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1 Hyperspectral Unmixing Via L1/2 Sparsityconstrained Nonnegative Matrix Factorization
"... 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 endmembers. As an important constra ..."
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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 endmembers. As an important constraint for NMF, sparsity has been modeled making use of the L1 regularizer. Unfortunately, the L1 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 L1/2 sparsity constraint, which we name L1/2NMF. The L1/2 regularizer not only induces sparsity, but is also a better choice among Lq(0 < q < 1) regularizers. We propose an iterative estimation algorithm for L1/2NMF, which provides sparser and more accurate results than those delivered using the L1 norm. We illustrate the utility of our method on synthetic and real hyperspectral data and compare our results to those yielded by other stateoftheart methods.
Directly Measuring Material Proportions Using Hyperspectral Compressive Sensing
"... AbstractA compressive sensing framework is described for hyperspectral imaging. It is based on the widely used linear mixing model, LM M , which represents hyperspectral pixels as convex combinations of small numbers of endmember (material) spectra. The coefficients of the endmembers for each pixe ..."
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AbstractA compressive sensing framework is described for hyperspectral imaging. It is based on the widely used linear mixing model, LM M , which represents hyperspectral pixels as convex combinations of small numbers of endmember (material) spectra. The coefficients of the endmembers for each pixel are called proportions. The endmembers and proportions are often the sought after quantities; the full image is an intermediate representation used to calculate them. Here a method for estimating proportions and endmembers directly from compressively sensed hyperspectral data based on LM M is shown. Consequently, proportions and endmembers can be calculated directly from compressively sensed data with no need to reconstruct full hyperspectral images. If spectral information is required, endmembers can be reconstructed using compressive sensing reconstruction algorithms. Furthermore, given known endmembers, the proportions of the associated materials can be measured directly using a compressive sensing imaging device. This device would produce a multiband image; the bands would directly represent the material proportions.