A method for finding structured sparse solutions to nonnegative least squares problems with applications

Ernie Esser Yifei Lou Jack Xin

Numerical Analysis and Scientific Computing mathscidoc:1912.43842

SIAM Journal on Imaging Sciences, 6, (4), 2010-2046, 2013.10
Unmixing problems in many areas such as hyperspectral imaging and differential optical absorption spectroscopy (DOAS) often require finding sparse nonnegative linear combinations of dictionary elements that match observed data. We show how aspects of these problems, such as misalignment of DOAS references and uncertainty in hyperspectral endmembers, can be modeled by expanding the dictionary with grouped elements and imposing a structured sparsity assumption that the combinations within each group should be sparse or even 1-sparse. If the dictionary is highly coherent, it is difficult to obtain good solutions using convex or greedy methods, such as nonnegative least squares (NNLS) or orthogonal matching pursuit. We use penalties related to the Hoyer measure, which is the ratio of the l_1 and l_1 norms, as sparsity penalties to be added to the objective in NNLS-type models. For solving the
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@inproceedings{ernie2013a,
  title={A method for finding structured sparse solutions to nonnegative least squares problems with applications},
  author={Ernie Esser, Yifei Lou, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210134190811406},
  booktitle={SIAM Journal on Imaging Sciences},
  volume={6},
  number={4},
  pages={2010-2046},
  year={2013},
}
Ernie Esser, Yifei Lou, and Jack Xin. A method for finding structured sparse solutions to nonnegative least squares problems with applications. 2013. Vol. 6. In SIAM Journal on Imaging Sciences. pp.2010-2046. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210134190811406.
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