park, S.C., Park, M.K., Kang, M.G.: ‘Super-resolution image construction – a technical overview’, IEEE Signal Process. Mag., 2003, 20, pp. 21–36.
    40. 40)
      • 55. Pei, S.C., Tam, I.K.: ‘Effective color interpolation in CCD color filter arrays using signal correlation’, IEEE Trans. Circuits Syst. Video Technol., 2003, 13, (6), pp. 503–513.
    41. 41)
      • 26. Velisavljevic, V., Coquoz, R.: ‘Image interpolation with directionlets’. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, 2008, pp. 837–840.
    42. 42)
      • 19. Carey, W.K., Chang, D.B., Hermami, S.S.: ‘Regularity-preserving image interpolation’, IEEE Trans. Image Process., 1999, 8, (5), pp. 1293–1297.
    43. 43)
      • 38. Zhang, X.J., Wu, X.L.: ‘Image interpolation by adaptive 2-D autoregressive modeling and soft-decision estimation’, IEEE Trans. Image Process., 2008, 17, (6), pp. 887–896.
    44. 44)
      • 49. Papoulis, A.: ‘Generalized sampling expansion’, IEEE Trans. Circuit Syst., 1977, CAS-24, (11), pp. 652–654.
    45. 45)
      • 47. Griffin, L.D.: ‘The second order local image structure solid’, IEEE Trans. Pattern Anal. Mach. Intell., 2007, 29, (8), pp. 1355–1366.
    46. 46)
      • 14. Han, J.W., Kim, J.H., Sull, S.: ‘New edge-adaptive image interpolation using anisotropic Gaussian filters’, Digit. Signal Process., 2013, 20, (1), pp. 110–117.
    47. 47)
      • 8. Fifman, S.: ‘Digital rectification of ERTS multispectral imagery’. Proc. Symp. on Significant Results Obtained from the Earth Resources Technology Satellite-1, 1973, vol. 1, pp. 1131–1142.
    48. 48)
      • 40. Ozaktas, H.M., Zalevsky, Z., Kutay, M.A.: ‘The Fractional Fourier transform with applications in optics and signal processing’ (Wiley, New York, 2001).
    49. 49)
      • 44. Shi, J., Chi, Y., Zhang, N.: ‘Multichannel sampling and reconstruction of bandlimited signals in fractional domain’, IEEE Signal Process. Lett., 2010, 17, (11), pp. 909–912.
    50. 50)
      • 7. Sun, D., Gao, Q., Lu, Y., et al: ‘A high quality single-image super-resolution algorithm based on linear Bayesian MAP estimation with sparsity prior’, Digit. Signal Process., 2014, 35, pp. 45–52.
    51. 51)
      • 23. Ginesu, G., Dess, T., Atzori, L., et al: ‘Super-resolution reconstruction of video sequences based on back-projection and motion estimation’. Proc. Int. Conf. on Mobile Multimedia Communications, UK, 2009.
    52. 52)
      • 21. Demirel, H., Anbarjafari, G.: ‘Satellite image resolution enhancement using complex wavelet transform’, IEEE Geosci. Remote Sens. Lett., 2010, 7, (1), pp. 123–126.
    53. 53)
      • 56. Battiato, S., Gallo, G., Stanco, F.: ‘A locally-adaptive zooming algorithm for digital images’, Elsevier Image Vis. Comput. J., 2001, 20, (11), pp. 805–812.
    54. 54)
      • 35. Dong, W.S., Zhang, L., Lukac, R., et al: ‘Sparse representation based image interpolation with nonlocal autoregressive modeling’, IEEE Trans. Image Process., 2013, 22, (4), pp. 1382–1394.
    55. 55)
      • 28. Huang, H., He, H., Fan, X., et al: ‘Super-resolution of human face image using canonical correlation analysis’, Pattern Recognit., 2010, 43, pp. 2532–2543.
    56. 56)
      • 34. Lakshman, H., Lim, W.Q., Schwarz, H.: ‘Image interpolation using shearlet based iterative refinement’. Computer Vision and Pattern Recognition, 2013.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-spr.2015.0444
Loading

Related content

content/journals/10.1049/iet-spr.2015.0444
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
Print this page
This is a required field
Please enter a valid email address