Revealing implicit assumptions of the component substitution pansharpening methods

Abstract

The component substitution (CS) pansharpening methods have been developed for almost three decades and have become better understood recently by generalizing them into one framework. However, few studies focus on the statistical assumptions implicit in the CS methods. This paper reveals their implicit statistical assumptions from a Bayesian data fusion framework and suggests best practices for histogram matching of the panchromatic image to the intensity image, a weighted summation of the multispectral images, to better satisfy these assumptions. The purpose of histogram matching was found to make the difference between the high-resolution panchromatic and intensity images as small as possible, as one implicit assumption claims their negligible difference. The statistical relationship between the high-resolution panchromatic and intensity images and the relationship between their corresponding low-resolution images are the same, as long as the low resolution panchromatic image is derived by considering the modulation transfer functions of the multispectral sensors. Hence, the histogram-matching equation should be derived from the low-resolution panchromatic and intensity images, but not derived from the high-resolution panchromatic and expanded low-resolution intensity images. Experiments using three example CS methods, each using the two different histogram-matching equations, was conducted on the four-band QuickBird and eight-bandWorldView-2 top-of-atmosphere reflectance data. The results verified the best practices and showed that the histogram-matching equation derived from the high-resolution panchromatic and expanded low-resolution intensity images provides more-blurred histogram-matched panchromatic image and, hence less-sharpened pansharpened images than that derived from the low-resolution image pair. The usefulness of the assumptions revealed in this study for method developers is discussed. For example, the CS methods can be improved by satisfying the assumptions better, e.g., classifying the images into homogenous areas before pansharpening, and by changing the assumptions to be more general to address their deficiencies.