Nonnegative Matrix Factorization With Data-Guided Constraints For Hyperspectral Unmixing

Huang, Risheng; Li, Xiaorun; Zhao, Liaoying

doi:10.3390/rs9101074

Cited by 11 publications

(6 citation statements)

References 39 publications

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“…Algorithms such as projective gradient and multiplicative iteration [ 21 ] are used to solve the NMF problems, these algorithms minimize the objective function starting from two non-negative matrices and iterate continuously, and the process decreases. Although the minimization problem of Equation (1) is separately convex in

and

, it is not simultaneously convex in both matrices.…”

Section: Linear Spectral Mixture Modelmentioning

confidence: 99%

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Non-Negative Matrix Factorization Based on Smoothing and Sparse Constraints for Hyperspectral Unmixing

Jia

Guo

2022

Sensors

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Hyperspectral unmixing (HU) is a technique for estimating a set of pure source signals (end members) and their proportions (abundances) from each pixel of the hyperspectral image. Non-negative matrix factorization (NMF) can decompose the observation matrix into the product of two non-negative matrices simultaneously and can be used in HU. Unfortunately, a limitation of many traditional NMF-based methods, i.e., the non-convexity of the objective function, may lead to a sub-optimal solution. Thus, we put forward a new unmixing method based on NMF under smoothing and sparse constraints to obtain a better solution. First, considering the sparseness of the abundance matrix, a weight sparse regularization is introduced into the NMF model to ensure the sparseness of the abundance matrix. Second, according to the similarity prior of the same feature in the adjacent pixels, a Total Variation regularization is further added to the NMF model to improve the smoothness of the abundance map. Finally, the signatures of each end member are modified smoothly in spectral space. Moreover, it is noticed that discontinuities may emerge due to the removal of noisy bands. Therefore, the spectral data are piecewise smooth in spectral space. Then, in this paper, a piecewise smoothness constraint is further applied to each column of the end-member matrix. Experiments are conducted to evaluate the effectiveness of the proposed method based on two different datasets, including a synthetic dataset and the real-life Cuprite dataset, respectively. Experimental results show that the proposed method outperforms several state-of-the-art HU methods. In the Cuprite hyperspectral dataset, the proposed method’s Spectral Angle Distance is 0.1694, compared to the TV-RSNMF method’s 0.1703, L1/2NMF method’s 0.1925, and VCA-FCLS method’s 0.1872.

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and

, it is not simultaneously convex in both matrices.…”

Section: Linear Spectral Mixture Modelmentioning

confidence: 99%

“…Therefore, the solutions are not unique, which is the biggest disadvantage of the NMF-based algorithm. The two most commonly used methods to solve this problem are to assign appropriate initial values and add constraints [ 21 ].…”

Section: Linear Spectral Mixture Modelmentioning

confidence: 99%

Non-Negative Matrix Factorization Based on Smoothing and Sparse Constraints for Hyperspectral Unmixing

Jia

Guo

2022

Sensors

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“…The results show that NMF-SMC outperforms both VCA and MVC-NMF algorithms. In [31], the authors introduce NMF with Data-Guided Constraint (DGC-NMF). The authors propose estimating the abundance map of the data by using unconstrained NMF as a first step.…”

Section: Introductionmentioning

confidence: 99%

FPGA Implementation of L_1/2 Sparsity Constrained Nonnegative Matrix Factorization Algorithm for Remotely Sensed Hyperspectral Image Analysis

et al. 2020

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Remotely sensed hyperspectral images provide data of the earth's surface components. The data provided is collected through airborne devices such as satellites with the capability to collect large amounts of data to be sent to ground stations for processing. The main disadvantage of this scenario is the limited bandwidth connection between the airborne devices and the ground station on Earth which affects the information sending and real time processing. A possible solution is to include an on-board data processor. Field-Programmable Gate Arrays (FPGAs) are excellent target platform that allows the design reconfigurability, powerful computing and high performance levels. One of the most commonly used techniques in hyperspectral data analysis is linear spectral unmixing. In the last decade, L 1/2 sparsity constrained Nonnegative Matrix Factorization (NMF), a linear spectral unmixing algorithm, and its extensions have been heavily studied to unmix the hyperspectral images and recover their material spectra. L 1/2 regularizer is proven to have much better results in terms of sparsity and accuracy than other regularizers yet, to the best of our knowledge, has not been implemented. In this paper, we present an FPGA design for the L 1/2 sparsity constrained NMF (L 1/2 -NMF) algorithm. The proposed design is tested on both synthetic and real data sets and implemented on Altera Family FPGAs. Implementation results show that the proposed design successfully unmixes the data with maximum frequency of 52.6 MHz and a speedup factor of 3.9 for the synthetic data set and a frequency of 104.32 MHz and a speedup factor of 1.14 for the real data set. The implementation results are compared to the simulation results and ground truth signatures using Spectral Angular Distance (SAD) measure. Calculations show that the implementation results have comparable SAD values to the simulation results.INDEX TERMS Field-programmable gate arrays (FPGAs), hyperspectral unmixing, L 1/2 nonnegative matrix factorization algorithm (NMF).

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“…Non-negative matrix factorization approaches for estimate the endmembers as well as abundance simultaneous incorporating regularization terms like low-rank constraints, total variation. The notable NMF based unmixing methods such as Huang et al [23], Wang et al [24], Tsinos et al [25], Arngren et al [26], Jia et al [27], Huck et al [28], Zhang et al [29] employ different regularization terms to constrain the solution. However, unsupervised unmixing methods can produce satisfactory performance only when some of the image pixels contain dominant endmembers.…”

Section: Introductionmentioning

confidence: 99%

Fast Semi-Supervised Unmixing of Hyperspectral Image by Mutual Coherence Reduction and Recursive PCA

Das¹,

Routray²,

Deb³

2018

Remote Sensing

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Dictionary pruning step is often employed prior to the sparse unmixing process to improve the performance of library aided unmixing. This paper presents a novel recursive PCA approach for dictionary pruning of linearly mixed hyperspectral data motivated by the low-rank structure of a linearly mixed hyperspectral image. Further, we propose a mutual coherence reduction method for pre-unmixing to enhance the performance of pruning. In the pruning step we, identify the actual image endmembers utilizing the low-rank constraint. We obtain an augmented version of the data by appending each image endmember and compute PCA reconstruction error, which is a convex surrogate of matrix rank. We identify the pruned library elements according to PCA reconstruction error ratio (PRER) and PCA reconstruction error difference (PRED) and employ a recursive formulation for repeated PCA computation. Our proposed formulation identifies the exact endmember set at an affordable computational requirement. Extensive simulated and real image experiments exhibit the efficacy of the proposed algorithm in terms of its accuracy, computational complexity and noise performance.

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Nonnegative Matrix Factorization With Data-Guided Constraints For Hyperspectral Unmixing

Cited by 11 publications

References 39 publications

Non-Negative Matrix Factorization Based on Smoothing and Sparse Constraints for Hyperspectral Unmixing

Non-Negative Matrix Factorization Based on Smoothing and Sparse Constraints for Hyperspectral Unmixing

FPGA Implementation of L_1/2 Sparsity Constrained Nonnegative Matrix Factorization Algorithm for Remotely Sensed Hyperspectral Image Analysis

Fast Semi-Supervised Unmixing of Hyperspectral Image by Mutual Coherence Reduction and Recursive PCA

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Nonnegative Matrix Factorization With Data-Guided Constraints For Hyperspectral Unmixing

Cited by 11 publications

References 39 publications

Non-Negative Matrix Factorization Based on Smoothing and Sparse Constraints for Hyperspectral Unmixing

Non-Negative Matrix Factorization Based on Smoothing and Sparse Constraints for Hyperspectral Unmixing

FPGA Implementation of L1/2 Sparsity Constrained Nonnegative Matrix Factorization Algorithm for Remotely Sensed Hyperspectral Image Analysis

Fast Semi-Supervised Unmixing of Hyperspectral Image by Mutual Coherence Reduction and Recursive PCA

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FPGA Implementation of L_1/2 Sparsity Constrained Nonnegative Matrix Factorization Algorithm for Remotely Sensed Hyperspectral Image Analysis