Interband structure modeling for oversampled multiresolution analysis-based Pan-sharpening of very high resolution multispectral images

This paper addresses the modeling of wavelet coefficients for multispectral (MS) band sharpening based on undecimated multiresolution analysis (MRA). The coarse MS bands are sharpened by injecting highpass details taken from a high resolution panchromatic (Pan) image. Besides the MRA, crucial point is modeling the relationships between detail coefficients of a generic MS band and the Pan image at the same resolution. Once calculated at the coarser resolution, where both types of data are available, such a model shall be extrapolated to the finer resolution in order to weight the Pan details to be injected. The goal is that the merged MS images are most similar to what the MS sensor would collect if it had the same resolution as the broadband Pan imager. Three injection models embedded in an "a trous" wavelet decomposition will be described and compared on a test set of very high resolution QuickBird MS+Pan data. Two models work on approximation and detail coefficients, respectively, and provide a certain degree of unmixing of coarse MS pixels. The third model is based on spectral fidelity of the merged image to the (resampled) original MS data, that is, no unmixing is attempted. It is much simpler than the other two because it does not require, calculation of local statistics. Fusion comparisons on spatially degraded data, of which higher-resolution true MS data are available for reference, show that the former two models yield better results than the latter, in terms of both radiometric and spectral fidelity. The latter, however, yields a reliable sharpening unaffected by local. artifacts, regardless of landscape complexity. When local statistics of wavelet coefficients are utilized, the model estimated on approximation yields slightly better but considerably stabler results than that calculated starting from bandpass details