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The point spread function (PSF) is ubiquitous in remote sensing. This paper investigated the effect of the PSF on the downscaling of continua. Geostatistical approaches were adopted to incorporate explicitly, and reduce the influence of, the PSF effect in downscaling. Two general cases were considered: univariate and multivariate. In the univariate case, the input coarse spatial resolution image is the only image available for downscaling. Area-to-point kriging was demonstrated to be a suitable solution in this case. For the multivariate case, a finer spatial resolution image (or images) observed under different conditions (e.g., at a different wavelength) is available as auxiliary data for downscaling. Area-to-point regression kriging was shown to be a suitable solution for this case. Moreover, a new solution was developed for estimating the PSF in image scale transformation. The experiments show that the PSF effect influences downscaling greatly and that downscaling can be enhanced obviously by considering the PSF effect through the geostatistical approaches and the PSF estimation solution proposed. [ABSTRACT FROM AUTHOR]

Pan-sharpening is a technique to combine the fine spatial resolution panchromatic (PAN) band with the coarse spatial resolution multispectral bands of the same satellite to create a fine spatial resolution multispectral image. In this paper, area-to-point regression kriging (ATPRK) is proposed for pan-sharpening. ATPRK considers the PAN band as the covariate. Moreover, ATPRK is extended with a local approach, called adaptive ATPRK (AATPRK), which fits a regression model using a local, non-stationary scheme such that the regression coefficients change across the image. The two geostatistical approaches, ATPRK and AATPRK, were compared to the 13 state-of-the-art pan-sharpening approaches summarized in Vivone et al. (2015) in experiments on three separate datasets. ATPRK and AATPRK produced more accurate pan-sharpened images than the 13 benchmark algorithms in all three experiments. Unlike the benchmark algorithms, the two geostatistical solutions precisely preserved the spectral properties of the original coarse data. Furthermore, ATPRK can be enhanced by a local scheme in AATRPK, in cases where the residuals from a global regression model are such that their spatial character varies locally. [ABSTRACT FROM AUTHOR]