Identifiability-Guaranteed Simplex-Structured Post-Nonlinear Mixture Learning via Autoencoder

Lyu, Qi; Fu, Xiao

doi:10.1109/tsp.2021.3096806

Cited by 8 publications

(9 citation statements)

References 33 publications

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“…Therefore, computing α (t) and β (t) takes O(R 3 ) flops, but R is normally small. In the AP solver, (19b) costs O(IJR log R) flops via the water-filling type algorithm, the SVD in (20) takes O(IJLR), and the projection in (21) takes O(max{I, J} 3 R + min{I, J} log min{I, J}).…”

Section: E Computational Complexitymentioning

confidence: 99%

See 1 more Smart Citation

Fast and Structured Block-Term Tensor Decomposition For Hyperspectral Unmixing

Ding¹,

Xiao²,

Zhao³

2022

Preprint

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The block-term tensor decomposition model with multilinear rank-(Lr, Lr, 1) terms (or, the "LL1 tensor decomposition" in short) offers a valuable alternative for hyperspectral unmixing (HU) under the linear mixture model. Particularly, the LL1 decomposition ensures the endmember/abundance identifiability in scenarios where such guarantees are not supported by the classic matrix factorization (MF) approaches. However, existing LL1-based HU algorithms use a three-factor parameterization of the tensor (i.e., the hyperspectral image cube), which leads to a number of challenges including high per-iteration complexity, slow convergence, and difficulties in incorporating structural prior information. This work puts forth an LL1 tensor decomposition-based HU algorithm that uses a constrained two-factor re-parameterization of the tensor data. As a consequence, a two-block alternating gradient projection (GP)-based LL1 algorithm is proposed for HU. With carefully designed projection solvers, the GP algorithm enjoys a relatively low per-iteration complexity. Like in MF-based HU, the factors under our parameterization correspond to the endmembers and abundances. Thus, the proposed framework is natural to incorporate physics-motivated priors that arise in HU. The proposed algorithm often attains orders-of-magnitude speedup and substantial HU performance gains compared to the existing three-factor parameterization-based HU algorithms.

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Section: E Computational Complexitymentioning

confidence: 99%

“…Interested readers are referred to surveys in [18], [19]. More recent developments using neural networks can be found in the literature as well; see, e.g., [20], [21]. Nonetheless, we focus on the more classic and more widely used LMM in this work.…”

Section: Introductionmentioning

confidence: 99%

Fast and Structured Block-Term Tensor Decomposition For Hyperspectral Unmixing

Ding¹,

Xiao²,

Zhao³

2022

Preprint

Self Cite

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show abstract

“…In fact, numerical evidence shows that the LMM can oftentimes explain the vast majority of pixels with high accuracy; see, e.g., [15]. It is worth noting that many nonlinear mixture models are also proposed for HU; see [16] and recent developments using neural networks, e.g., [17]. Nonlinear models are used to capture the complex dynamics and data generating mechanisms that could not be interpreted by the LMM, which reduces modeling errors and enhances the HU performance.…”

mentioning

confidence: 99%

“…Nonlinear models are used to capture the complex dynamics and data generating mechanisms that could not be interpreted by the LMM, which reduces modeling errors and enhances the HU performance. However, using nonlinear models is not without price-the computational problems under nonlinear models are in general much harder to tackle (especially when deep neural networks are involved); see, e.g., [17]. In fact, the LMM often allows us to design algorithms that strike a good balance between modeling accuracy and computational convenience.…”

mentioning

confidence: 99%

Fast and Structured Block-Term Tensor Decomposition for Hyperspectral Unmixing

Ding

Zhao

2023

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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The block-term tensor decomposition model with multilinear rank-(L r , L r , 1) terms (or the "LL1 tensor decomposition" in short) offers a valuable alternative formulation for hyperspectral unmixing (HU), which ensures the identifiability of the endmembers/abundances in cases where classic matrix factorization (MF) approaches cannot provide such guarantees. However, the existing LL1-tensor-decomposition-based HU algorithms use a three-factor parameterization of the tensor (i.e., the hyperspectral image cube), which causes difficulties in incorporating structural prior information arising in HU. Consequently, their algorithms often exhibit high per-iteration complexity and slow convergence. This article focuses on LL1 tensor decomposition under structural constraints and regularization terms in HU. Our algorithm uses a two-factor reparameterization of the tensor model. Like in the MF-based approaches, the factors correspond to the endmembers and abundances in the context of HU. Thus, the proposed framework is natural to incorporate physics-motivated priors in HU. To tackle the formulated optimization problem, a two-block alternating gradient projection (GP)-based algorithm is proposed. Carefully designed projection solvers are proposed to implement the GP algorithm with a relatively low per-iteration complexity. An extrapolation-based acceleration strategy is proposed to expedite the GP algorithm. Such an extrapolated multiblock algorithm only had asymptotic convergence assurances in the literature. Our analysis shows that the algorithm converges to the vicinity of a stationary point within finite iterations, under reasonable conditions. Empirical study shows that the proposed algorithm often attains orders-of-magnitude speedup and substantial HU performance gains compared with the existing LL1-decomposition-based HU algorithms.

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“…A supervised autoencoder was used in [24] for Fan, bilinear, and PPNM, in which radial basis function (RBF) kernels and K-means clustering were used for the estimation of the number of endmembers and the endmember spectra, respectively. Most DL-based nonlinear unmixing techniques are autoencoder-based architectures based on PPNM and, therefore suffer from the drawbacks of the bilinear models mentioned above [25], [26], [27]. A deep autoencoder was proposed in [28] where the encoder utilizes an extra nonlinear layer to model the nonlinearity in the data.…”

mentioning

confidence: 99%

HapkeCNN: Blind Nonlinear Unmixing for Intimate Mixtures Using Hapke Model and Convolutional Neural Network

Rasti

Koirala

Scheunders

2022

IEEE Trans. Geosci. Remote Sensing

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This paper proposes a blind nonlinear unmixing technique for intimate mixtures using the Hapke model and convolutional neural networks (HapkeCNN). We use the Hapke model and a fully convolutional encoder-decoder deep network for the nonlinear unmixing. Additionally, we propose a novel loss function that includes three terms; 1) a quadratic term based on the Hapke model, that captures the nonlinearity, 2) the reconstruction error of the reflectances, to ensure the fidelity of the reconstructed reflectance, and 3) a minimum volume total variation term that exploits the geometrical information to estimate the endmembers in the absence of pure pixels in the hyperspectral data. The proposed method is evaluated using two simulated and two real datasets. We compare the results of endmember and abundance estimation with a number of nonlinear, and projection-based linear unmixing techniques. The experimental results confirm that HapkeCNN considerably outperforms the state-of-the-art nonlinear approaches.The proposed method was implemented in Python (3.8) using PyTorch as the platform for the deep network and is available at: https://github.com/BehnoodRasti/HapkeCNN.

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Identifiability-Guaranteed Simplex-Structured Post-Nonlinear Mixture Learning via Autoencoder

Cited by 8 publications

References 33 publications

Fast and Structured Block-Term Tensor Decomposition For Hyperspectral Unmixing

Fast and Structured Block-Term Tensor Decomposition For Hyperspectral Unmixing

Fast and Structured Block-Term Tensor Decomposition for Hyperspectral Unmixing

HapkeCNN: Blind Nonlinear Unmixing for Intimate Mixtures Using Hapke Model and Convolutional Neural Network

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