IEEE Trans Image Process. 2015 Nov;24(11):3441-9. doi: 10.1109/TIP.2015.2446196. Epub 2015 Jun 16.
The linear mixture model (LMM) plays a crucial role in the spectral unmixing of hyperspectral data. Under the assumption of LMM, the solution with the minimum reconstruction error is considered to be the ideal endmember. However, for practical hyperspectral data sets, endmembers that enclose all the pixels are physically meaningless due to the effect of noise. Therefore, in many cases, it is not sufficient to consider only the reconstruction error, some constraints (for instance, volume constraint) need to be added to the endmembers. The two terms can be considered as serving two forces: minimizing the reconstruction error forces the endmembers to move outward and thus enlarges the volume of the simplex while the endmember constraint acts in the opposite direction by driving the endmembers to move inward so as to constrain the volume to be smaller. Many existing methods obtain their solution just by balancing the two contradictory forces. The solution acquired in this way can not only minimize the reconstruction error but also be physically meaningful. Interestingly, we find, in this paper, that the two forces are not completely contradictory with each other, and the reconstruction error can be further reduced without changing the volume of the simplex. And more interestingly, our method can further optimize the solution provided by all the endmember extraction methods (both endmember selection methods and endmember generation methods). After optimization, the final endmembers outperform the initial solution in terms of reconstruction error as well as accuracy. The experiments on simulated and real hyperspectral data verify the validation of our method.
线性混合模型 (LMM) 在高光谱数据的光谱解混中起着至关重要的作用。在 LMM 的假设下，具有最小重建误差的解被认为是理想的端元。然而，对于实际的高光谱数据集，由于噪声的影响，包含所有像素的端元在物理上是没有意义的。因此，在许多情况下，仅仅考虑重建误差是不够的，需要给端元添加一些约束（例如，体积约束）。这两个术语可以被认为是两种力：最小化重建误差迫使端元向外移动，从而增大单形的体积，而端元约束则通过驱使端元向内移动以约束体积较小而起到相反的作用。许多现有的方法只是通过平衡这两种相互矛盾的力来获得它们的解。这种方法获得的解不仅可以最小化重建误差，而且具有物理意义。有趣的是，我们在本文中发现，这两种力并不是完全相互矛盾的，在不改变单形体积的情况下，重建误差可以进一步降低。更有趣的是，我们的方法可以进一步优化所有端元提取方法（端元选择方法和端元生成方法）提供的解。经过优化，最终的端元在重建误差和准确性方面都优于初始解。对模拟和真实高光谱数据的实验验证了我们方法的有效性。
