Hyperspectral unmixing by the alternating direction method of multipliers

Russell E.  Warren; Stanley J.  Osher

doi:10.3934/ipi.2015.9.917

Article Contents

2015, Volume 9, Issue 3: 917-933. Doi: 10.3934/ipi.2015.9.917

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Hyperspectral unmixing by the alternating direction method of multipliers

Russell E. Warren^1, and
Stanley J. Osher^2,

1.
EO-Stat Inc. of North Carolina, 10010 Vail Dr., Chapel Hill, NC, 27517
2.
Department of Mathematics, University of California, Los Angeles, CA, 90095

Received: May 31, 2014

Revised: August 31, 2014

Published: July 2015

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Abstract

We have developed a method for hyperspectral image data unmixing that requires neither pure pixels nor any prior knowledge about the data. Based on the well-established Alternating Direction Method of Multipliers, the problem is formulated as a biconvex constrained optimization with the constraints enforced by Bregman splitting. The resulting algorithm estimates the spectral and spatial structure in the image through a numerically stable iterative approach that removes the need for separate endmember and spatial abundance estimation steps. The method is illustrated on data collected by the SpecTIR imaging sensor.

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Mathematics Subject Classification: 65K10, 65F22, 15A23, 49K30.

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References

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