TY - JOUR
T1 - Gradient Type Methods for Linear Hyperspectral Unmixing
AU - Xu , Fangfang
AU - Wang , Yating
AU - Li , Yanyan
AU - Liu , Lu
AU - Tian , Tonghua
JO - CSIAM Transactions on Applied Mathematics
VL - 1
SP - 109
EP - 132
PY - 2022
DA - 2022/03
SN - 3
DO - http://doi.org/10.4208/csiam-am.SO-2021-0001
UR - https://global-sci.org/intro/article_detail/csiam-am/20291.html
KW - Hyperspectral unmixing, minimum volume simplex, linear mixture model, alternating minimization, proximal gradient method, adaptive moments method, stochastic variance reduction strategy.
AB - <p style="text-align: justify;">Hyperspectral unmixing (HU) plays an important role in terrain classification, agricultural monitoring, mineral recognition and quantification, and military
surveillance. The existing model of the linear HU requires the observed vector to be a
linear combination of the vertices. Due to the presence of noise, or any other perturbation source, we relax this linear constraint and penalize it to the objective function.
The obtained model is solved by a sequence of gradient type steps which contain a
projection onto the simplex constraint. We propose two gradient type algorithms for
the linear HU, which can find vertices of the minimum volume simplex containing
the observed hyper-spectral vectors. When the number of given pixels is huge, the
computational time and complexity are so large that solving HU efficiently is usually
challenging. A key observation is that our objective function is a summation of many
similar simple functions. Then the computational time and complexity can be reduced
by selecting a small portion of data points randomly. Furthermore, a stochastic variance reduction strategy is used. Preliminary numerical results showed that our new
algorithms outperformed state-of-the-art algorithms on both synthetic and real data.</p>