Image fusion methods based on a linear mixing model of multispectral remote sensing data

Model based analysis or explicit definition/listing of all models or assumptions used in the derivation of an image fusion method allows us to understand the rationale or properties of existing methods and shows a way for a proper usage or proposal/selection of new methods ‘better’ satisfying the needs of a particular application. Most existing pan-sharpening methods are based mainly on the two models or assumptions: spectral consistency for high resolution multispectral data (physical relationship between multispectral and panchromatic data in a high resolution scale) and spatial consistency for multispectral data (so-called Wald’s protocol first property or relationship between multispectral data in different resolution scales). Additionally, it can be seen/shown easily that the following two popular groups of methods: spectral transformation (e.g. Intensity-Hue-Saturation (IHS), Principal Component Analysis (PCA) and Gram–Schmidt orthogonalization (GS)) and filtering (e.g. High Pass Filtering (HPF) and Multi-Resolution Analysis (MRA)) based methods are based implicitly on a pure pixels assumption. Thus, their usage for mixed pixels (quite common situation in real remote sensing applications) can lead to wrong image fusion results. Very few methods exist which can treat mixed pixels in a correct way. Two methods, one based on a linear unmixing model and another one based on spatial unmixing, are described/proposed/modified which respect models assumed and thus can produce correct or physically justified fusion results.