| Signal sparsity is an extremely powerful feature in many classical signal processing applications. Recently, with the emerging of the compressed sensing framework, applications of sparse representation have been extended to the area of computer vision and pattern recognition and achieved state-of-the-art performance. These applications are mainly based on the observation that signals belonging to the same class approximately lie in a low-dimensional subspace. Therefore, for every typical sample there exists a sparse representation with respect to certain proper basis which contains the semantic information.;In hyperspectral imaging, remote sensors capture digital images in hundreds of continuous and narrow spectral bands. Different materials usually reflect electromagnetic energy differently, enabling discrimination of materials based on their spectral characteristics. In this work, we propose new sparse representation-based algorithms for discrimination tasks in hyperspectral images. Our approach relies on the assumption that a hyperspectral pixel can be sparsely represented by a linear combination of training samples from all classes. The sparse representation vector is discriminative and then used to determine the class label of the test pixel. Two different approaches are proposed in order to employ the important contextual information. In the first approach, an explicit Laplacian smoothing constraint is imposed on the optimization problem formulation. The second approach is via a joint sparsity model where neighboring pixels are simultaneously represented by a few common training samples, although they can be weighted with a different set of coefficients for each pixel.;The linear sparse representation models are then extended to a high-dimensional feature space induced by a kernel function, in which the data becomes more separable. Spatial coherency across neighboring pixels is also incorporated through either a kernelized joint sparsity model or a composite kernel approach that combines kernels dedicated to the spectral and spatial features. Kernel greedy optimization algorithms are suggested to solve the kernel versions of the single-pixel and multi-pixel joint sparsity-based recovery problems.;The proposed sparsity-based classifiers are applied to real hyperspectral data sets for target detection and classification. Experimental results show that the proposed technique outperforms classical algorithms in a majority of the cases. Both contextualization and kernelization of the pixel-wise linear model significantly improves the performance.;At the end of this work, we also examine the effects of several linear dimensionality techniques on the performance of detection and classification algorithms for hyperspectral images. The linear projections considered includes computationally feasible methods that can be integrated directly into the imaging sensor, as well as sophisticated but data-dependant methods. It is demonstrated that the dimensionality of hyperspectral pixels can be significantly reduced without severely affecting the algorithm performance, even with a completely random projection matrix. |
