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Single frame image super-resolution: should we process locally or globally?

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Abstract

In this paper we study the usefulness of different local and global, learning-based, single-frame image super-resolution reconstruction techniques in handling three specific tasks, namely, de-blurring, de-noising and alias removal. We start with the global, iterative Papoulis–Gerchberg method for super-resolving a scene. Next we describe a PCA-based global method which faithfully reproduces a super-resolved image from a blurred and noisy low resolution input. We also study several multi-resolution processing schemes for super-resolution where the best edges are learned locally from an image database. We show that the PCA-based global method is efficient in handling blur and noise in the data. The local methods are adept in capturing the edges properly. However, both local and global approaches cannot properly handle the aliasing present in the low resolution observation. Hence we propose an alias removal technique by designing an alias-free upsampling scheme. Here the unknown high frequency components of the given partially aliased (low resolution) image is generated by minimizing the total variation of the interpolant subject to the constraint that part of alias free spectral components in the low resolution observation are known precisely and under the assumption of sparsity in the data.

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References

  • Bertalmio M., Caselles V., Sapiro G., & Ballester C. (2000). Image inpainting. In Proceedings of the SIGGRAPH. New Orleans, USA.

  • Bishop C.M., Blake A., & Marthi B. (2003). Super-resolution enhancement of video. In International Conference on Artificial Intelligence and Statistics, Key West, Florida

  • Bose N.K., Ng M.K., & Yau A.C. (2005). Super-resolution image restoration from blurred observations. In Proceedings of the ISCAS, (pp. 6296–6299). Kobe, Japan.

  • Burt P.J., Adelson E.H. (1983). The Laplacian pyramid as a compact image code. IEEE Transactions on Communication 31(4): 532–540

    Article  Google Scholar 

  • Candes E., Romberg J., Tao T. (2006). Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory 52(2): 489–509

    Article  MathSciNet  Google Scholar 

  • Chan T., & Kang S.H. (2004). Error analysis for image inpainting. UCLA CAM report 04-72

  • Chang H., Yeung D.Y., & Xiong Y. (2004). Super-resolution through neighbor embedding. In Proceedings of the IEEE conferences on computer vision and pattern recognition (pp. 275–282). Washington.

  • Chappalli M.B., Bose N.K. (2005). Simultaneous noise filtering and super-resolution with second-generation wavelets. Signal Processing Letters 12(11): 772–775

    Google Scholar 

  • Chaudhuri S., Joshi M.V. (2005). Motion-free super-resolution. New york, Springer

    MATH  Google Scholar 

  • Do M.N. (2001). Directional multiresolution image representations. Ph.D. thesis. Lausanne, Switzerland: Swiss Federal Institute of Technology.

  • Do M.N., Vetterli M. (2005). The contourlet transform: An efficient directional multiresolution image representation. IEEE Transactions on Image Processing 14(12): 2091–2106

    Article  MathSciNet  Google Scholar 

  • Donoho D.L., Elad M. (2003). Maximal sparsity representation via l 1 minimization. The Proceedings of the National Academy of Sciences 100: 2197–2202

    Article  MATH  MathSciNet  Google Scholar 

  • Elad M., Feuer A. (1997). Restoration of a single superresolution image from several blurred, noisy and undersampled measured images. IEEE Transactions on Image Processing 6(12): 1646–1658

    Article  Google Scholar 

  • Freeman W.T., Jones T.R., Pasztor E.C. (2002). Example-based super-resolution. IEEE Computer Graphics and Applications 22(2): 56–65

    Article  Google Scholar 

  • Gerchberg R.W. (1974). Super-resolution through error energy reduction. Optica Acta 21: 709–720

    Google Scholar 

  • Harris J.L. (1964). Diffraction and resolving power. Journal of Optical Society America 54, 931–936

    Article  Google Scholar 

  • Jain A.K. (2001). Fundamentals of digital image processing. Upper Saddle River, Prentice Hall of India Private Limited

    Google Scholar 

  • Jiji C.V., & Chaudhuri S. (2004). PCA based generalized interpolation for image super-resolution. In Proceedings of the Indian conference on computer vision graphics and image processing, (pp. 139–144). Kolkata

  • Jiji C.V., & Chaudhuri S. (2006). Single frame image super-resolution through contourlet learning. EURASIP Journal of Applied Signal Processing, 2006, 1–11

  • Jiji C.V., Joshi M.V., Chaudhuri S. (2004). Single frame image super-resolution using learned wavelet coefficients. International Journal of Imaging Systems and Technology 14(3): 105–112

    Article  Google Scholar 

  • Kim S.P., & Bose N.K. (1990). Reconstruction of 2-D bandlimited discrete signals from nonuniform samples. IEE Proceedings, 137,pt. F, (3), 197–204

  • Levy S., Fullagar P.K. (1981). Reconstruction of a sparse spike train from a portion of its spectrum and application to high-resolution deconvolution. GEOPHYSICS 46(9): 1235–1243

    Article  Google Scholar 

  • Lin Z., Shum H.Y. (2004). Fundamental limits of reconstruction-based super-resolution algorithms under local translation. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(1): 83–97

    Article  Google Scholar 

  • Papoulis A. (1975). A new algorithm in spectral analysis and band-limited extrapolation. IEEE Transactions on Circuits and Systems CAS-22(9): 735–742

    Article  MathSciNet  Google Scholar 

  • Park S.C., Park M.K., Kang M.G. (2003). Super-resolution image reconstruction: A technical overview. IEEE Signal Processing Magazine, Special issue of Super-Resolution Image Reconstruction 20(3): 21–36

    Google Scholar 

  • Phoong S.M., Kim C.W., Vaidyanathan P.P., Ansari R. (1995). A new class of Two-channel biorthogonal filter banks and wavelet bases. IEEE Transactions on Signal Processing 43(3): 649–665

    Article  Google Scholar 

  • Pickup L.C., Roberts S.J., Zisserman A. (2004). A sampled texture prior for image super-resolution. In: Thrun S., Saul L., Schölkopf B. (eds), Advances in neural information processing systems 16. Cambridge MA, MIT Press, pp. 1587–1594

    Google Scholar 

  • Rajagopalan, Chaudhuri S. (1998). Performance analysis of maximum likelihood estimator for recovery of depth from defocused images and optimal selection of camera parameters. International Journal of Computer Vision 30(3): 175–190

    Article  Google Scholar 

  • Rajan D., Chaudhuri S. (2002). Generation of super-resolution images from blurred observations using an MRF model. Journal of Mathematical Imaging and Vision 16, 5–15

    Article  MATH  MathSciNet  Google Scholar 

  • Roweis S.T., Saul L.K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326

    Article  Google Scholar 

  • Santosa F., Symes W.W. (1986). Linear inversion of band-limited reflection seismograms. SIAM Journal of Scientific and Statistical Computing 7, 1307–1330

    Article  MATH  MathSciNet  Google Scholar 

  • Shahram M., Milanfar P. (2004). Imaging below the diffraction limit: A statistical analysis. IEEE Transactions on Image Processing 13(5): 677–689

    Article  Google Scholar 

  • Strohmer T. (1995). On discrete band-limited signal extrapolation. Contemporary Mathematics 190, 323–337

    MathSciNet  Google Scholar 

  • Strohmer T. (1997). Computationally attractive reconstruction of bandlimited images from irregular samples. IEEE Transactions on Image Processing 6(4): 540–548

    Article  MathSciNet  Google Scholar 

  • Turk M., Pentland A. (1991). Eigenfaces for recognition. Journal of Cognitive Neuroscience 3(1): 71–86

    Article  Google Scholar 

  • Vandewalle P., Susstrunk S., & Vetterli M. (2003). Superresolution images reconstructed from aliased images. In T. Ebrahimi & T. Sikora (Eds.), SPIE/IS&T visual communication and image processing conference, vol. 5150 (pp. 1398–1405).

  • Vetterli M., Herley C. (1992). Wavelets and filter banks: Theory and design. IEEE Transactions on Signal Processing 40(9): 2207–2232

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology-Bombay, Mumbai, 400076, India

    C. V. Jiji, Subhasis Chaudhuri & Priyam Chatterjee

Authors
  1. C. V. Jiji
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  2. Subhasis Chaudhuri
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  3. Priyam Chatterjee
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Correspondence to Subhasis Chaudhuri.

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Jiji, C.V., Chaudhuri, S. & Chatterjee, P. Single frame image super-resolution: should we process locally or globally?. Multidim Syst Sign Process 18, 123–152 (2007). https://doi.org/10.1007/s11045-007-0024-1

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  • DOI: https://doi.org/10.1007/s11045-007-0024-1

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