Skip to content


  • Research Article
  • Open Access

A Fast Algorithm for Image Super-Resolution from Blurred Observations

EURASIP Journal on Advances in Signal Processing20062006:035726

  • Received: 1 December 2004
  • Accepted: 7 April 2005
  • Published:


We study the problem of reconstruction of a high-resolution image from several blurred low-resolution image frames. The image frames consist of blurred, decimated, and noisy versions of a high-resolution image. The high-resolution image is modeled as a Markov random field (MRF), and a maximum a posteriori (MAP) estimation technique is used for the restoration. We show that with the periodic boundary condition, a high-resolution image can be restored efficiently by using fast Fourier transforms. We also apply the preconditioned conjugate gradient method to restore high-resolution images in the aperiodic boundary condition. Computer simulations are given to illustrate the effectiveness of the proposed approach.


  • Fourier Transform
  • Computer Simulation
  • Fast Fourier Transform
  • Periodic Boundary
  • Quantum Information

Authors’ Affiliations

Spatial and Temporal Signal Processing Center, Department of Electrical Engineering, The Pennsylvania State University, University Park, PA 16802, USA
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Department of Mathematics, Faculty of Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China


  1. Bose NK, Boo KJ: High-resolution image reconstruction with multisensors. International Journal of Imaging Systems and Technology 1998, 9(4):294-304. 10.1002/(SICI)1098–1098(1998)9:4<294::AID-IMA11>3.0.CO;2-XView ArticleGoogle Scholar
  2. 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. 10.1109/83.650118View ArticleGoogle Scholar
  3. Elad M, Feuer A: Super-resolution restoration of an image sequence: adaptive filtering approach. IEEE Transactions on Image Processing 1999, 8(3):387–395. 10.1109/83.748893View ArticleGoogle Scholar
  4. Gillette JC, Stadtmiller TM, Hardie RC: Aliasing reduction in staring infrared imagers utilizing subpixel techniques. Optical Engineering 1995, 34(11):3130–3137. 10.1117/12.213590View ArticleGoogle Scholar
  5. Hardie RC, Barnard KJ, Bognar JG, Armstrong EE, Watson EA: High resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system. Optical Engineering 1998, 37(1):247–260. 10.1117/1.601623View ArticleGoogle Scholar
  6. Irani M, Peleg S: Improving resolution by image registration. CVGIP: Graphical Models and Image Processing 1991, 53(3):231–239. 10.1016/1049-9652(91)90045-LGoogle Scholar
  7. Jacquemod G, Odet C, Goutte R: Image resolution enhancement using subpixel camera displacement. Signal Processing 1992, 26(1):139–146. 10.1016/0165-1684(92)90060-AView ArticleGoogle Scholar
  8. 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. 10.1109/29.56062View ArticleGoogle Scholar
  9. Komatsu T, Aizawa K, Igarashi T, Saito T: Signal-processing based method for acquiring very high resolution images with multiple cameras and its theoretical analysis . IEE Proceedings. I, Communications, Speech and Vision 1993, 140(1):19–24. 10.1049/ip-i-2.1993.0005View ArticleGoogle Scholar
  10. Patti AJ, Sezan MI, Murat Tekalp A: Super-resolution video reconstruction with arbitrary sampling lattices and nonzero aperture time. IEEE Transactions on Image Processing 1997, 6(8):1064–1076. 10.1109/83.605404View ArticleGoogle Scholar
  11. Rhee SH, Kang MG: Discrete cosine transform based regularized high-resolution image reconstruction algorithm. Optical Engineering 1999, 38(8):1348–1356. 10.1117/1.602177View ArticleGoogle Scholar
  12. Schultz RR, Stevenson RL: Extraction of high-resolution frames from video sequences. IEEE Transactions on Image Processing 1996, 5(6):996–1011. 10.1109/83.503915View ArticleGoogle Scholar
  13. Stark H, Oskoui P: High-resolution image recovery from image-plane arrays, using convex projections. Journal of the Optical Society of America A 1989, 6(11):1715–1726. 10.1364/JOSAA.6.001715View ArticleGoogle Scholar
  14. Patti AJ, Sezan MI, Murat Tekalp A: Super-resolution video reconstruction with arbitrary sampling lattices and nonzero aperture time. IEEE Transactions on Image Processing 1997, 6(8):1064–1076. 10.1109/83.605404View ArticleGoogle Scholar
  15. Tsai RY, Huang TS: Multiframe image restoration and registration. In Advances in Computer Vision and Image Processing: Image Reconstruction from Incomplete Observations. Volume 1. Edited by: Huang TS. JAI Press, Greenwich, Conn, USA; 1984:317–339. chapter 7Google Scholar
  16. Kim SP, Bose NK: Reconstruction of 2-D bandlimited discrete signals from nonuniform samples. IEE Proceedings. F, Radar and Signal Processing 1990, 137(3):197–204.View ArticleGoogle Scholar
  17. Kim SP, Su W-Y: Recursive high-resolution reconstruction of blurred multiframe images. IEEE Transactions on Image Processing 1993, 2(4):534–539. 10.1109/83.242363View ArticleGoogle Scholar
  18. Bose NK, Kim HC, Valenzuela HM: Recursive total least squares algorithm for image reconstruction from noisy, undersampled frames. Multidimensional Systems and Signal Processing 1993, 4(3):253–268. 10.1007/BF00985891MATHView ArticleGoogle Scholar
  19. Bose NK, Kim HC, Zhou B: Performance analysis of the TLS algorithm for image reconstruction from a sequence of undersampled noisy and blurred frames. Proceedings of IEEE International Conference on Image Processing (ICIP '94), November 1994, Austin, Tex, USA 3: 571–574.View ArticleGoogle Scholar
  20. Poletto L, Nicolosi P: Enhancing the spatial resolution of a two-dimensional discrete array detector. Optical Engineering 1999, 38(10):1748–1757. 10.1117/1.602228View ArticleGoogle Scholar
  21. Koeck PJB: Ins and outs of digital electron microscopy. Microscopy Research and Technique 2000, 49(3):217–223. 10.1002/(SICI)1097-0029(20000501)49:3<217::AID-JEMT1>3.0.CO;2-3View ArticleGoogle Scholar
  22. Peled S, Yeshurun Y: Super-resolution in MRI: application to human white matter fiber tract visualization by diffusion tensor imaging. Magnetic Resonance in Medicine 2001, 45(1):29–35. 10.1002/1522-2594(200101)45:1<29::AID-MRM1005>3.0.CO;2-ZView ArticleGoogle Scholar
  23. 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. 10.1109/83.935034MATHView ArticleGoogle Scholar
  24. Mann S, Picard RW: Video orbits of the projective group a simple approach to featureless estimation of parameters. IEEE Transactions on Image Processing 1997, 6(9):1281–1295. 10.1109/83.623191View ArticleGoogle Scholar
  25. Lertrattanapanich S, Bose NK: Latest results on high-resolution reconstruction from video sequences. In IEICE Tech. Rep. DSP99-140. The Institution of Electronic, Information and Communication Engineers, Tokyo, Japan; 1999. pp. 59–65Google Scholar
  26. Ng MK, Koo J, Bose NK: Constrained total least-squares computations for high-resolution image reconstruction with multisensors . International Journal of Imaging Systems and Technology 2002, 12(1):35–42. 10.1002/ima.10004View ArticleGoogle Scholar
  27. Sauer K, Allebach J: Iterative reconstruction of bandlimited images from nonuniformly spaced samples. IEEE Transactions on Circuits and Systems 1987, 34(12):1497–1506. 10.1109/TCS.1987.1086088View ArticleGoogle Scholar
  28. Ur H, Gross D: Improved resolution from subpixel shifted pictures. CVGIP: Graphical Models and Image Processing 1992, 54(2):181–186. 10.1016/1049-9652(92)90065-6Google Scholar
  29. Bose NK, Lertrattanapanich S: Polynomial matrix factorization, multidimensional filter banks, and wavelets. In Sampling, Wavelets, and Tomography. Edited by: Benedetto JJ, Zayed AI. Birkhäuser, Boston, Mass, USA; 2004:137–156. chapter 6MATHView ArticleGoogle Scholar
  30. Lertrattanapanich S, Bose NK: High resolution image formation from low resolution frames using Delaunay triangulation. IEEE Transactions on Image Processing 2002, 11(12):1427–1441. 10.1109/TIP.2002.806234MathSciNetView ArticleGoogle Scholar
  31. Nguyen N, Milanfar P: A wavelet-based interpolation-restoration method for super-resolution (Wavelet Superresolution). Circuits Systems Signal Processing 2000, 19(4):321–338. 10.1007/BF01200891MATHView ArticleGoogle Scholar
  32. Bascle B, Blake A, Zisserman A: Motion deblurring and super-resolution from an image sequence. In Proceedings of 4th European Conference on Computer Vision (ECCV '96), April 1996, Cambridge, UK. Volume 2. Springer; 573–582.Google Scholar
  33. Rajan D, Chaudhuri S: An MRF-based approach to generation of super-resolution images from blurred observations. Journal of Mathematical Imaging and Vision 2002, 16(1):5–15. 10.1023/A:1013961817285MathSciNetMATHView ArticleGoogle Scholar
  34. Golub GH, Van Loan CF: Matrix Computations. 2nd edition. Johns Hopkins University Press, Baltimore, Md, USA; 1989.MATHGoogle Scholar
  35. Biggs DSC, Andrews M: Asymmetric iterative blind deconvolution of multiframe images. Advanced Signal Processing Algorithms, Architectures, and Implementations VIII, July 1998, San Diego, Calif, USA, Proceedings of SPIE 3461: 328–338.Google Scholar
  36. Chappalli MB, Bose NK: Enhanced Biggs-Andrews asymmetric iterative blind deconvolution. accepted for publication, August 2005, in Multidimensional Systems and Signal Processing and to appear in print in 2006Google Scholar
  37. 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.2003.1227986View ArticleGoogle Scholar
  38. Bose NK, Boo KJ: Asymptotic eigenvalue distribution of block-Toeplitz matrices. IEEE Transactions on Information Theory 1998, 44(2):858–861. 10.1109/18.661535MathSciNetMATHView ArticleGoogle Scholar


© Bose et al. 2006