Adaptive Estimation of Component Proportion in a Pixel of a Multispectral Image

Spectral unmixing is a method by which to estimate the proportion of each component in a pixel using multispectral data. In conventional analysis of remotely sensed images, each pixel is classified into a single object category. However, the actual land surface corresponding to a pixel does not necessarily consist of only one category of objects. Therefore, estimating the proportion of components that exist in a pixel is often useful. The most commonly used method of spectral unmixing assumes that the component spectra are determined from training data. However, available training data do not always correctly represent the spectral characteristics of the categories within the objective area. In such cases, large errors may appear in the results of unmixing. We propose herein the adaptive spectral unmixing method, which estimates suitable component spectra from the actual observed data and thus requires no training data. By adaptively estimating the component spectra from the set of observed data in the objective area, we can correctly estimate the proportion of components even if the spectral characteristics change with the location of objective area. In the proposed method, the spectral reflectance of pixels is expressed by vectors in multi-dimensional space, which can be written as linear combinations of component spectra weighted according to component proportion. We determine the component spectra by finding the minimum volume of simplex containing all of the reflectance vectors, where the vertexes of the simplex correspond to the component spectra. We estimated the degree of errors by numerical simulation and compared the performance of the proposed adaptive method and that of the conventional method. We confirmed that the proposed method of adaptive unmixing provides better results than the conventional method when the spectral characteristics change with the location of the objective area.