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

摘要

For hyperspectral image (HSI) classification, it is challenging to adopt the methodology of sparse-representation-based classification. In this paper, we first propose an -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 -minimization on HSIs in a probabilistic framework. This approach takes into account not only the recovery probability under the given support length of the -norm solution but also the 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 - and