IEIE Transactions on Smart Processing and Computing

The Institute of Electronics and Information Engineers (대한전자공학회)
권호 표지
DOI QR코드

DOI QR Code

Review of the Application of Wavelet Theory to Image Processing

  • Vyas, Aparna (Image Processing and Intelligent Systems Laboratory, Graduate School of Advanced Imaging Science, Multimedia, and Film, Chung Ang University) ;
  • Paik, Joonki (Image Processing and Intelligent Systems Laboratory, Graduate School of Advanced Imaging Science, Multimedia, and Film, Chung Ang University)
  • Received : 2016.11.16
  • Accepted : 2016.12.06
  • Published : 2016.12.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper reviews recent published works dealing with the application of wavelets to image processing based on multiresolution analysis. After revisiting the basics of wavelet transform theory, various applications of wavelets and multiresolution analysis are reviewed, including image denoising, image enhancement, super-resolution, and image compression. In addition, we introduce the concept and theory of quaternion wavelets for the future advancement of wavelet transform and quaternion multiresolution applications.

Keywords

References

  1. Grossmann, A. and J. Morlet, "Decomposition of Hardy functions into square integrable wavelets of constant shape", SIAM J. Anal. 15, pp. 723-736, 1984. Article (CrossRefLink) https://doi.org/10.1137/0515056
  2. C. K. Chui, "An Introduction to Wavelets", Boston, Academic Press, 1992.
  3. I. Daubechies, "Ten Lectures on Wavelets", Capital City Press, 1992. Article (CrossRefLink)
  4. Y. Meyer, "Wavelets Algorithms and Applications", Philadelphia:SIAM, 1993.
  5. Hernandez and Weiss, "A first course on Wavelets", CRC Press, 1996.
  6. G. Kaiser, "A Friendly Guide to Wavelets", Boston, Birkhauser, 1994.
  7. S. G. Mallat, "A theory for multiresolution signal decomposition: the wavelet representation", IEEE Trans Pattern Analysis and Machine Intelligence, 11(7), 674-93, 1989. Article (CrossRefLink) https://doi.org/10.1109/34.192463
  8. S. G. Mallat, "Multiresolution approximations and wavelet orthonormal bases of L^2(R)", Trans. Amer. Math. Soc., 315(1), 69-87, 1989. Article (CrossRefLink), Article (CrossRefLink) https://doi.org/10.1090/S0002-9947-1989-1008470-5
  9. S. G. Mallat, "A wavelet tour of signal processing", Academic press, San Diego, California, USA, 1998.
  10. S. Mallat and W. L. Hwang, "Singularity detection and processing with Wavelets", IEEE Transactions on Information Theory, 38 (2), 617-643, 1992. Article (CrossRefLink) https://doi.org/10.1109/18.119727
  11. Y. Xu, B. Weaver and D. M. Healy, "Wavelet transform domain filters: A spatially selective noise filtration technique", IEEE Transactions on Image Processing, 3(6), 217-237, 1994.
  12. D. L Donoho and I. M. John stone, "Ideal spatial adaptation via wavelet shrinkage", Biometrika, 81 (3), 425-455, 1994. Article (CrossRefLink) https://doi.org/10.1093/biomet/81.3.425
  13. D. L Donoho, "De-Noising by Soft-Threshold", IEEE Transactions on Information Theory, 41(3), 613-627, 1995. Article (CrossRefLink) https://doi.org/10.1109/18.382009
  14. D. L. Donoho and I. M. John stone, "Adapting to Unknown Smoothness via Wavelet Shrinkage", Journal of American Stat Assoc, 12, 1200- 1224, 1995. Article (CrossRefLink)
  15. J. C. Wood and K. Johnson, "Wavelet-denoising of complex magnetic resonance images", IEEE, 1998. Article (CrossRefLink)
  16. W. L. Rosenbaum, M. S. Atkinsa and G. E. Sarty, "Classification and performance of denoising algorithms for low signal to noise ratio magnetic resonance images", SPIE, 3979 , 2000.
  17. F. Argenti and G. Torricelli, "Speckle suppression in ultrasonic images based on undecimated wavelets", EURASIP Journal on Applied Signal Processing, 2003. Article (CrossRefLink)
  18. J. Xie, D. Zhang, and W. Xu, "Spatially adaptive wavelet denoising using the minimum description length principle", IEEE Transactions on Image Processing, 13(2) ,2004. Article (CrossRefLink)
  19. A. M. Wink and Jos B. T. M. Roerdink, "Denoising functional MR Images - a comparison of wavelet denoising and gaussian smoothing", IEEE Transactions on Medical Imaging, 23(3), 2004. Article (CrossRefLink)
  20. H. Choi and R. G. Baranuik, "Multiple wavelet basis image denoising using besov ball projections", IEEE Signal Processing Letters, 11(9), 2004. Article (CrossRefLink)
  21. B. J. Yoon and P. P. Vaidyanathan, "Wavelet-based denoising by customized thresholding". IEEE Int. Conf. on Acoustics, Speech, and signal processing (ICASSP), 2004.
  22. T. C. Hsung, D. P. Kong Lun and K. C. Ho, "Optimizing the multiwavelet shrinkage denoising", IEEE Transactions on Signal Processing, 53(1), 2005.
  23. S. Poornachandra, "Wavelet-based denoising using subband dependent threshold for ECG signals", Digital Signal Processing, 18, 49-55, 2008. Article (CrossRefLink) https://doi.org/10.1016/j.dsp.2007.09.006
  24. D. Giaouris and J. W. Finch, "Denoising using wavelets on electrive drive applications", Electric Power Systems Research, Article (CrossRefLink).
  25. Sachin D Ruikar, Dharampal D Doye, "Wavelet based image denoising technique", International Journal of Advanced Computer Science and Applications, 2(3), 2011.
  26. Rakesh Kumar and B. S. Saini , "Improved Image Denoising Technique Using Neighboring Wavelet Coefficients of Optimal Wavelet with Adaptive Thresholding", International Journal of Computer Theory and Engineering , 4(3), 2012. Article (CrossRefLink)
  27. P.V. Leena, G. Remmiya Devi, V. Sowmya and K. P. Somam, "Least square based image denoising using wavelet filters", Indian journal of science and technology, 9(30), 2016.
  28. Rafael, C. Gonzalez and Richard E. Woods. "Digital Image Processing," 2nd edition, Prentice Hall, 2002.
  29. A. Toet, "Multiscale color image enhancement", in Proc. SPIE Int. Conf. Image Processing and Its Applications, 583-585, 1992. Article (CrossRefLink)
  30. K. V. Velde, "Multi-scale color image enhancement", Proc. Int. Conf. Image Processing, 3, 584-587, 1999. Article (CrossRefLink)
  31. Dileep MD, and A. Sreenivasa Murthy, "A Comparison Between Different Color Image Contrast Enhancement Algorithms", Proceedings of IEEE ICETECT, 708-712, 2011.
  32. M. C. Hanumantharaju, M. Ravishankar, D. R. Rameshbabu, and S. Ramchandran, "Color Image Enhancement using Multiscale Retinex with Modified Color Restoration Technique", Second International Conference on Emerging Applications of Information Tecnology, 93-97, 2011. Article (CrossRefLink)
  33. E. Land, "Recent advances in retinex theory", Vis. Res., 26(1), 7-21, 1986. Article (CrossRefLink) https://doi.org/10.1016/0042-6989(86)90067-2
  34. D. J. Jobson, Z. Rahman, and G. A. Woodell, "Properties and performance of a center/surround Retinex", IEEE Trans. Image Processing, 6, 451-462, 1997. Article (CrossRefLink) https://doi.org/10.1109/83.557356
  35. Z. Rahman, D. J. Jobson, and G. A. Woodell, "Multi-scale retinex for color image enhancement", IEEE Int. Conf. Image Processing, 1996. Article (CrossRefLink)
  36. H. A. Mallot, "Computational Vision: Information Processing in Perception and Visual Behavior", Cambridge, MA: MIT Press, 2000.
  37. C. Munteanu and A. Rosa, "Color image enhancement using evolutionary principles and the retinex theory of color constancy", Proc. Of IEEE Signal Processing Society Workshop on Neural Networks for Signal Processing XI, 393-402, 2001. Article (CrossRefLink)
  38. D. J. Jobson, Z. Rahman, and G. A. Woodell, "A multi-scale retinex for bridging the gap between color images and the human observation of scenes", IEEE Trans. Image Processing, 6, 965-976, 1997. Article (CrossRefLink) https://doi.org/10.1109/83.597272
  39. K. Barnard and B. Funt, "Investigations into multiscale Retinex", Color Imaging: Vision and Technology, New York: Wiley, 9-17, 1999.
  40. S. Kim, W. Kang, E. Lee, and J. Paik, "Wavelet-Domain Color Image Enhancement using Filtered Directional Bases and Frequency- Adaptive Shrinkage", IEEE Trans. on consumer Electronics, 56(2), 2010. Article (CrossRefLink)
  41. F. Xiao, M. Zhou, and G. Geng, "Detail Enhancement and Noise Reduction with Color Image Detection Based on Wavelet Multi-scale", Proceedings of the 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce. Zhengzhou, China: IEEE Press, 1061-1064, 2011. Article (CrossRefLink)
  42. E. Provenzi and Vicent Caselles, "A Wavelet Perceptive on Variational Perceptually-Inspired Color Enhancement", Int. J. Comput. Vis., 106, 153-171, 2014. Article (CrossRefLink) https://doi.org/10.1007/s11263-013-0651-y
  43. T. S. Huang and R. Y. Tsay, "Multiple frame image restoration and registration", Advances in Computer Vision and Image Processing, 1, 317-339, 1984.
  44. S. Lertrattanapanich and N. Bose, "High resolution image formation from low resolution frames using delaunay triangulation", IEEE Transactions on Image Processing, 11(12), 1427-1441, 2002. Article (CrossRefLink) https://doi.org/10.1109/TIP.2002.806234
  45. X. Gao, K. Zhang, D. Tao, and X. Li, "Joint learning for single-image super-resolution via a coupled constraint", IEEE Transactions on Image Processing, 21(2), 469-480, 2012. Article (CrossRefLink) https://doi.org/10.1109/TIP.2011.2161482
  46. S. Dai, M. Han, W. Xu, Y. Wu, Y. Gong, and A. Katsaggelos, "Softcuts: A soft edge smoothness prior for color image super-resolution", IEEE Transactions on Image Processing, 18(5), 969-981, 2009. Article (CrossRefLink) https://doi.org/10.1109/TIP.2009.2012908
  47. J. Yang, J. Wright, T. S. Huang, and Y. Ma, "Image super-resolution via Sparse Representation", IEEE Transactions on Image Processing, 19(11), 2861-2873, 2010. Article (CrossRefLink) https://doi.org/10.1109/TIP.2010.2050625
  48. C. Ford and D. M. Etter, "Wavelet basis reconstruction of nonuniformly sampled data", IEEE Transactions on Circuits and Systems, 45, 1165-1168, 1998. Article (CrossRefLink) https://doi.org/10.1109/82.718832
  49. N. Nguyen and P. Milanfar, "A wavelet-based interpolation-restoration, method for superresolution (wavelet superresolution)", IEEE Transactions on Circuits and Systems, 19, 321-338, 2000. Article (CrossRefLink)
  50. N. Nguyen, P. Milanfar, and G. H. Golub, "A computationally efficient superresolution image reconstruction algorithm", IEEE Transactions on Image Processing, 10(4), 573-583, 2001. Article (CrossRefLink) https://doi.org/10.1109/83.913592
  51. N. Nguyen and P. Milanfar, "An efficient waveletbased algorithm for image Superresolution", ICIP, 2000. Article (CrossRefLink)
  52. D. Glasner, S. Bagon, and M. Irani, "Superresolution from a single image", ICCV, 2009. Article (CrossRefLink)
  53. X. Li and M. T. Orchard, "New edge-directed interpolation", IEEE Transactions on Image Processing, 10, 1521-1527, 2001. Article (CrossRefLink) https://doi.org/10.1109/83.951537
  54. L. Zhang and X. Wu, "An edge-guided image interpolation algorithm via directional filtering and data fusion", IEEE Transactions on Image Processing, 15, 2226-2238, 2006. Article (CrossRefLink) https://doi.org/10.1109/TIP.2006.877407
  55. S. Mallat and G. Yu, "Super-resolution with sparse mixing estimators", IEEE Transactions Image Processing, 19(11), 2889-2900, 2010. Article (CrossRefLink) https://doi.org/10.1109/TIP.2010.2049927
  56. Y. Piao, I. Shin, and H. W. Park, "Image resolution enhancement using inter-subband correlation in wavelet domain", Proceedings International Conference on Image Processing, 1, 445-448, 2007. Article (CrossRefLink)
  57. H. Demirel and G. Anbarjafari, "Satellite image resolution enhancement using complex wavelet transform", IEEE Geoscience and Remote Sensing Letter, 7(1), 123-126, 2010. Article (CrossRefLink) https://doi.org/10.1109/LGRS.2009.2028440
  58. C. B. Atkins, C. A. Bouman, and J. P. Allebach, "Optimal image scaling using pixel classification", Proc. International Conference on Image Processing, 3, 864-867, 2001. Article (CrossRefLink)
  59. H. Demirel and G. Anbarjafari, "Image Resolution Enhancement by Using Discrete and Stationary Wavelet Decomposition", IEEE Transactions on Image Processing, 20(5), 1458-1460, 2011. Article (CrossRefLink) https://doi.org/10.1109/TIP.2010.2087767
  60. H. Chavez-Roman and V. Ponomaryov, "Super Resolution Image Generation Using Wavelet Domain Interpolation With Edge Extraction via a Sparse Representation", IEEE Geoscience and remote sensing Letters, 11(10), 1777-17781, 2014. Article (CrossRefLink) https://doi.org/10.1109/LGRS.2014.2308905
  61. K. Sowmya, P. Surya Kumari, A. Ranga, "Single Image Super Resolution with Wavelet Domain Transformation and Sparse Representation", International Journal of Innovative Research in Computer Science & Technology (IJIRCST), ISSN: 2347-5552, 4(1), 2016.
  62. Z. Liu, "Context-Based and Perceptual-Based wavelet Image Compression with Application to JPEG2000", Arizona State University, 2003.
  63. J. C. Feauveau, "Analyse multirésolution avec un facteur de resolution", J. de traitement du signal, 7(2), 117-128, 1990.
  64. R.A. DeVore, B. Jawerth, B.J. Lucier, "Image compression through wavelet transform coding", IEEE Trans. on Information Theory, 38(2), 719-746, 1992. Article (CrossRefLink) https://doi.org/10.1109/18.119733
  65. Vetterli, M. and Kovacevic, "J. Wavelets and Subband Coding, Englewood Cliffs", NJ, Prentice Hall, 1995.
  66. A. Averbuch, D. Lazar, and M. Israeli, "Image Compression Using Wavelet Transform and Multiresolution Decomposition", IEEE Transactions on Image Processing, 5(1), 1996. Article (CrossRefLink)
  67. N. Farvardin, H. Jafarkhani, J. Johnson, R. Bhattacharya, "Real-time wavelet-based video compression system using multiple TMS320C40s", Application Report of Texas Instrument, 1997.
  68. M. N. Do and M. Vetterli, "The finite ridgelet transform for image representation", IEEE Trans. on Image Processing, 12(1), 16-28, 2003. Article (CrossRefLink) https://doi.org/10.1109/TIP.2002.806252
  69. H. Farid and S. Lyu, "Higher-order wavelet statistics and their application to digital forensics", Proc. of IEEE Workshop on Statitical Analysis in Computer Vision, Madison (Wisconsin), 2003. Article (CrossRefLink)
  70. K. H. Talukder and K. Harada, "A Scheme of Wavelet Based Compression of 2D Image", Proc. IMECS, Hong Kong, 531-536, 2006.
  71. K. H. Talukder, and K. Harada, "Haar Wavelet Based Approach for Image Compression and Quality Assessment of Compressed Image," IAENG International Journal of Applied Mathematics, 36(1), 2007.
  72. A. Khashman, and K. Dimililer, "Image Compression using Neural Networks and Haar Wavelet", WSEAS Transactions on Image Processing, 4(5), 330-339, 2008.
  73. G Boopathi, Dr.S. Arockiasamy "Image Compression: An approach using Wavelet Transform and Modified FCM", International Journal of Computer Applications, 28(2), 2011.
  74. V. Elamaran, and A. Praveen, "Comparison of DCT and wavelets in image coding", International Conference on Computer Communication and Informatics (ICCCI), IEEE, 1-4 ,2012. Article (CrossRefLink)
  75. M. Gupta and A. K. Garg, "Analysis Of Image Compression Algorithm Using DCT", International Journal of Engineering Research and Applications (IJERA), 2(1), 515-521, 2012.
  76. M. M. H. Chowdhury, and A. Khatun, "Image Compression Using Discrete Wavelet Transform", International Journal of Computer Science, 9(4), 327-330, 2012.
  77. Tarlok Singh; Pooja and P. Manchanda, "Image Compression Using Wavelets", International Journal of Computer Science, 11(4), No 2, 2014, ISSN (Print): 1694-0814 ; ISSN (Online): 1694-0784.
  78. E. B. Corrochano, "Multiresolution image analysis using the quaternion wavelet transform", Numerical Algorithms, 39 (2005), 35-55. Article (CrossRefLink) https://doi.org/10.1007/s11075-004-3619-8
  79. E. B. Corrochano, "The theory and the use of the quaternion wavelet transform", Journal of Mathematical Imaging and Vision, 24(1),19-35, (2006). Article (CrossRefLink) https://doi.org/10.1007/s10851-005-3605-3
  80. M. Yin, W. Liu, J. Shui and J. Wu, "Quaternion wavelet analysis and application in Image Denoising", Mathematical problems in Engineering, Hindwai publishing Corporation, (2012).
  81. N. Kingsbury, "Image processing with complex wavelets", Phil. Trans. Roy. Soc. London Ser, A 357,2543-2560, (1999). https://doi.org/10.1098/rsta.1999.0447