Pan-sharpening is a common post-processing operation for captured multispectral satellite imagery, where the spatial resolution of images gathered in various spectral bands is enhanced by fusing them with a panchromatic image captured at a higher resolution. Previously proposed pan-sharpening techniques operate on a per-channel basis, sharpening each multispectral band independently based on the panchromatic image, often in an ad hoc manner. In contrast with most prior techniques, we formulate pan-sharpening as the problem of jointly estimating the high resolution multispectral images to minimize the combined squared residual error in physically motivated observation models of the low resolution multispectral and the high resolution panchromatic images. To realize pan-sharpening using our proposed formulation, we develop an iterative algorithm to solve the joint minimization resulting in an overall algorithm with modest computational complexity. We evaluate our proposed algorithm and benchmark it against previously proposed methods using established quantitative measures of SNR, SAM, ERGAS, Q, and Q4 indices. Both the quantitative results and visual evaluation demonstrate that the proposed joint formulation provides superior results compared with pre-existing methods.Index Terms-pan-sharpening, satellite imagery, image fusion, spectral imaging
INTRODUCTIONFor reasons of cost, bandwidth, and to maintain adequate image quality in the presence of noise, satellite based multi and hyper spectral image capture systems use on-board imaging sensors that vary in spatial resolution: typical sensor configurations, capture a high resolution panchromatic image spanning a wide spectral band and lower resolution images for individual spectral bands. For applications using the satellite imagery, once data is received on the ground, the spectral band images are post-processed to obtain versions that match the higher resolution sampling of the panchromatic image. This process, commonly referred to as pan-sharpening, merges together low resolution and spectral information captured in spectral channels with high resolution detail from the panchromatic image. Several image pan-sharpening methods have been proposed in the literature. A majority of these techniques operate using a component or subband substitution framework where the multispectral and the panchromatic images are mapped into a transform domain and in the transform domain, some component or subband data of the panchromatic image is inserted or used to replace the data in the multispectral image, and the inverse transform is then applied to this modified transform domain spectral image to obtain the pan-sharpened version. Common examples in the substitution framework include: a) methods based purely on "color", i.e. channel transforms, such as intensity-hue-saturation (IHS) substitution [1][2][3], Brovey transform, principal component replacement, Gram-Schmidt transform [4], and b) methods based on spatial transforms, such as the multi-scale wavelet decomposition...