Gabor  Collaborative Representation for spectral Imagery

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.