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Super-resolution reconstruction based on linear interpolation of wavelet coefficients

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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.

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References

  • 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.

  • Bose N., Boo K. (1998) High-resolution image reconstruction with multisensors. International Journal of Imaging Systems and Technology 9: 294–304

    Article  Google Scholar 

  • 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.

  • Chan R.H., Chan T.F., Shen L., Shen Z. (2003) Wavelet algorithms for high-resolution image reconstruction. SIAM Journal on Scientific Computing 24: 1408–1432

    Article  MATH  MathSciNet  Google Scholar 

  • Chan R.H., Ng M.K. (1996) Conjugate gradient methods for toeplitz systems. SIAM Review 38(3): 427–482

    Article  MATH  MathSciNet  Google Scholar 

  • 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: 91–115

    Article  MATH  MathSciNet  Google Scholar 

  • 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.

  • 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): 1621–1633

    Article  Google Scholar 

  • 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.

  • 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: 2002

    Google Scholar 

  • Kazubek M. (2003) Wavelet domain image denoising by thresholding and wiener filtering. IEEE Signal Processing Letters 10(11): 324–326

    Article  Google Scholar 

  • 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: 1013–1027

    Article  Google Scholar 

  • Kim S., Su W. (1993) Recursive high-resolution reconstruction of blurred multiframe images. IEEE Transactions on Image Processing 2(4): 534–539

    Article  Google Scholar 

  • 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.

  • 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.

  • Patti A., Sezan M., Tekalp A. (1997) Superresolution video reconstruction with arbitrary sampling lattices and nonzero aperture time. IEEE Transactions Image Processing 6: 1064–1076

    Article  Google Scholar 

  • Shen L., Sun Q. (2004) Bi-orthogonal wavelet system for high-resolution image reconstruction. IEEE Transactions on Signal Processing 52: 1997–2011

    Article  MathSciNet  Google Scholar 

  • 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.

  • Tsai R.Y., Huang T.S. (1984) Multiframe image restoration and registration. Advances in Computer Vision and Image Processing 1: 317–339

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    C. S. Tong & K. T. Leung

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  1. C. S. Tong
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  2. K. T. Leung
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Correspondence to K. T. Leung.

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Tong, C.S., Leung, K.T. Super-resolution reconstruction based on linear interpolation of wavelet coefficients. Multidim Syst Sign Process 18, 153–171 (2007). https://doi.org/10.1007/s11045-007-0023-2

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  • DOI: https://doi.org/10.1007/s11045-007-0023-2

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