Semisupervised hyperspectral unmixing finds the ratio of spectral library members in the mixture of hyperspectral pixels to find the proportion of pure materials in a natural scene. The two main challenges are noise in observed spectral vectors and high mutual coherence of spectral libraries. To tackle these challenges, we propose a probabilistic sparse regression method for linear hyperspectral unmixing, which utilizes the implicit relations of neighboring pixels. We partition the hyperspectral image into rectangular patches. The sparse coefficients of pixels in each patch are assumed to be generated from a Laplacian scale mixture model with the same latent variables. These latent variables specify the probability of existence of endmembers in the mixture of each pixel. Experiments on synthetic and real hyperspectral images illustrate the superior performance of the proposed method over alternatives.

In this letter, a spatially weighted sparse unmixing approach is proposed as a front-end for hyperspectral image classification using a linear SVM. The idea is to partition the pixels of a hyperspectral image into a number of disjoint spatial neighborhoods. Since neighboring pixels are often composed of similar materials, their sparse codes are encouraged to have similar sparsity patterns. This is accomplished by means of a reweighted ℓ1framework where it is assumed that fractional abundances of neighboring pixels are distributed according to a common Laplacian Scale Mixture (LSM) prior with a shared scale parameter. This shared parameter determines which endmembers contribute to the group of pixels. Experiments on the AVIRIS Indian Pines show that the model is very effective in finding discriminative representations for HSI pixels, especially when the training data is limited.

This paper presents a structured dictionary-based model for hyperspectral data that incorporates both spectral and contextual characteristics of spectral samples. The idea is to partition the pixels of a hyperspectral image into a number of spatial neighborhoods called contextual groups and to model the pixels inside a group as members of a common subspace. That is, each pixel is represented using a linear combination of a few dictionary elements learned from the data, but since pixels inside a contextual group are often made up of the same materials, their linear combinations are constrained to use common elements from the dictionary. To this end, dictionary learning is carried out with a joint sparse regularizer to induce a common sparsity pattern in the sparse coefficients of a contextual group. The sparse coefficients are then used for classification using a linear support vector machine. Experimental results on a number of real hyperspectral images confirm the effectiveness of the proposed representation for hyperspectral image classification. Moreover, experiments with simulated multispectral data show that the proposed model is capable of finding representations that may effectively be used for classification of multispectral resolution samples.

In this paper, a novel discriminative dictionary learning approach is proposed that attempts to preserve the local structure of the data while encouraging discriminability. The reconstruction error and sparsity inducing ℓ1-penalty of dictionary learning are minimized alongside a locality preserving and discriminative term. In this setting, each data point is represented by a sparse linear combination of dictionary atoms with the goal that its k-nearest same-label neighbors are preserved. Since the class of a new data point is unknown, its sparse representation is found once for each class. The class that produces the lowest error is associated with that point. Experimental results on five common classification datasets, show that this method outperforms state-of-the-art classifiers, especially when the training data is limited.

Sparse representation techniques for visual tracking have rarely taken advantage of the similarity between target objects in consecutive frames. In this paper, the target is divided into disjoint patches, and the sparse representation of corresponding consecutive target patches is assumed to be distributed according to a common Laplacian Scale Mixture (LSM) with a shared scale parameter. The target patches collaborate to determine this shared parameter, which in turn encourages smooth temporal variation in their representations. The target's appearance is modeled using a dictionary composed of patch templates. This patchwise treatment allows occluded patches to be detected and excluded when updating the dictionary. Experimental results on 6 challenging video sequences, show superior performance, especially in scenarios with considerable appearance change.

This paper presents a robust tracking approach to handle challenges such as occlusion and appearance change. Here, the target is partitioned into a number of patches. Then, the appearance of each patch is modeled using a dictionary composed of corresponding target patches in previous frames. In each frame, the target is found among a set of candidates generated by a particle filter, via a likelihood measure that is shown to be proportional to the sum of patch-reconstruction errors of each candidate. Since the target's appearance often changes slowly in a video sequence, it is assumed that the target in the current frame and the best candidates of a small number of previous frames, belong to a common subspace. This is imposed using joint sparse representation to enforce the target and previous best candidates to have a common sparsity pattern. Moreover, an occlusion detection scheme is proposed that uses patch-reconstruction errors and a prior probability of occlusion, extracted from an adaptive Markov chain, to calculate the probability of occlusion per patch. In each frame, occluded patches are excluded when updating the dictionary. Extensive experimental results on several challenging sequences shows that the proposed method outperforms state-of-the-art trackers.