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Hyperspectral unmixing has the objective of quantifying the reflectance properties of different materials on the Earth. It includes estimating the number of constituent materials, i.e., “endmembers,” in the data, extracting their spectral signatures, and estimating the corresponding ground cover fractions called “abundances.” The need for spectral unmixing has been increased by the development of powerful hyperspectral sensors in the field of remote sensing. These sensors acquire a set of coregistered images of a scene with hundreds of narrow and contiguous bands covering the visible, near-infrared, and mid-infrared wavelengths of the electromagnetic spectrum. Due to the limited spatial (ground) resolution supported by high-altitude sensors, the materials are often spatially mixed. One can unmix them by finding the number of endmembers, their signatures, and their abundances using algorithmic approaches. This kind of analysis yields myriad data products in remote sensing, defense and military, agricultural development, urban planning, and many other areas. It is difficult to obtain a closed-form solution for unmixing because of the physical constraints involved while using the mixing model. Because this is a severely ill-posed problem, the use of regularization can significantly improve the solution. In this book, we discuss the role of regularization for unmixing. The use of appropriate priors is shown in order to obtain better estimates of endmembers and abundances. We also highlight the regularization-based algorithms in other important areas of remote sensing.
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