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A signal processing perspective on hyperspectral unmixing: Insights from remote sensing
 IEEE Signal Processing Magazine
, 2014
"... Blind hyperspectral unmixing (HU), also known as unsupervised HU, is one of the most prominent research topics in signal processing for hyperspectral remote sensing [1, 2]. Blind HU aims at identifying materials present in a captured scene, ..."
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Blind hyperspectral unmixing (HU), also known as unsupervised HU, is one of the most prominent research topics in signal processing for hyperspectral remote sensing [1, 2]. Blind HU aims at identifying materials present in a captured scene,
The why and how of nonnegative matrix factorization
 REGULARIZATION, OPTIMIZATION, KERNELS, AND SUPPORT VECTOR MACHINES. CHAPMAN & HALL/CRC
, 2014
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SelfDictionary Sparse Regression for Hyperspectral Unmixing: Greedy Pursuit and Pure Pixel Search Are Related
"... Abstract—This paper considers a recently emerged hyperspectral unmixing formulation based on sparse regression of a selfdictionary multiple measurement vector (SDMMV) model, wherein the measured hyperspectral pixels are used as the dictionary. Operating under the pure pixel assumption, this SD ..."
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Abstract—This paper considers a recently emerged hyperspectral unmixing formulation based on sparse regression of a selfdictionary multiple measurement vector (SDMMV) model, wherein the measured hyperspectral pixels are used as the dictionary. Operating under the pure pixel assumption, this SDMMV formalism is special in that it allows simultaneous identification of the endmember spectral signatures and the number of endmembers. Previous SDMMV studies mainly focus on convex relaxations. In this study, we explore the alternative of greedy pursuit, which generally provides efficient and simple algorithms. In particular, we design a greedy SDMMV algorithm using simultaneous orthogonal matching pursuit. Intriguingly, the proposed greedy algorithm is shown to be closely related to some existing pure pixel search algorithms, especially, the successive projection algorithm (SPA). Thus, a link between SDMMV and pure pixel search is revealed. We then perform exact recovery analyses, and prove that the proposed greedy algorithm is robust to noiseincluding its identification of the (unknown) number of endmembersunder a sufficiently low noise level. The identification performance of the proposed greedy algorithm is demonstrated through both synthetic and realdata experiments. Index Terms—Greedy pursuit, hyperspectral unmixing, number of endmembers estimation, selfdictionary sparse regression.
Successive Nonnegative Projection Algorithm for Robust Nonnegative Blind Source Separation
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Robustness Analysis of Structured Ma trix Factorization via SelfDictionary MixedNorm Optimization
"... Abstract—We are interested in a lowrank matrix factorization problem where one of the matrix factors has a special structure; specifically, its columns live in the unit simplex. This problem finds applications in diverse areas such as hyperspectral unmixing, video summarization, spectrum sensing, a ..."
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Abstract—We are interested in a lowrank matrix factorization problem where one of the matrix factors has a special structure; specifically, its columns live in the unit simplex. This problem finds applications in diverse areas such as hyperspectral unmixing, video summarization, spectrum sensing, and blind speech separation. Prior works showed that such a factorization problem can be formulated as a selfdictionary sparse optimization problem under some assumptions that are considered realistic in many applications, and convex mixed norms were employed as optimization surrogates to realize the factorization in practice. Numerical results have shown that the mixednorm approach demonstrates promising performance. In this letter, we conduct performance analysis of the mixednorm approach under noise perturbations. Our result shows that using a convex mixed norm can indeed yield provably good solutions. More importantly, we also show that using nonconvex mixed (quasi) norms is more advantageous in terms of robustness against noise. Index Terms—Matrix factorization, performance analysis, selfdictionary sparse optimization. I.
1 Blind and fully constrained unmixing of hyperspectral images
"... This paper addresses the problem of blind and fully constrained unmixing of hyperspectral images. Unmixing is performed without the use of any dictionary, and assumes that the number of constituent materials in the scene and their spectral signatures are unknown. The estimated abundances satisfy the ..."
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This paper addresses the problem of blind and fully constrained unmixing of hyperspectral images. Unmixing is performed without the use of any dictionary, and assumes that the number of constituent materials in the scene and their spectral signatures are unknown. The estimated abundances satisfy the desired sumtoone and nonnegativity constraints. Two models with increasing complexity are developed to achieve this challenging task, depending on how noise interacts with hyperspectral data. The first one leads to a convex optimization problem, and is solved with the Alternating Direction Method of Multipliers. The second one accounts for signaldependent noise, and is addressed with a Reweighted Least Squares algorithm. Experiments on synthetic and real data demonstrate the effectiveness of our approach. 2 I.