To fulfill these constraints, numerous special algorithms have been proposed to solve the hyperspectral unmixing problem under the LSMM assumption, including the approaches of convex geometry, Bayesian source separation, and nonnegative matrix factorization (NMF).
In this paper, we propose a novel multi-objective based algorithm to solve the sparse unmixing problem without any relaxation.
This constitutes the classical linear unmixing problem [28, 29].
In this article, the hyperspectral unmixing problem is solved with the nonnegative matrix factorization (NMF) algorithm.
The identified results illustrate the difficulty of the unmixing problem for real data.
Interestingly, this particular type of dependence arises in modeling material abundances in the spectral unmixing problem of remote sensed images.
In this section, we choose SISAL as the compared algorithm because it is able to deal with the unmixing problem without the pure pixel assumption as the NMF algorithms.
In hyperspectral imagery, the number of spectral bands usually exceeds the number of pure spectral components and the unmixing problem is cast in terms of an overdetermined system of equations in which given the correct set of endmembers allows determination of the actual endmember abundance fractions through a numerical inversion process.
The hard geometric unmixing problem in Section 2.1.1 is a non-convex objective in the present parameterization, and was shown by Packer (2002) to be NP-hard when k + 1 ≥ log(s).
Therefore, it is necessary to tackle the unsupervised pattern unmixing problem: given a large collection of images, where none has been tagged as being a representative of a fundamental pattern, map all images into a set of mixture coefficients automatically derived from the data.
We have previously presented some methods that address this pattern unmixing problem in a supervised setting: given images of fundamental patterns (e.g. nuclear and endoplasmic reticulum in the above example) and mixed images, map mixed images into a set of coefficients, one for each fundamental pattern (Peng et al., 2010; Zhao et al., 2005).
