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

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 enable 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 sensitiveness, 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 3-D 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 the capture of geometrical and statistical spectral-spatial structures. After the 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 the 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 data sets.