Sen Jia

Constrained Nonnegative Matrix Factorization for Hyperspectral Unmixing

Hyperspectral unmixing is a process to identify the constituent materials and estimate the corresponding fractions from the mixture. During the last few years, nonnegative matrix factorization (NMF), as a suitable candidate for the linear spectral mixture model, has been applied to unmix hyperspectral data. Unfortunately, the local minima caused by the nonconvexity of the objective function makes the solution nonunique, thus only the nonnegativity constraint is not sufficient enough to lead to a well-defined problem. Therefore, in this paper, two inherent characteristics of hyperspectral data, piecewise smoothness (both temporal and spatial) of spectral data and sparseness of abundance fraction of every material, are introduced to NMF. The adaptive potential function from discontinuity adaptive Markov random field model is used to describe the smoothness constraint while preserving discontinuities in spectral data. At the same time, two NMF algorithms, nonsmooth NMF and NMF with sparseness constraint, are used to quantify the degree of sparseness of material abundances. A gradient-based optimization algorithm is presented, and the monotonic convergence of the algorithm is proved. Three important facts are exploited in our method: First, both the spectra and abundances are nonnegative; second, the variation of the material spectra and abundance images is piecewise smooth in wavelength and spatial spaces, respectively; third, the abundance distribution of each material is almost sparse in the scene. Experiments using synthetic and real data demonstrate that the proposed algorithm provides an effective unsupervised technique for hyperspectral unmixing.

Hyperspectral Unmixing via

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 end-members. As an important constraint for NMF, sparsity has been modeled making use of the <i>L</i>₁ regularizer. Unfortunately, the <i>L</i>₁ 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 <i>L</i>_1/2 sparsity constraint, which we name <i>L</i>_1/2 -NMF. The <i>L</i>_1/2 regularizer not only induces sparsity but is also a better choice among <i>Lq</i>(0 <; <i>q</i> <; 1) regularizers. We propose an iterative estimation algorithm for <i>L</i>_1/2-NMF, which provides sparser and more accurate results than those delivered using the <i>L</i>₁ norm. We illustrate the utility of our method on synthetic and real hyperspectral data and compare our results to those yielded by other state-of-the-art methods.

L_{1/2}

The rich information available in hyperspectral imagery has provided significant opportunities for material classification and identification. Due to the problem of the “curse of dimensionality” (called Hughes phenomenon) posed by the high number of spectral channels along with small amounts of labeled training samples, dimensionality reduction is a necessary preprocessing step for hyperspectral data. Generally, in order to improve the classification accuracy, noise bands generated by various sources (primarily the sensor and the atmosphere) are often manually removed in advance. However, the removal of these bands may discard some important discriminative information, eventually degrading the classification accuracy. In this paper, we propose a new strategy to automatically select bands without manual band removal. Firstly, wavelet shrinkage is applied to denoise the spatial images of the whole data cube. Then affinity propagation, which is a recently proposed feature selection approach, is used to choose representative bands from the noise-reduced data. Experimental results on three real hyperspectral data collected by two different sensors demonstrate that the bands selected by our approach on the whole data (containing noise bands) could achieve higher overall classification accuracies than those by other state-of-the-art feature selection techniques on the manual-band-removal (MBR) data, even better than the bands identified by the proposed approach on the MBR data, indicating that the removed “noise” bands are valuable for hyperspectral classification, which should not be eliminated.

Sparsity-Constrained Nonnegative Matrix Factorization

The rich information available in hyperspectral imagery not only poses significant opportunities but also makes big challenges for material classification. Discriminative features seem to be crucial for the system to achieve accurate and robust performance. In this paper, we propose a 3-D Gabor-wavelet-based approach for pixel-based hyperspectral imagery classification. A set of complex Gabor wavelets with different frequencies and orientations is first designed to extract signal variances in space, spectrum, and joint spatial/spectral domains. The magnitude of the response at each sampled location (x, y) for spectral band b contains rich information about the signal variances in the local region. Each pixel can be well represented by the rich information extracted by Gabor wavelets. A feature selection and fusion process has also been developed to reduce the redundancy among Gabor features and make the fused feature more discriminative. The proposed approach was fully tested on two real-world hyperspectral data sets, i.e., the widely used Indian Pine site and Kennedy Space Center. The results show that our method achieves as high as 96.04% and 95.36% accuracies, respectively, even when only few samples, i.e., 5% of the total samples per class, are labeled.

Unsupervised Band Selection for Hyperspectral Imagery Classification Without Manual Band Removal

Hyperspectral unmixing, which decomposes pixel spectra into a collection of constituent spectra, is a preprocessing step for hyperspectral applications like target detection and classification. It can be considered as a blind source separation (BSS) problem. Independent component analysis, which is a widely used method for performing BSS, models a mixed pixel as a linear mixture of its constituent spectra weighted by the correspondent abundance fractions (sources). The sources are assumed to be independent and stationary. However, in many instances, this assumption is not valid. In this paper, a complexity-based BSS algorithm is introduced, which studies the complexity of sources instead of the independence. We extend the 1-D temporal complexity, which is called complexity pursuit that was proposed by Stone, to the 2-D spatial complexity, which is named spatial complexity BSS (SCBSS), to describe the spatial autocorrelation of each abundance fraction. Further, the temporal complexity of spectrum is combined into SCBSS to account for the spectral smoothness, which is termed spectral and spatial complexity BSS. More importantly, a strict theoretic interpretation is given, showing that the complexity-based BSS is very suitable for hyperspectral unmixing. Experimental results on synthetic and real hyperspectral data demonstrate the advantages of the proposed two algorithms with respect to other methods.

Three-Dimensional Gabor Wavelets for Pixel-Based Hyperspectral Imagery Classification

Sparse-representation-based classification (SRC) assigns a test sample to the class with minimum representation error via a sparse linear combination of all the training samples, which has successfully been applied to several pattern recognition problems. According to compressive sensing theory, the l1-norm minimization could yield the same sparse solution as the l0 norm under certain conditions. However, the computational complexity of the l1-norm optimization process is often too high for large-scale high-dimensional data, such as hyperspectral imagery (HSI). To make matter worse, a large number of training data are required to cover the whole sample space, which is difficult to obtain for hyperspectral data in practice. Recent advances have revealed that it is the collaborative representation but not the l1-norm sparsity that makes the SRC scheme powerful. Therefore, in this paper, a 3-D Gabor feature-based collaborative representation (3GCR) approach is proposed for HSI classification. When 3-D Gabor transformation could significantly increase the discrimination power of material features, a nonparametric and effective l2-norm collaborative representation method is developed to calculate the coefficients. Due to the simplicity of the method, the computational cost has been substantially reduced; thus, all the extracted Gabor features can be directly utilized to code the test sample, which conversely makes the l2-norm collaborative representation robust to noise and greatly improves the classification accuracy. The extensive experiments on two real hyperspectral data sets have shown higher performance of the proposed 3GCR over the state-of-the-art methods in the literature, in terms of both the classifier complexity and generalization ability from very small training sets.

Spectral and Spatial Complexity-Based Hyperspectral Unmixing

Through imaging the same spatial area by hyperspectral sensors at different spectral wavelengths simultaneously, the acquired hyperspectral imagery often contains hundreds of band images, which provide the possibility to accurately analyze and identify a ground object. However, due to the difficulty of obtaining sufficient labeled training samples in practice, the high number of spectral bands unavoidably leads to the problem of a “dimensionality disaster” (also called the Hughes phenomenon), and dimensionality reduction should be applied. Concerning band (or feature) selection, conventional methods choose the representative bands by ranking the bands with defined metrics (such as non-Gaussianity) or by formulating the band selection problem as a clustering procedure. Because of the different but complementary advantages of the two kinds of methods, it can be beneficial to use both methods together to accomplish the band selection task. Recently, a fast density-peak-based clustering (FDPC) algorithm has been proposed. Based on the computation of the local density and the intracluster distance of each point, the product of the two factors is sorted in decreasing order, and cluster centers are recognized as points with anomalously large values; hence, the FDPC algorithm can be considered a ranking-based clustering method. In this paper, the FDPC algorithm has been enhanced to make it suitable for hyperspectral band selection. First, the ranking score of each band is computed by weighting the normalized local density and the intracluster distance rather than equally taking them into account. Second, an exponential-based learning rule is employed to adjust the cutoff threshold for a different number of selected bands, where it is fixed in the FDPC. The proposed approach is thus named the enhanced FDPC (E-FDPC). Furthermore, an effective strategy, which is called the isolated-point-stopping criterion, is developed to automatically determine the appropriate number of bands to be selected. That is, the clustering process will be stopped by the emergence of an isolated point (the only point in one cluster). Experimental results on three real hyperspectral data demonstrate that the bands selected by our E-FDPC approach could achieve higher classification accuracy than the FDPC and other state-of-the-art band selection techniques, whereas the isolated-point-stopping criterion is a reasonable way to determine the preferable number of bands to be selected.

Gabor Feature-Based Collaborative Representation for Hyperspectral Imagery Classification

Feature extraction based on three-dimensional (3D) wavelet transform is capable of improving the classification accuracy of hyperspectral imagery data by simultaneously capturing the geometrical and statistical spectral-spatial structure of the data. Nevertheless, the design of wavelets is always proceeded with empirical parameters, which tends to involve a large number of irrelevant and redundant spectral-spatial features and results in suboptimal configuration. This paper proposes a 3D Gabor wavelet feature extraction in a memetic framework, named M3DGFE, for hyperspectral imagery classification. Particularly, the parameter setting of 3D Gabor wavelet feature extraction is optimized using memetic algorithm so that discriminative and parsimonious feature set is acquired for accurate classification. M3DGFE is characterized by an efficient fitness evaluation function and a pruning local search. In the fitness evaluation function, a new concept of redundancy-free relevance based on conditional mutual information is proposed to measure the goodness of the extracted candidate features. The pruning local search is specially designed to eliminate both irrelevant and redundant features without sacrificing the discriminability of the obtained feature subset. M3DGFE is tested on both pixel-level and image-level classification using real-world hyperspectral remote sensing data and hyperspectral face data, respectively. The experimental results show that M3DGFE achieves promising classification accuracy with parsimonious feature subset.

A Novel Ranking-Based Clustering Approach for Hyperspectral Band Selection

Three-dimensional Gabor wavelets have recently been successfully applied for hyperspectral image classification due to their ability to extract joint spatial and spectrum information. However, the dimension of the extracted Gabor feature is incredibly huge. In this letter, we propose a symmetrical-uncertainty-based and Markov-blanket-based approach to select informative and nonredundant Gabor features for hyperspectral image classification. The extracted Gabor features with large dimension are first ranked by their information contained for classification and then added one by one after investigating the redundancy with already selected features. The proposed approach was fully tested on the widely used Indian Pine site data. The results show that the selected features are much more efficient and can achieve similar performance with previous approach using only hundreds of features.

Three-dimensional Gabor feature extraction for hyperspectral imagery classification using a memetic framework

Hundreds of narrow contiguous spectral bands collected by a hyperspectral sensor have provided the opportunity to identify the various materials present on the surface. Moreover, spatial information, enforcing the assumption that the adjacent pixels belong to the same class with a high probability, is a valuable complement to the spectral information. In this paper, two predominant approaches have been developed to exploit the spatial information. First, by decomposing each pixel and the spatial neighborhood into a low-rank form, the spatial information can be efficiently integrated into the spectral signatures. Meanwhile, in order to describe the low-rank structure of the decomposed data more precisely, an ℓ1/2 norm regularization is introduced and a discrete algorithm is proposed to solve the combined optimization problem by the augmented Lagrange multiplier (ALM) and a half-threshold operator. Second, a graph cuts segmentation algorithm has been applied on the sparse-representation-based probability estimates of the hyperspectral data to further improve the spatial homogeneity of the material distribution. Experimental results on four real hyperspectral data with different spectral and spatial resolutions have demonstrated the effectiveness and versatility of the proposed spatial information-fused approaches for hyperspectral image classification.