Next Article in Journal
Fuzzy Classification for Shoreline Change Monitoring in a Part of the Northern Coastal Area of Java, Indonesia
Previous Article in Journal
Interpretation of Forest Resources at the Individual Tree Level in Japanese Conifer Plantations Using Airborne LiDAR Data
Article Menu

Export Article

Open AccessArticle
Remote Sens. 2016, 8(3), 187; doi:10.3390/rs8030187

0-Norm Sparse Hyperspectral Unmixing Using Arctan Smoothing

Department of Electrical and Computer Engineering, Walter Light Hall, Queen’s University, Kingston, ON K7L 3N6, Canada
*
Authors to whom correspondence should be addressed.
Academic Editors: Lenio Soares Galvao, Richard Gloaguen and Prasad S. Thenkabail
Received: 23 September 2015 / Revised: 3 February 2016 / Accepted: 16 February 2016 / Published: 26 February 2016
View Full-Text   |   Download PDF [799 KB, uploaded 26 February 2016]   |  

Abstract

The goal of sparse linear hyperspectral unmixing is to determine a scanty subset of spectral signatures of materials contained in each mixed pixel and to estimate their fractional abundances. This turns into an ℓ0 -norm minimization, which is an NP-hard problem. In this paper, we propose a new iterative method, which starts as an ℓ1 -norm optimization that is convex, has a unique solution, converges quickly and iteratively tends to be an ℓ0 -norm problem. More specifically, we employ the arctan function with the parameter σ ≥ 0 in our optimization. This function is Lipschitz continuous and approximates ℓ1 -norm and ℓ0 -norm for small and large values of σ, respectively. We prove that the set of local optima of our problem is continuous versus σ. Thus, by a gradual increase of σ in each iteration, we may avoid being trapped in a suboptimal solution. We propose to use the alternating direction method of multipliers (ADMM) for our minimization problem iteratively while increasing σ exponentially. Our evaluations reveal the superiorities and shortcomings of the proposed method compared to several state-of-the-art methods. We consider such evaluations in different experiments over both synthetic and real hyperspectral data, and the results of our proposed methods reveal the sparsest estimated abundances compared to other competitive algorithms for the subimage of AVIRIS cuprite data. View Full-Text
Keywords: sparse spectral unmixing; hyperspectral imaging; linear mixing model; spectral library; smoothed 0-norm sparse spectral unmixing; hyperspectral imaging; linear mixing model; spectral library; smoothed 0-norm
Figures

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Esmaeili Salehani, Y.; Gazor, S.; Kim, I.-M.; Yousefi, S. 0-Norm Sparse Hyperspectral Unmixing Using Arctan Smoothing. Remote Sens. 2016, 8, 187.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Remote Sens. EISSN 2072-4292 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top