Hyperspectral Image Classification Based on Structured Sparse Logistic Regression and Three-Dimensional Wavelet Texture Features

Yuntao Qian, Minchao Ye, Jun Zhou
<span title="">2013</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4odsbtjobjalfki6xxabjpdu6y" style="color: black;">IEEE Transactions on Geoscience and Remote Sensing</a> </i> &nbsp;
Hyperspectral remote sensing imagery contains rich information on spectral and spatial distributions of distinct surface materials. Owing to its numerous and continuous spectral bands, hyperspectral data enables more accurate and reliable material classification than using panchromatic or multispectral imagery. However, high-dimensional spectral features and limited number of available training samples have caused some difficulties in the classification, such as overfitting in learning, noise
more &raquo; ... nsitiveness, overloaded computation, and lack of meaningful physical interpretability. In this paper, we propose a hyperspectral feature extraction and pixel classification method based on structured sparse logistic regression and three-dimensional discrete wavelet transform (3D-DWT) texture features. The 3D-DWT decomposes a hyperspectral data cube at different scales, frequencies and orientations, during which the hyperspectral data cube is considered as a whole tensor instead of adapting the data to a vector or matrix. This allows capture of geometrical and statistical spectral-spatial structures. After feature extraction step, sparse representation/modeling is applied for data analysis and processing via sparse regularized optimization, which selects a small subset of the original feature variables to model the data for regression and classification purpose. A linear structured sparse logistic regression model is proposed to simultaneously select the discriminant features from the pool of 3D-DWT texture features and learn the coefficients of linear classifier, in which the prior knowledge about feature structure can be mapped into the various sparsity-inducing norms such as lasso, group and sparse group lasso. Furthermore, to overcome the limitation of linear models, we extended the linear sparse model to nonlinear classification by partitioning the feature space into subspaces of linearly separable samples. The advantages of our methods are validated on the real hyperspectral remote sensing datasets. DRAFT Hyperspectral imaging has opened up new opportunities for analyzing a variety of materials due to the rich information on spectral and spatial distributions of the distinct materials in hyperspectral imagery. In many hyperspectral applications, pixel classification is an important task, which can be used for material recognition, target detection, geoindexing, and so on. The state-of-the-art classification techniques have increased the possibility of assigning each pixel with an accurate class label [1] . However, such efforts still face some challenges. This is partly due to the high-dimension low-sample-size classification problem caused by the large number of narrow spectral bands with a small number of available labeled training samples. This problem, coupled with other difficulties such as high variations of the spectral signature from identical material, high similarities of spectral signatures between some different materials, and noise from the sensors and environment, will significantly decrease the classification accuracy. Many methods have been proposed to address these problems. A main strategy is to explore the intrinsic/hidden discriminant features that are useful to classification, while reducing the noisy/redundant features that impair the performance of classification. For hyperspectral imagery classification, spatial distribution is the most important information other than the spectral signatures. Therefore, pixel-wise classification followed by spatial-filtering preprocessing becomes a simple and effective method to implement this strategy [2] . Compared with the original spectral signatures, the filtered features have less intraclass variability and higher spatial smoothness, with somehow reduced noises. Another widely used method is to combine the spatial and spectral information into a classifier. Different from pixel-wise classification methods that do not consider spatial structure, spectral-spatial-hybrid classification tries to preserve the local consistency of the class labels in the pixel neighborhood. In [3], [4], such a method was proposed to combine the results of a pixel-wise classification with a segmentation map in order to form a spectral-spatial classification map. The segmentation map is built by the use of both a clustering algorithm and Gaussian mixtures [3], and by the use of both multiple classifiers and a minimum spanning forest [4]. For the same purpose, Markov random field (MRF) and conditional random field based spectral-spatial structure modeling have been reported in [5], [6], [7], [8]. The MRF model incorporates spatial information into a classification step by modifying the form of a probabilistic discriminative function via adding a term of contextual correlation. In a similar manner, Li et al combined the posterior class densities, which are generated by a subspace multinomial logistic regression classifier, and spatial contextual information that is represented by MRF-based multilevel logistic prior into a combinatorial optimization problem, and solved this maximum a posteriori segmentation problem by graph cuts algorithm [8]. To enhance kernel classification methods such as support vector machine (SVM) and Gaussian process, a full framework of composite kernels for hyperspectral classification was proposed that combines contextual and spectral information into kernel distance function [9] . In addition, other information, such as the intrinsic structure between spectral bands, unlabeled pixels, and labeled pixels in another area, is also commonly used in filtering [10], semi-supervised learning [11], [12], active learning [13] , and transfer learning [14] methods. In recent years, wavelet transform has been investigated owing to its solid and formal mathematical framework for
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