Spectral–Spatial Classification of Hyperspectral Images via Spatial Translation-Invariant Wavelet-Based Sparse Representation

For hyperspectral image (HSI) classification, it is challenging to adopt the methodology of sparse-representation-based classification. In this paper, we first propose an l 1 -minimization-based spectral-spatial classification method for HSIs via a spatial translation-invariant wavelet (STIW)-based sparse representation (STIW-SR), wherein both the spectrum dictionary and the analyzed signal are formed with STIW features. Due to the capability of a STIW to reduce both the observation noise and the spatial nonstationarity while maintaining the ideal spectra, which is proved with our signal-interference-noise spectrum model involved, it is expected that the pixels in the same class congregate in a lower dimensional subspace, and the separations among class-specific subspaces are enhanced, thus yielding a highly discriminative sparse representation. Then, we develop an approach to evaluate the sparsity recoverability of an l 1 -minimization on HSIs in a probabilistic framework. This approach takes into account not only the recovery probability under the given support length of the l 0 -norm solution but also the apriori probability of the support length; consequently, it overcomes the inability of traditional mutual/cumulative coherence conditions to address high-coherence HSIs. This paper reveals that the higher sparsity recoverability of a STIW-SR leads to its higher classification accuracy and that the increasing coherence does not necessarily lead to a reduced sparsity recovery probability, and this paper verifies the connection between l 0 and l 1 -minimizations on HSIs. Experimental results from realworld HSIs suggest that our classification method significantly outperforms several representative spectral-spatial classifiers and support vector machines.