Skip to main content

Super-Resolution Using Hidden Markov Model and Bayesian Detection Estimation Framework


This paper presents a new method for super-resolution (SR) reconstruction of a high-resolution (HR) image from several low-resolution (LR) images. The HR image is assumed to be composed of homogeneous regions. Thus, the a priori distribution of the pixels is modeled by a finite mixture model (FMM) and a Potts Markov model (PMM) for the labels. The whole a priori model is then a hierarchical Markov model. The LR images are assumed to be obtained from the HR image by lowpass filtering, arbitrarily translation, decimation, and finally corruption by a random noise. The problem is then put in a Bayesian detection and estimation framework, and appropriate algorithms are developed based on Markov chain Monte Carlo (MCMC) Gibbs sampling. At the end, we have not only an estimate of the HR image but also an estimate of the classification labels which leads to a segmentation result.


  1. 1.

    Foroosh H, Zerubia JB, Berthod M: Extension of phase correlation to subpixel registration. IEEE Transactions on Image Processing 2002, 11(3):188-200. 10.1109/83.988953

    Article  Google Scholar 

  2. 2.

    Argyriou V, Vlachos T: Sub-pixel motion estimation using gradient cross-correlation. Proceedings of 7th IEEE International Symposium on Signal Processing and its Applications (ISSPA '03), July 2003, Paris, France 2: 215–218.

    Google Scholar 

  3. 3.

    Humblot F, Collin B, Mohammad-Djafari A: Evaluation and practical issues of subpixel image registration using phase correlation methods. Proceedings of Physics in Signal and Image Processing (PSIP '05), January–February 2005, Toulouse, France

    Google Scholar 

  4. 4.

    Molina R, Mateos J, Katsaggelos AK, Vega M: Bayesian multichannel image restoration using compound Gauss-Markov random fields. IEEE Transactions on Image Processing 2003, 12(12):1642–1654. 10.1109/TIP.2003.818015

    Article  Google Scholar 

  5. 5.

    Molina R, Vega M, Abad J, Katsaggelos AK: Parameter estimation in Bayesian high-resolution image reconstruction with multisensors. IEEE Transactions on Image Processing 2003, 12(12):1655–1667. 10.1109/TIP.2003.818117

    Article  Google Scholar 

  6. 6.

    Tsai RY, Huang TS: Multi-frame image restoration and registration. Advances in Computer Vision on Image Processing 1984, 1: 317–339.

    Google Scholar 

  7. 7.

    Schulz TJ: Multiframe image restoration. In Handbook of Image and Video Processing. Edited by: Bovik A. Academic Press, New York, NY, USA; 2000:175–189. chapter 3.8

    Google Scholar 

  8. 8.

    Borman S: Topics in multiframe super-resolution restoration, M.S. thesis. University of Notre Dame, Notre Dame, Ind, USA; May 2004.

    Google Scholar 

  9. 9.

    Hong M-C, Kang MG, Katsaggelos AK: A regularized multichannel restoration approach for globally optimal high resolution video sequence. Visual Communications and Image Processing (VCIP '97), February 1997, San Jose, Claif, USA, Proceedings of SPIE 3024: 1306–1316.

    Article  Google Scholar 

  10. 10.

    Elad M, Feuer A: Restoration of a single super-resolution image from several blurred, noisy, and undersampled measured images. IEEE Transactions on Image Processing 1997, 6(12):1646–1658. 10.1109/83.650118

    Article  Google Scholar 

  11. 11.

    Nguyen N, Milanfar P, Golub G: A computationally efficient super-resolution image reconstruction algorithm. IEEE Transactions on Image Processing 2001, 10(4):573–583. 10.1109/83.913592

    Article  Google Scholar 

  12. 12.

    Farsiu S, Robinson MD, Elad M, Milanfar P: Fast and robust multiframe super-resolution. IEEE Transactions on Image Processing 2004, 13(10):1327–1344. 10.1109/TIP.2004.834669

    Article  Google Scholar 

  13. 13.

    Gillette JC, Stadtmiller TM, Hardie RC: Aliasing reduction in staring infrared imagers utilizing subpixel techniques. Optical Engineering 1995, 34(11):3130–3137. 10.1117/12.213590

    Article  Google Scholar 

  14. 14.

    Snoussi H, Mohammad-Djafari A: Fast joint separation and segmentation of mixed images. Journal of Electronic Imaging 2004, 13(2):349–361. 10.1117/1.1666873

    Article  Google Scholar 

  15. 15.

    Snoussi H, Mohammad-Djafari A: Information geometry and prior selection. In Proceedings of 22nd International workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt '02), August 2002, Moscow, Idaho, USA Edited by: Williams CJ. 307–327.

    Google Scholar 

  16. 16.

    Snoussi H: A Bayesian approach to source separation. Applications in imagery, M.S. thesis. University of Paris–Sud, Orsay, France; September 2003.

    Google Scholar 

  17. 17.

    Féron O, Mohammad-Djafari A: Image fusion and unsupervised joint segmentation using a HMM and MCMC algorithm. Journal of Electronic Imaging 2005, 14(2):1–12.

    Article  Google Scholar 

  18. 18.

    Rochefort G, Champagnat F, Le Besnerais G, Giovannelli J-F: Super-resolution from a sequence of undersampled image under affine motion. submitted to in IEEE Transactions on Image Processing, March 2005

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Fabrice Humblot.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Humblot, F., Mohammad-Djafari, A. Super-Resolution Using Hidden Markov Model and Bayesian Detection Estimation Framework. EURASIP J. Adv. Signal Process. 2006, 036971 (2006).

Download citation


  • Information Technology
  • Markov Chain
  • Markov Model
  • Mixture Model
  • Hide Markov Model