Atmospheric corrections for pansharpening

Among remote sensing image fusion applications, panchromatic (Pan) sharpening, or pansharpening, of a multispectral (MS) image has received considerable attention over the last quarter of century. Pansharpening techniques take advantage of the complementary characteristics of spatial and spectral resolutions of MS and Pan data, in order to synthesize a unique product that exhibits as many spectral bands as the original MS image, each with same spatial resolution as the Pan image. After the MS bands have been interpolated and co-registered to the Pan image, spatial details are extracted from Pan and added to the MS bands according to a certain injection model. The detail extraction step may follow the spectral approach, originally known as component substitution (CS) or the spatial approach, which may rely on multiresolution analysis (MRA). The Pan image is preliminarily histogram-matched, that is, radiometrically transformed by constant gain and offset in such a way that its low-pass version (PanL) exhibits mean and variance same as the component that shall be replaced, for CS methods, or the MS band that shall be sharpened for MRA methods. In some cases, histogram matching is implicitly performed by the injection model. The latter rules the combination of the low-pass MS image with the spatial detail extracted from Pan. Such a model is stated between each of the re-sampled MS bands and a low-pass version of the Pan image having same spatial frequency content as the MS bands. Although several models have been introduced, the most popular are: i) the projection model, which may be derived from the Gram-Schmidt (GS) orthogonalization procedure, representing the basis of the GS spectral sharpening and of the context-based decision (CBD); ii) the multiplicative or modulation model, which is the basis of such techniques as high-pass modulation (HPM), Brovey transform (BT), synthetic variable ratio (SVR), Zhang's UNB pansharp, smoothing filter-based intensity modulation (SFIM) and additive wavelet luminance proportional (AWLP). Unlike the projection model, which may be either global, as for GS, or local, as for CBD, the multiplicative model is inherently local, because the injection gain changes at each pixel. The pioneering paper that introduced SFIM firstly gave an interpretation of the multiplicative injection model in terms of the radiative transfer model ruling the acquisition of an MS image from a real-world scene. Accordingly, the kth MS band interpolated at the pixel scale of Pan represents a low spatial resolution spectral radiance, that is, a radiance with a spectral diversity. Pan represents the high spatial resolution solar irradiance, which bears no spectral information, but only spatial and radiometric information. Thus, its lowpass-filtered version, PanL, having the same spatial frequency content as the interpolated MS bands, is a low-resolution irradiance and conveys radiometric information at the spatial resolution of MS. Ultimately, a high resolution MS (HRMS) is synthesized at each pixel as low resolution MS (LRMS) divided by PanL and multiplied by Pan. Since the ratio of spectral radiance to solar irradiance is an estimate of spectral reflectance, when the ratio between LRMS and PanL is multiplied by Pan, a low-resolution reflectance is multiplied by a high resolution irradiance. So far, very few authors have ever considered the path radiance of the kth band, which is an energy scattered by the atmosphere that reaches the aperture of the instrument without being reflected by the Earth's surface. Thus, the path radiance of each band, which appears as a haze in a color composite display of the MS bands, should be estimated and removed from the band before the modulation is accomplished and re-inserted after the