This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Fundamental Limits of Reconstruction-Based Superresolution Algorithms under Local Translation
January 2004 (vol. 26 no. 1)
pp. 83-97
ASCII Text
x 
 
Zhouchen Lin, Heung-Yeung Shum, "Fundamental Limits of Reconstruction-Based Superresolution Algorithms under Local Translation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 1, pp. 83-97, January, 2004.
 
 
BibTex
x
 
@article{ 10.1109/TPAMI.2004.10003,
author = {Zhouchen Lin and Heung-Yeung Shum},
title = {Fundamental Limits of Reconstruction-Based Superresolution Algorithms under Local Translation},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {26},
number = {1},
issn = {0162-8828},
year = {2004},
pages = {83-97},
doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2004.10003},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Fundamental Limits of Reconstruction-Based Superresolution Algorithms under Local Translation
IS - 1
SN - 0162-8828
SP83
EP97
EPD - 83-97
A1 - Zhouchen Lin,
A1 - Heung-Yeung Shum,
PY - 2004
KW - Superresolution
KW - reconstruction-based algorithms
KW - conditioning analysis
KW - fundamental limits
KW - magnification factor.
VL - 26
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 

Abstract—Superresolution is a technique that can produce images of a higher resolution than that of the originally captured ones. Nevertheless, improvement in resolution using such a technique is very limited in practice. This makes it significant to study the problem: “Do fundamental limits exist for superresolution?” In this paper, we focus on a major class of superresolution algorithms, called the reconstruction-based algorithms, which compute high-resolution images by simulating the image formation process. Assuming local translation among low-resolution images, this paper is the first attempt to determine the explicit limits of reconstruction-based algorithms, under both real and synthetic conditions. Based on the perturbation theory of linear systems, we obtain the superresolution limits from the conditioning analysis of the coefficient matrix. Moreover, we determine the number of low-resolution images that are sufficient to achieve the limit. Both real and synthetic experiments are carried out to verify our analysis.

[1] S. Baker and T. Kanade, “Hallucinating Faces,” Technical Report CMU-RI-TR-99-32, The Robotics Inst., Carnegie Mellon Univ. 1999.
[2] S. Baker and T. Kanade, “Limits on Super-Resolution and How to Break Them,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 372-379, 2000.
[3] D.F. Barbe, Charge-Coupled Devices. Springer-Verlag, 1980.
[4] B. Bascle, A. Blake, and A. Zisserman, “Motion Deblurring and Super-Resolution from an Image Sequence,” Proc. European Conf. Computer Vision, pp. 573-581, 1996.
[5] S. Borman and R.L. Stevenson, “Spatial Resolution Enhancement of Low-Resolution Image Sequences: A Comprehensive Review with Directions for Future Research,” technical report, Univ. of Notre Dame, 1998.
[6] N.K. Bose, H.C. Kim, and H.M. Valenzuela, “Recursive Implementation of Total Least Squares Algorithm for Image Reconstruction from Noisy, Undersampled Multiframes,” Proc. IEEE Int'l Conf. Acoustics, Speech, and Signal Processing, vol. 5, pp. 269-272, 1993.
[7] P. Cheeseman, B. Kanefsky, R. Kraft, and J. Stutz, “Super-Resolved Surface Reconstruction from Multiple Images,” Technical Report FIA-94-12, NASA, 1994.
[8] M. Elad and A. Feuer, “Restoration of Single Super-Resolution Image from Several Blurred, Noisy and Down-Sampled Measured Images,” IEEE Trans. Image Processing, vol. 6, no. 12, pp. 1646-1658, 1997.
[9] K. Forbes and V.V. Anh, “Condition of System Matrices in Image Restoration,” J. Optical Soc. Am., vol. 11, no. 6, pp. 1727-1735, 1994.
[10] W.T. Freeman and E.C. Pasztor, “Learning Low-Level Vision,” Proc. Int'l Conf. Computer Vision, pp. 1182-1189, 1999.
[11] G.H. Golub and C.F. Van Loan, Matrix Computations, third ed. Baltimore: The John Hopkins Univ. Press, 1996.
[12] R.C. Hardie, K.J. Barnard, and E.E. Amstrong, “Joint Map Registration and High-Resolution Image Estimation Using a Sequence of Undersampled Images,” IEEE Trans. Image Processing, vol. 6, no. 12, pp. 1621-1633, 1997.
[13] N.J. Higham, “A Survey of Componentwise Perturbation Theory in Numerical Linear Algebra,” Math. Computation 1943-1993: Proc. Symposia in Applied Math., vol. 48, pp. 49-77. 1994.
[14] T.S. Huang and R. Tsai, “Multi-Frame Image Restoration and Registration,” Advances in Computer Vision and Image Processing, vol. 1, pp. 317-339, 1984.
[15] M. Irani and S. Peleg, “Improving Resolution by Image Restoration,” Computer Vision, Graphics, and Image Processing, vol. 53, pp. 231-239, 1991.
[16] Z. Lin and H.-Y. Shum, “On the Fundamental Limits of Reconstruction-Based Super-Resolution Algorithms,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 1171-1176, Dec. 2001.
[17] S. Mann and R.W. Picard, “Virtual Bellows: Constructing High Quality Stills from Video,” Proc. IEEE Conf. Image Processing, pp. 363-367, Nov. 1994.
[18] F. Milinazzo, C. Zala, and I. Barrodale, “On The Rate of Growth of Condition Numbers for Convolution Matrices,” IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 35, no. 4, pp. 471-475, 1987.
[19] A.J. Patti, M.I. Sezan, and A.M. Tekalp, “Superresolution Video Reconstruction with Arbitrary Sampling Lattices and Nonzero Aperture Time,” IEEE Trans. Image Processing, vol. 6, no. 8, pp. 1064-1076, 1997.
[20] D. Rajan and S. Chauhuri, “Simultaneous Estimation of Super-Resolved Intensity and Depth Maps from Low Resolution Defocused Observations of a Scene,” Proc. Int'l Conf. Computer Vision, pp. 113-118, July 2001.
[21] R. Schultz and R. Stevenson, “Extraction of High-Resolution Frames from Video Sequences,” IEEE Trans. Image Processing, vol. 5, no. 6, pp. 996-1011, 1996.
[22] S. Xu, The Theory and Methods of Matrix Computation (in Chinese). Beijing, China: Peking Univ. Press, 1995.

Index Terms:
Superresolution, reconstruction-based algorithms, conditioning analysis, fundamental limits, magnification factor.
Citation:
Zhouchen Lin, Heung-Yeung Shum, "Fundamental Limits of Reconstruction-Based Superresolution Algorithms under Local Translation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 1, pp. 83-97, Jan. 2004, doi:10.1109/TPAMI.2004.10003
Usage of this product signifies your acceptance of the Terms of Use.