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  • Abstract - Response to the Comments on "Fundamental Limits of Reconstruction-Based Superresolution Algorithms under Local Translation'
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Response to the Comments on "Fundamental Limits of Reconstruction-Based Superresolution Algorithms under Local Translation'
May 2006 (vol. 28 no. 5)
pp. 847
Wang and Feng [1] pointed out that the deduction in [2] overlooked the validity of the perturbation theorem used in [2]. In this paper, we show that, when the perturbation theorem is invalid, the probability of successful superresolution is very low. Therefore, we only have to derive the limits under the condition that validates the perturbation theorem, as done in [2].

[1] L. Wang and J. Feng, “Comments on `Fundamental Limits of Reconstruction-Based Superresolution Algorithms under Local Translation',” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 5, p. 846, May 2006.
[2] Z. Lin and H.-Y. Shum, “Fundamental Limits of Reconstruction-Based Superresolution Algorithms under Local Translation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 1, pp. 83-97, Jan. 2004.
[3] G.H. Golub and C.F. Van Loan, Matrix Computations, third ed. Baltimore: The John Hopkins Univ. Press, 1996.
[4] S. Baker and T. Kanade, “Limits on Super-Resolution and How to Break Them,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 9, pp. 1167-1183, Sept. 2002.

Index Terms:
Superresolution, reconstruction-based algorithms, perturbation theory.
Citation:
Zhouchen Lin, Heung-Yeung Shum, "Response to the Comments on "Fundamental Limits of Reconstruction-Based Superresolution Algorithms under Local Translation'," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 5, pp. 847, May 2006, doi:10.1109/TPAMI.2006.105
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