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Many powerful pansharpening approaches exploit the functional relation between the fusion of PANchromatic (PAN) and MultiSpectral (MS) images. To this purpose, the modulation transfer function of the MS sensor is typically used, being easily approximated as a Gaussian filter whose analytic expression is fully specified by the sensor gain at the Nyquist frequency. However, this characterization is often inadequate in practice. In this paper, we develop an algorithm for estimating the relation between PAN and MS images directly from the available data through an efficient optimization procedure. The effectiveness of the approach is validated both on a reduced scale data set generated by degrading images acquired by the IKONOS sensor and on full-scale data consisting of images collected by the QuickBird sensor. In the first case, the proposed method achieves performances very similar to that of the algorithm that relies upon the full knowledge of the degrading filter. In the second, it is shown to outperform several very credited state-of-the-art approaches for the extraction of the details used in the current literature.
Vivone et al. (Fri,) studied this question.