Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization

By Y. Qian, Sen Jia, Jun Zhou, Antonio Robles-Kelly. IEEE Transactions on Geoscience and Remote Sensing, 2011

558 citations recorded by the source corpus.

Hyperspectral unmixing is a crucial preprocessing step for material classification and recognition. In the last decade, nonnegative matrix factorization (NMF) and its extensions have been intensively studied to unmix hyperspectral imagery and recover the material end-members. As an important constraint for NMF, sparsity has been modeled making use of the <i>L</i>₁ regularizer. Unfortunately, the <i>L</i>₁ regularizer cannot enforce further sparsity when the full additivity constraint of material abundances is used, hence limiting the practical efficacy of NMF methods in hyperspectral unmixing. In this paper, we extend the NMF method by incorporating the <i>L</i>_1/2 sparsity constraint, which we name <i>L</i>_1/2 -NMF. The <i>L</i>_1/2 regularizer not only induces sparsity but is also a better choice among <i>Lq</i>(0 <; <i>q</i> <; 1) regularizers. We propose an iterative estimation algorithm for <i>L</i>_1/2-NMF, which provides sparser and more accurate results than those delivered using the <i>L</i>₁ norm. We illustrate the utility of our method on synthetic and real hyperspectral data and compare our results to those yielded by other state-of-the-art methods.

Subfields: Computational Mechanics, Media Technology

View Paper: https://www.semanticscholar.org/paper/3c89873fa414456d6e8a5c17e28f0172193bcbe9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Antonio J. Plaza
2. José M. Bioucas-Dias
3. Marian-Daniel Iordache
4. Jocelyn Chanussot
5. Paul D. Gader
6. Y. Qian
7. Mario Parente
8. Nicolas Dobigeon

In Media Technology

1. José M. Bioucas-Dias
2. Antonio J. Plaza
3. Jocelyn Chanussot
4. Nicolas Gillis
5. Y. Qian
6. Shutao Li
7. Paul D. Gader
8. Nicolas Dobigeon

Citations in the corpus

• Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches (2012, methodology): “The L1/2-NMF method introduced in [146] formulates a nonnegative matrix factorization problem similar to (11), where the volume regularizer is replaced with the sparsity-enforcing regularizer ‖S‖1/2 ≡ ∑p i=1 ∑n j=1 |αij |1/2.”
• Manifold Regularized Sparse NMF for Hyperspectral Unmixing (2013, methodology): “Recently, a novel NMF method named L1/2-NMF [24] has been introduced to unmix hyperspectral data.”
• Hyperspectral Image Spatial Super-Resolution via 3D Full Convolutional Neural Network (2017, background): “Such analysis can be fulfilled by extracting endmembers [9,10] and estimating their fractional abundance [11] separately, or treating these two problems simultaneously as a blind signal decomposition problem, for which non-negative matrix factorization (NMF) [12,13], convex optimization [14], and Ne”
• Hyperspectral Image Classification Based on Structured Sparse Logistic Regression and Three-Dimensional Wavelet Texture Features (2013, background): “The dictionary of endmembers and the corresponding abundances can also be learned at the same time from a hyperspectral imagery by sparse models [36], [37].”
• Total Variation Spatial Regularization for Sparse Hyperspectral Unmixing (2012, methodology): “In [51], a sparsity constraint is included in non-negative matrix factorization, a widely used technique to unmix hyperspectral images and recover the material endmembers [52], [53].”
• A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing (2014, methodology): “Specifically, we carry out the following heuristic: for , , ,k N1 f= determine an estimate IEEE SIGNAL PROCESSING MAGAZINE [74] JANUARY 2014 { [ ], , [ ]},arg maxb P f b x x L1s.t. conv b Fk k k2 2”