Sparse representation techniques for hyperspectral imaging

Hyperspectral imaging quantizes scene radiance against several narrow wavelength ranges, thereby preserving the fine spectral details that are lost in conventional RGB cameras. This makes it an ideal imaging modality in numerous applications ranging from remote sensing to forensics and medical diagnostics. However, the low resolution of hyperspectral sensors, due to hardware constraints, hinders their pervasive use. In remote sensing, the low sensor resolution results in mixing the reflectances of materials, leading to errors in Earth exploration. In groundbased applications, the orders of magnitude difference between the contemporary RGB cameras and hyperspectral cameras makes the former preferable despite their inferior spectral characteristics. Organized as a series of papers published by or submitted at prestigious venues in the fields of computer vision, remote sensing and artificial intelligence, this dissertation addresses the key problems in hyperspectral imaging to enable extensive use of this technology. It presents generic techniques and algorithms for (a) hyperspectral unmixing, (b) hyperspectral super-resolution and (c) image classification. The proposed techniques exploit the sparse representation framework that is grounded in optimization and non-parametric Bayesian theory. The proposed algorithms are systematically derived by capitalizing on the physical attributes of the signals that lead to state-of-the-art performance by the proposed techniques. For hyperspectral unmixing, the proposed methods construct dictionaries from the libraries of pure material spectra provided by NASA and sparsely represent hyperspectral images over these dictionaries to separate their pixel constituents. The thesis presents two novel algorithms for sparse unmixing. The first algorithm, OMPStar, makes the Orthogonal Matching Pursuit (OMP) strategy robust to the high mutual coherence of the spectral dictionaries. The second algorithm performs efficient Sparse Unmixing via Greedy Pursuit (SUnGP) by iteratively constructing and pruning the subspace of the likely constituents of the pixels. An effective technique for unsupervised unmixing is also proposed. It performs robust non-negative matrix factorization for unmixing, keeping in view the physical properties of the image. Three different methods for hyperspectral super-resolution are proposed in this thesis. The first method extracts the constituent spectra of a hyperspectral image using dictionary learning. These spectra are transformed according to the spectral quantization of an RGB image, which is later represented over the transformed spectra. The resulting representations are combined with the original spectra to obtain a hyperspectral image with a resolution equal to that of the RGB image. The non-parametric Bayesian framework is used for the first time for hyperspectral super-resolution in the second method, that also proposes a generic Bayesian sparse coding strategy to infer an ensemble of codes that are used to compute optimal super-resolution images. The third method incorporates the often-observed spatiospectral smoothness of hyperspectral images into the Bayesian model with spatial and spectral kernels. This thesis theoretically dismisses the misconception that using sparse representation for classification is inexpedient. It also proposes a generic discriminative Bayesian dictionary learning framework that shows state-of-the-art performance in various computer vision classification tasks. This framework is then extended to employ a joint representation model and to learn a classifier simultaneously along a Bayesian dictionary. This model is finally tailored to hyperspectral image classification by incorporating spectral smoothness into the basis with Gaussian Processes and exploiting contextual information in sparse coding. Effectiveness of the proposed method is shown on multiple real hyperspectral image datasets.