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Multidimensional Systems and Signal Processing

, Volume 18, Issue 2–3, pp 153–171 | Cite as

Super-resolution reconstruction based on linear interpolation of wavelet coefficients

  • C. S. Tong
  • K. T. Leung
Original Article

Abstract

High resolution image reconstruction is an image process to reconstruct a high resolution image from a set of blurred, degraded and shifted low resolution images. In this paper, the reconstruction problem is treated as a function approximation. We use linear interpolation to build up an algorithm to obtain the relationship between the detail coefficients in wavelet subbands and the set of low resolution images. We use Haar wavelet as an example and establish the connection between the Haar wavelet subband and the low resolution images. Experiments show that we can use just 3 low resolution images to obtain a high resolution image which has better quality than Tikhonov least-squares approach and Chan et al. Algorithm 3 in low noise cases. We also propose an error correction extension for our method which can lead to very good results even in noisy cases. Moreover, our approach is very simple to implement and very efficient.

Keywords

High resolution image reconstruction Haar Wavelet NormalShrink Local Wiener filtering 

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References

  1. Ahuja, N., Lertrattanapanich, S., & Bose, N. K. (2005). Properties determining choice of mother wavelet. In IEEE proceedings-vision image and signal processing, Vol. 152, No. 5, Oct 2005, pp. 659–664.Google Scholar
  2. Bose N., Boo K. (1998) High-resolution image reconstruction with multisensors. International Journal of Imaging Systems and Technology 9: 294–304CrossRefGoogle Scholar
  3. Chan, R., Chan, T., Ng, M., Tang, W., & Wong, C. (1998). Preconditioned iterative methods for high-resolution image reconstruction from multisensors. In F. Luk (Ed.), Proceedings to the SPIE symposium on advanced signal processing: Algorithms, architectures, and implementations, Vol. 3461, San Diego, CA, 1998, pp. 348–357.Google Scholar
  4. Chan R.H., Chan T.F., Shen L., Shen Z. (2003) Wavelet algorithms for high-resolution image reconstruction. SIAM Journal on Scientific Computing 24: 1408–1432MATHCrossRefMathSciNetGoogle Scholar
  5. Chan R.H., Ng M.K. (1996) Conjugate gradient methods for toeplitz systems. SIAM Review 38(3): 427–482MATHCrossRefMathSciNetGoogle Scholar
  6. Chan R.H., Riemenschneider S.D., Shen L., Shen Z. (2004) Tight frame: An efficient way for high-resolution imagereconstruction. Applied and Computational Harmonic Analysis 17: 91–115MATHCrossRefMathSciNetGoogle Scholar
  7. Connolly, T. J., & Lane, R. G. (1997). Gradient methods for superresolution. In Proceedings of the international conference on image processing, Vol. 1, Santa Barbara, California, 26–29 Oct. 1997, pp. 917–920.Google Scholar
  8. Hardie R.C., Barnard K.J., Armstrong E.E. (1997) Joint map registration and high-resolution image estimation using a sequence of undersampled images. IEEE Transactions on Image Processing 6(12): 1621–1633CrossRefGoogle Scholar
  9. Kaltenbacher, E., & Hardie, R. C. (1996). High resolution infrared image reconstruction using multiple, low resolution, aliased frames. In O. Dayton (Ed.), Proceedings of the IEEE national aerospace electronics conference (NAECON), Vol. 2, USA, 1996, pp. 702–709.Google Scholar
  10. Kaur L., Gupta S., Chauhan R.C. (2002) Image denoising using wavelet thresholding. Third conference on computer vision, graphics and image processing, India, December 16–18: 2002Google Scholar
  11. Kazubek M. (2003) Wavelet domain image denoising by thresholding and wiener filtering. IEEE Signal Processing Letters 10(11): 324–326CrossRefGoogle Scholar
  12. Kim S.P., Bose N.K., Valenzuela H.M. (1990) Recursive reconstruction of high resolution image from noisy undersampled multiframes. IEEE Transactions on Acoustics, Speech and Signal Processing 38: 1013–1027CrossRefGoogle Scholar
  13. Kim S., Su W. (1993) Recursive high-resolution reconstruction of blurred multiframe images. IEEE Transactions on Image Processing 2(4): 534–539CrossRefGoogle Scholar
  14. Leung, K. T., & Tong, C. S. (2006). Super-resolution reconstruction using haar wavelet estimation. In Wavelet analysis and applications, ser. Applied and numerical harmonic analysis (pp. 419–430). Birkhauser Verlag Basel.Google Scholar
  15. Patti, A., Sezan, M., & Tekalp, A. (1993). Image sequence restoration and de-interlacing by motioncompensated kalman filtering. In Proceedings of SPIE, Vol. 1903, San Jose, CA, USA, 1993, pp. 59–70.Google Scholar
  16. Patti A., Sezan M., Tekalp A. (1997) Superresolution video reconstruction with arbitrary sampling lattices and nonzero aperture time. IEEE Transactions Image Processing 6: 1064–1076CrossRefGoogle Scholar
  17. Shen L., Sun Q. (2004) Bi-orthogonal wavelet system for high-resolution image reconstruction. IEEE Transactions on Signal Processing 52: 1997–2011CrossRefMathSciNetGoogle Scholar
  18. Tekalp, A., Ozkan, M., & Sezan, M. (1992). High-resolution image reconstruction from lowerresolution image sequences and space-varying image restoration. In Proceedings of the IEEE international conference on acoustics, speech, and signal process, Vol. 3, San Francisco, CA, USA, 1992, pp. 169–172.Google Scholar
  19. Tsai R.Y., Huang T.S. (1984) Multiframe image restoration and registration. Advances in Computer Vision and Image Processing 1: 317–339Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsHong Kong Baptist UniversityKowloon TongHong Kong

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