Response to the comments on "Fundamental limits of reconstruction-based superresolution algorithms under local translation"

Wang and Feng (IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 5, p 846, May 2006) pointed out that the deduction in (Z. Lin and H. Y. Shum, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 1, pp. 83-97, Jan. 2004) overlooked the validity of the perturbation theorem used in (Z. Lin and H. Y. Shum, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 1, pp. 83-97, Jan. 2004). 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 (Z. Lin and H. Y. Shum, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 1, pp. 83-97, Jan. 2004).