Skip to main content
EURASIP Journal on Advances in Signal Processing
Download PDF
  • Research Article
  • Open access
  • Published:

A Lorentzian Stochastic Estimation for a Robust Iterative Multiframe Super-Resolution Reconstruction with Lorentzian-Tikhonov Regularization

EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 034821 (2007) Cite this article

Abstract

Recently, there has been a great deal of work developing super-resolution reconstruction (SRR) algorithms. While many such algorithms have been proposed, the almost SRR estimations are based on L1 or L2 statistical norm estimation, therefore these SRR algorithms are usually very sensitive to their assumed noise model that limits their utility. The real noise models that corrupt the measure sequence are unknown; consequently, SRR algorithm using L1 or L2 norm may degrade the image sequence rather than enhance it. Therefore, the robust norm applicable to several noise and data models is desired in SRR algorithms. This paper first comprehensively reviews the SRR algorithms in this last decade and addresses their shortcomings, and latter proposes a novel robust SRR algorithm that can be applied on several noise models. The proposed SRR algorithm is based on the stochastic regularization technique of Bayesian MAP estimation by minimizing a cost function. For removing outliers in the data, the Lorentzian error norm is used for measuring the difference between the projected estimate of the high-resolution image and each low-resolution image. Moreover, Tikhonov regularization and Lorentzian-Tikhonov regularization are used to remove artifacts from the final answer and improve the rate of convergence. The experimental results confirm the effectiveness of our method and demonstrate its superiority to other super-resolution methods based on L1 and L2 norms for several noise models such as noiseless, additive white Gaussian noise (AWGN), poisson noise, salt and pepper noise, and speckle noise.

References

  1. Segall CA, Molina R, Katsaggelos AK: High-resolution images from low-resolution compressed video. IEEE Signal Processing Magazine 2003,20(3):37-48. 10.1109/MSP.2003.1203208

    Article  Google Scholar 

  2. Kundur D, Hatzinakos D: Blind image deconvolution. IEEE Signal Processing Magazine 1996,13(3):43-64. 10.1109/79.489268

    Article  Google Scholar 

  3. Rajan D, Chaudhuri S, Joshi MV: Multi-objective super resolution: concepts and examples. IEEE Signal Processing Magazine 2003,20(3):49-61. 10.1109/MSP.2003.1203209

    Article  Google Scholar 

  4. Demoment G: Image reconstruction and restoration: overview of common estimation structures and problems. IEEE Transactions on Acoustics, Speech, and Signal Processing 1989,37(12):2024-2036. 10.1109/29.45551

    Article  Google Scholar 

  5. Ng MK, Bose NK: Mathematical analysis of super-resolution methodology. IEEE Signal Processing Magazine 2003,20(3):62-74. 10.1109/MSP.2003.1203210

    Article  Google Scholar 

  6. Kang MG, Chaudhuri S: Super-resolution image reconstruction. IEEE Signal Processing Magazine 2003,20(3):19-20. 10.1109/MSP.2003.1203206

    Article  Google Scholar 

  7. Chaudhuri S, Taur DR: High-resolution slow-motion sequencing. IEEE Signal Processing Magazine 2005,22(2):16-24.

    Article  Google Scholar 

  8. Park SC, Park MK, Kang MG: Super-resolution image reconstruction: a technical overview. IEEE Signal Processing Magazine 2003,20(3):21–36. 10.1109/MSP.2003.1203207

    Article  Google Scholar 

  9. Banham MR, Katsaggelos AK: Digital image restoration. IEEE Signal Processing Magazine 1997,14(2):24-41. 10.1109/79.581363

    Article  Google Scholar 

  10. Huang TS, Tsan RY: Multiple frame image restoration and registration. In Advances in Computer Vision and Image Processing. Volume 1. Edited by: Huang TS. JAI Press, Greenwich, Conn, USA; 1984:317-339.

    Google Scholar 

  11. Kim SP, Bose NK, Valenzuela HM: Recursive reconstruction of high resolution image from noisy undersampled multiframes. IEEE Transactions on Acoustics, Speech, and Signal Processing 1990,38(6):1013-1027. 10.1109/29.56062

    Article  Google Scholar 

  12. Kim SP, Su W-Y: Recursive high-resolution reconstruction of blurred multiframe images. IEEE Transactions on Image Processing 1993,2(4):534-539. 10.1109/83.242363

    Article  Google Scholar 

  13. Ng MK, Bose NK: Analysis of displacement errors in high-resolution image reconstruction with multisensors. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 2002,49(6):806-813. 10.1109/TCSI.2002.1010035

    Article  Google Scholar 

  14. Bose NK, Ng MK, Yau AC: A fast algorithm for image super-resolution from blurred observations. EURASIP Journal on Applied Signal Processing 2006, 2006: 14 pages.

    Google Scholar 

  15. Patti AJ, Altunbasak Y: Artifact reduction for set theoretic super resolution image reconstruction with edge adaptive constraints and higher-order interpolants. IEEE Transactions on Image Processing 2001,10(1):179-186. 10.1109/83.892456

    Article  Google Scholar 

  16. Altunbasak Y, Patti AJ, Mersereau RM: Super-resolution still and video reconstruction from MPEG-coded video. IEEE Transactions on Circuits and Systems for Video Technology 2002,12(4):217-226. 10.1109/76.999200

    Article  Google Scholar 

  17. Gunturk BK, Altunbasak Y, Mersereau RM: Super-resolution reconstruction of compressed video using transform-domain statistics. IEEE Transactions on Image Processing 2004,13(1):33-43. 10.1109/TIP.2003.819221

    Article  Google Scholar 

  18. Hasegawa H, Ono T, Yamada I, Sakaniwa K: An iterative MPEG super-resolution with an outer approximation of framewise quantization constraint. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 2005,E88-A(9):2427-2434. 10.1093/ietfec/e88-a.9.2427

    Article  Google Scholar 

  19. Elfadel IM, Picard RW: Miscibility matrices explain the behavior of grayscale textures generated by Gibbs random fields. Intelligent Robots and Computer Vision IX: Algorithms and Techniques, November 1991, Boston, Mass, USA, Proceedings of SPIE 1381: 524–535.

    Google Scholar 

  20. Elfadel IM, Picard RW: Gibbs random fields, cooccurrences, and texture modeling. In Perceptual Computing Group Tech. Rep. #204. Media Laboratory, MIT, Cambridge, Mass, USA; 1993:1–34.

    Google Scholar 

  21. Elfadel IM, Picard RW: Gibbs random fields, cooccurences, and texture modeling. IEEE Transactions on Pattern Analysis and Machine Intelligence 1994,16(1):24-37. 10.1109/34.273719

    Article  Google Scholar 

  22. Elfadel IM, Picard RW: On the structure of aura and co-occurrence matrices for the Gibbs texture model. In Perceptual Computing Group Tech. Rep. #160. Media Laboratory, MIT, Cambridge, Mass, USA; 1994:1–24.

    Google Scholar 

  23. Picard RW: Gibbs random fields: temperature and parameter analysis. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '92), March 1992, San Francisco, Calif, USA 3: 45–48.

    Google Scholar 

  24. Popat K, Picard RW: Cluster-based probability model applied to image restoration and compression. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '94), April 1994, Adelaide, SA, Australia 5: 381–384.

    Google Scholar 

  25. Picard RW, Elfadel IM, Pentland AP: Markov/Gibbs texture modeling: aura matrices and temperature effects. Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR '91), June 1991, Maui, Hawaii, USA 371–377.

    Google Scholar 

  26. Picard RW: Gibbs random fields: temperature and parameter analysis. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '92), March 1992, San Francisco, Calif, USA 3: 45–48.

    Google Scholar 

  27. Bouman C, Sauer K: A generalized Gaussian image model for edge-preserving MAP estimation. IEEE Transactions on Image Processing 1993,2(3):296-310. 10.1109/83.236536

    Article  Google Scholar 

  28. Schultz RR, Stevenson RL: A Bayesian approach to image expansion for improved definition. IEEE Transactions on Image Processing 1994,3(3):233-242. 10.1109/83.287017

    Article  Google Scholar 

  29. Schultz RR, Stevenson RL: Extraction of high-resolution frames from video sequences. IEEE Transactions on Image Processing 1996,5(6):996-1011. 10.1109/83.503915

    Article  Google Scholar 

  30. Pan R, Reeves SJ: Efficient Huber-Markov edge-preserving image restoration. IEEE Transactions on Image Processing 2006,15(12):3728-3735.

    Article  MathSciNet  Google Scholar 

  31. Kundur D, Hatzinakos D: Blind image deconvolution revisited. IEEE Signal Processing Magazine 1996,13(6):61–63. 10.1109/79.543976

    Article  Google Scholar 

  32. Thompson AM, Brown JC, Kay JW, Titterington DM: A study of methods of choosing the smoothing parameter in image restoration by regularization. IEEE Transactions on Pattern Analysis and Machine Intelligence 1991,13(4):326-339. 10.1109/34.88568

    Article  Google Scholar 

  33. Mesarovic VZ, Galatsanos NP, Katsaggelos AK: Regularized constrained total least squares image restoration. IEEE Transactions on Image Processing 1995,4(8):1096-1108. 10.1109/83.403444

    Article  Google Scholar 

  34. Geman D, Yang C: Nonlinear image recovery with half-quadratic regularization. IEEE Transactions on Image Processing 1995,4(7):932-946. 10.1109/83.392335

    Article  Google Scholar 

  35. Kang MG, Katsaggelos AK: General choice of the regularization functional in regularized image restoration. IEEE Transactions on Image Processing 1995,4(5):594-602. 10.1109/83.382494

    Article  Google Scholar 

  36. Kang MG, Katsaggelos AK: Simultaneous multichannel image restoration and estimation of the regularization parameters. IEEE Transactions on Image Processing 1997,6(5):774-778. 10.1109/83.568936

    Article  Google Scholar 

  37. Molina R, Katsaggelos AK, Mateos J: Bayesian and regularization methods for hyperparameter estimation in image restoration. IEEE Transactions on Image Processing 1999,8(2):231–246. 10.1109/83.743857

    Article  MathSciNet  MATH  Google Scholar 

  38. 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 

  39. Rajan D, Chaudhuri S: Simultaneous estimation of super-resolved scene and depth map from low resolution defocused observations. IEEE Transactions on Pattern Analysis and Machine Intelligence 2003,25(9):1102-1117. 10.1109/TPAMI.2003.1227986

    Article  Google Scholar 

  40. He H, Kondi LP: Resolution enhancement of video sequences with adaptively weighted low-resolution images and simultaneous estimation of the regularization parameter. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '04), May 2004, Montreal, Que, Canada 3: 213–216.

    Google Scholar 

  41. He H, Kondi LP: Resolution enhancement of video sequences with simultaneous estimation of the regularization parameter. Journal of Electronic Imaging 2004,13(3):586-596. 10.1117/1.1762889

    Article  Google Scholar 

  42. He H, Kondi LP: A regularization framework for joint blur estimation and super-resolution of video sequences. Proceedings of International Conference on Image Processing (ICIP '05), September 2005, Genova, Italy 3: 329–332.

    Google Scholar 

  43. He H, Kondi LP: An image super-resolution algorithm for different error levels per frame. IEEE Transactions on Image Processing 2006,15(3):592-603.

    Article  Google Scholar 

  44. Vega M, Molina R, Katsaggelos AK: A Bayesian super-resolution approach to demosaicing of blurred images. EURASIP Journal on Applied Signal Processing 2006, 2006: 12 pages.

    Google Scholar 

  45. Elad M, Feuer A: Restoration of a single superresolution 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 

  46. Elad M, Feuer A: Superresolution restoration of an image sequence: adaptive filtering approach. IEEE Transactions on Image Processing 1999,8(3):387-395. 10.1109/83.748893

    Article  Google Scholar 

  47. Elad M, Feuer A: Super-resolution restoration of continuous image sequence—adaptive filtering approach. In Tech. Rep. #942. The Technion, the Electrical Engineering Faculty, Israel Institute of Technology, Haifa, Israel; 1994:1–12.

    Google Scholar 

  48. Elad M, Feuer A: Super-resolution reconstruction of image sequences. IEEE Transactions on Pattern Analysis and Machine Intelligence 1999,21(9):817-834. 10.1109/34.790425

    Article  Google Scholar 

  49. Elad M, Hel-Or Y: A fast super-resolution reconstruction algorithm for pure translational motion and common space-invariant blur. IEEE Transactions on Image Processing 2001,10(8):1187-1193. 10.1109/83.935034

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  51. Elad M: On the origin of the bilateral filter and ways to improve it. IEEE Transactions on Image Processing 2002,11(10):1141–1151. 10.1109/TIP.2002.801126

    Article  MathSciNet  Google Scholar 

  52. Farsiu S, Robinson D, Elad M, Milanfar P: Advances and challenges in super-resolution. International Journal of Imaging Systems and Technology 2004,14(2):47-57. 10.1002/ima.20007

    Article  Google Scholar 

  53. Farsiu S, Robinson D, 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 

  54. Farsiu S, Elad M, Milanfar P: Multiframe demosaicing and super-resolution of color images. IEEE Transactions on Image Processing 2006,15(1):141–159.

    Article  Google Scholar 

  55. Farsiu S, Elad M, Milanfar P: Video-to-video dynamic super-resolution for grayscale and color sequences. EURASIP Journal on Applied Signal Processing 2006, 2006: 15 pages.

    Google Scholar 

  56. Patanavijit V, Jitapunkul S: An iterative super-resolution reconstruction of image sequences using a Bayesian approach and affine block-based registration. Proceedings of the 14th European Signal Processing Conference (EUSIPCO '06), September 2006, Florence, Italy

    Google Scholar 

  57. Rochefort G, Champagnat F, Le Besnerais G, Giovannelli J-F: An improved observation model for super-resolution under affine motion. IEEE Transactions on Image Processing 2006,15(11):3325-3337.

    Article  Google Scholar 

  58. Baker S, Kanade T: Limits on super-resolution and how to break them. IEEE Transactions on Pattern Analysis and Machine Intelligence 2002,24(9):1167-1183. 10.1109/TPAMI.2002.1033210

    Article  Google Scholar 

  59. Sun J, Zheng N-N, Tao H, Shum H-Y: Image hallucination with primal sketch priors. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR '03), June 2003, Madison, Wis, USA 2: 729–736.

    Google Scholar 

  60. Vandewalle P, Süsstrunk S, Vetterli M: Double resolution from a set of aliased images. Sensors and Camera Systems for Scientific, Industrial, and Digital Photography Applications V, January 2004, San Jose, Calif, USA, Proceedings of SPIE 5301: 374–382.

    Article  Google Scholar 

  61. Vandewalle P, Süsstrunk S, Vetterli M: A frequency domain approach to super-resolution imaging from aliased low resolution images. In Technical Journal. Department of Electrical Engineering and Computer Science, University of California, Berkeley, Calif, USA; 2004:1–21.

    Google Scholar 

  62. Vandewalle P, Sbaiz L, Vetterli M, Süsstrunk S: Super-resolution from highly undersampled images. Proceedings of International Conference on Image Processing (ICIP '05), September 2005, Genova, Italy 1: 889–892.

    Google Scholar 

  63. Vandewalle P, Süsstrunk S, Vetterll M: A frequency domain approach to registration of aliased images with application to super-resolution. EURASIP Journal on Applied Signal Processing 2006, 2006: 14 pages.

    Google Scholar 

  64. Trimeche M, Bilcu RC, Yrjänäinen J: Adaptive outlier rejection in image super-resolution. EURASIP Journal on Applied Signal Processing 2006, 2006: 12 pages.

    Google Scholar 

  65. Black MJ, Rangarajan A: On the unification of line processes, outlier rejection, and robust statistics with applications in early vision. International Journal of Computer Vision 1996,19(1):57-91. 10.1007/BF00131148

    Article  Google Scholar 

  66. Black MJ, Sapiro G, Marimont DH, Heeger D: Robust anisotropic diffusion: connections between robust statistics, line processing, and anisotropic diffusion. In Proceedings of the 1st International Conference on Scale-Space Theory in Computer Vision (Scale-Space '97), July 1997, Utrecht, The Netherlands, Lecture Notes in Computer Science. Volume 1252. Edited by: ter Haar Romeny B, Florack L, Koenderink J, Viergever M. Springer; 323–326.

    Chapter  Google Scholar 

  67. Black MJ, Sapiro G, Marimont DH, Heeger D: Robust anisotropic diffusion. IEEE Transactions on Image Processing 1998,7(3):421–432. 10.1109/83.661192

    Article  Google Scholar 

  68. Black MJ, Sapiro G: Edges as outliers: anisotropic smoothing using local image statistics. In Proceedings of the 2nd International Conference on Scale-Space Theories in Computer Vision (Scale-Space '99), September 1999, Corfu, Greece, Lecture Notes in Computer Science. Volume 1682. Springer; 259–270.

    Chapter  Google Scholar 

  69. Patanavijit V, Jitapunkul S: A robust iterative multiframe super-resolution reconstruction using a Bayesian approach with lorentzian norm. Proceedings of the 10th IEEE International Conference on Communication Systems (ICCS '06), October 2006, Singapore 1–5.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, 10330, Thailand

    V Patanavijit & S Jitapunkul

Authors
  1. V Patanavijit
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S Jitapunkul
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V Patanavijit.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://doi.org/creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Patanavijit, V., Jitapunkul, S. A Lorentzian Stochastic Estimation for a Robust Iterative Multiframe Super-Resolution Reconstruction with Lorentzian-Tikhonov Regularization. EURASIP J. Adv. Signal Process. 2007, 034821 (2007). https://doi.org/10.1155/2007/34821

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/2007/34821

Keywords