XU Huo-xi

Huanggang Normal University

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Fang Hao

China University of Petroleum, East China

Tao Wang

East China University of Science and Technology

Aihua Li

Central South University

Aihua Li

Xi'an High Tech University

Hongwei Chang

Xi'an High Tech University

Binlin Hu

University of Chinese Academy of Sciences

Zhigao Lan

Huanggang Normal University

Yinnian Liu

Shanghai Institute of Technical Physics

Chuan He

Xi'an High Tech University

Xiaolan Wang

Lanzhou University of Technology

Cooperative Institutions

Xi'an High Tech University

PLA Rocket Force University of Engineering

Huanggang Normal University

University of Chinese Academy of Sciences

Shanghai Institute of Technical Physics

Tsinghua University

China Electronics Technology Group Corporation

Chinese Academy of Sciences

Shenyang Ligong University

Liaocheng People's Hospital

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The expansive discussion on the article Rapidly determine the integral limit in the computation convolution by using graphic solution method

Journal of Huanggang Normal University (2007)

XU Huo-xi

In order to further discuss the article Rapidly determine the integral limit in the computation convolution by using graphic solution method(See Journal of Huanggang Normal University,Issue 6,2004),we give a classification and discussion for the choices of ±∞ which appears in the graphic solution within the convolution integral interval for the functions with value in infinite interval.The values of the functions are unequal to zero in infinite interval.Based on this,we summarize the method for determining the integral limit by using graphic solution partition to the convoluted functions whose values are unequal to zero in infinite interval,and exemplify its application.

Convolution (computer science)

Expansive

Convolution power

Interval arithmetic

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Hyperspectral unmixing using double-constrained multilayer NMF

Remote Sensing Letters (2018)

Fang Hao Aihua Li Tao Wang XU Huo-xi

Hyperspectral unmixing (HU) refers to the process decomposing the entire hyperspectral image into a set of endmembers and the corresponding abundance fractions. Nonnegative matrix factorization (NMF) has been widely used in HU due to its simplicity and effectiveness. Many extensions of NMF have been also developed since traditional NMF has a large solution space. On the other hand, the multilayer structure has shown great advantages in learning data representation. Inspired by these considerations, we added sparsity and geometric structure constraints to the multilayer NMF structure and proposed a double-constrained multilayer NMF (DCMLNMF) method for HU in this paper. The multilayer NMF structure was obtained by iteratively decomposing the target matrix into a number of layers. To improve the unmixing performance, a sparsity constraint term on the abundance matrix and a graph regularization term were both incorporated to each layer. Besides, a layer-wise optimization method based on Nesterov's optimal gradient method was further proposed to solve the multi-factor NMF problem. Experimental results based on both synthetic data and real data demonstrate that the proposed method outperforms several other state-of-art approaches.

Non-negative Matrix Factorization

Regularization

Endmember

10.1080/2150704x.2018.1541107

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Citations (12)

The Physical Explanation of FIR Digital Low Pass Filter

Journal of Daqing Normal University (2006)

XU Huo-xi

Using the calculating and mapping function of the MATLAB,considering the characteristics of digital signal processing,this paper analyzes the physical significance of the convolution operation in time domain and the productive operation in frequency domain with the digital low pass filter as an exemplification.

Exemplification

Convolution (computer science)

Half-band filter

SIGNAL (programming language)

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Hyperspectral unmixing using sparsity-constrained multilayer non-negative matrix factorization

Journal of Applied Remote Sensing (2018)

Fang Hao Aihua Li Tao Wang XU Huo-xi Yanzhao Su

Hyperspectral unmixing (HU) refers to the process of decomposing the hyperspectral image into a set of endmember spectra and the corresponding set of abundance fractions. Non-negative matrix factorization (NMF) has been widely used in HU. However, most NMF-based unmixing methods have single-decomposition structures, which may have poor performance for highly mixed and ill-conditioned data. We proposed a sparsity-constrained multilayer NMF (MLNMF) method for spectral unmixing of highly mixed data. The MLNMF structure was established by decomposing the abundance matrix layer-by-layer to acquire the endmember matrix and the abundance matrix in the next layer. To reduce the space of solutions, sparsity constraints were added to the multilayer model by incorporating an L1 regularizer to the abundance matrix in each layer. Moreover, a layerwise strategy based on the Nesterov’s optimal gradient method was also proposed to optimize the multifactor NMF problem. Experiments on both synthetic data and real data demonstrate that our proposed method outperforms several other state-of-art approaches.

Endmember

Non-negative Matrix Factorization

Matrix (chemical analysis)

Data set

10.1117/1.jrs.12.045009

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Sparsity-Constrained Deep Nonnegative Matrix Factorization for Hyperspectral Unmixing

IEEE Geoscience and Remote Sensing Letters (2018)

Fang Hao Aihua Li XU Huo-xi Tao Wang

Nonnegative matrix factorization (NMF) has been widely used in hyperspectral unmixing (HU). However, most NMF-based methods have single-layer structures, which may achieve poor performance for complex data. Deep learning, with its carefully designed hierarchical structure, has shown great advantages in learning data features. In this letter, we design a deep NMF structure by unfolding NMF into multilayers and present a sparsity-constrained deep NMF method for HU. In each layer, the abundance matrix is directly decomposed into the abundance matrix and endmember matrix of the next layer. Due to the nonconvexity of the NMF model, sparsity constraint is added to each layer using a L ₁ regularizer of the abundance matrix on each layer. To get better initial parameters for the deep NMF network, a layer-wise pretraining strategy based on Nesterov's accelerated gradient algorithm is put forward to initialize the network. An alternative update method is also proposed to further fine-tune the network to get final decomposition results. The experimental results based on synthetic data and real data demonstrate that the proposed method outperforms several other state-of-the-art unmixing approaches.

Non-negative Matrix Factorization

Endmember

Matrix (chemical analysis)

Deep belief network

10.1109/lgrs.2018.2823425

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Citations (26)

An Appreciable Audio Filter Based on the MATLAB

Journal of Hefei University (2006)

XU Huo-xi

This paper analyzes the physical significance of the time domain convolution operation and the frequency domain weight algorithm.And by using the MATLAB sound processing function as the data connection,the multimedia players as the interactive contact surface,the MATLAB FDATool as the filter design tool,designs a group of experiments for audio signal filter with the purpose of strengthening the understanding of the digital signal processing by comparing the change of the audio effect before and after the filter.

Convolution (computer science)

SIGNAL (programming language)

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Analysis and design of FIR digital high pass filter based on the MATLAB

Journal of Changchun University (2006)

XU Huo-xi

The physical significance of the convoluting in time domain and the weighting in frequency domain is analyzed in detail by using the digital high pass filter as the exemplification.And by taking the MATLAB sound processing function as the data connection,the multimedia players as the interactive contact surface,the FDATool of MATLAB as the filter design tool,a group of experiments for audio high pass filter is designed.The understanding of the digital signal processing could be strengthened by comparing the change of the audio effect before and after the filter.

Exemplification

Half-band filter

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A method of determination for the interval of convolution integral by use of the graphic partition

Journal of Dalian University (2006)

XU Huo-xi

A method for determining the interval of convolution integrating by use of the graphic partition is given in this paper,and the application and promotion of this method are exemplified.By use of this method,the interval of independent variable t and the mute variable τin the convolution integral can be determined quickly,only if in the two convoluted functions which value of the end point of the interval is unequal to zero is known,and the computational result is in closed form.This method can avoid the repetition and pretermission of integrating interval(or summarizing interval),especially in the convolution computation of multi-partition function.

Convolution (computer science)

Interval arithmetic

Ordinate

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Hyperspectral unmixing using graph-regularized and sparsity-constrained deep NMF

Optical Sensing and Imaging Technologies and Applications (2018)

Fang Hao Aihua Li Tao Wang Hongwei Chang XU Huo-xi

Nonnegative matrix factorization (NMF) is a widely used method of hyperspectral unmixing (HU) since it can simultaneously decompose the hyperspectral data matrix into two nonnegative matrices. While traditional NMF cannot guarantee the sparsity of the decomposition results and remain the geometric structure during the decomposition. On the other hand, deep learning, with carefully designed multi-layer structures, has shown great potential in learning data representation and been widely used in many fields. In this paper, we proposed a graph-regularized and sparsityconstrained deep NMF (GSDNMF) for hyperspectral unmixing. The deep NMF structure was acquired by unfolding NMF into multiple layers. To improve the unmixing performance, the L₁ regularizers of both the endmember and abundance matrices were used to add sparsity constraint. And the graph regularization term in each layer was also incorporated to remain the geometric structure. Since the model is a multi-factor NMF problem, it is difficult to optimize all the factors simutaneously. In order to acquire better intializations for the model, we proposed a layer-wise pretraining strategy to initialize the deep network based on the efficient NMF solver, NeNMF. An alternative update algorithm was also proposed to further fine-tune the network to obtain the final decompositon results. Experiments on both the synthetic data and real data demonstrate that our algorithm outperforms several state-of-art approaches.

Non-negative Matrix Factorization

Endmember

Regularization

10.1117/12.2505494

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Citations (4)

Unique extraction of U(VI), Pu(IV), Am(III) and Eu(III) from nitric acid medium using a phosphonium based ionic liquid consisting of novel anion, 1,1,1,5,5,5-hexafluoro-2,4-pentanedionate – Dual solvent behavior

Separation and Purification Technology (2021)

Huazhong Liu Xiaolan Wang Zhigao Lan XU Huo-xi

Nitric acid

Phosphonium

Diluent

Stripping (fiber)

10.1016/j.seppur.2021.118309

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Citations (21)