Jelena Kovačević

Siheng Chen, Rohan Varma, Aarti Singh et al.

In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution. However, no finite sample statistical guarantees and no computationally efficient optimal sampling strategies have been proposed. To evaluate the statistical properties of different sampling strategies, we propose a simple yet effective estimator, which is easy for theoretical analysis and is useful in multitask linear regression. We derive the exact mean square error of the proposed estimator for any given sampling scores. Based on minimizing the mean square error, we propose the optimal sampling scores for both estimator and predictor, and show that they are influenced by the noise-to-signal ratio. Numerical simulations match the theoretical analysis well.

Filipe Condessa, Jose Bioucas-Dias, Jelena Kovacevic

In this paper we present a novel method for robust hyperspectral image classification using context and rejection. Hyperspectral image classification is generally an ill-posed image problem where pixels may belong to unknown classes, and obtaining representative and complete training sets is costly. Furthermore, the need for high classification accuracies is frequently greater than the need to classify the entire image. We approach this problem with a robust classification method that combines classification with context with classification with rejection. A rejection field that will guide the rejection is derived from the classification with contextual information obtained by using the SegSALSA algorithm. We validate our method in real hyperspectral data and show that the performance gains obtained from the rejection fields are equivalent to an increase the dimension of the training sets.

Filipe Condessa, Jose Bioucas-Dias, Jelena Kovacevic

We present a supervised hyperspectral image segmentation algorithm based on a convex formulation of a marginal maximum a posteriori segmentation with hidden fields and structure tensor regularization: Segmentation via the Constraint Split Augmented Lagrangian Shrinkage by Structure Tensor Regularization (SegSALSA-STR). This formulation avoids the generally discrete nature of segmentation problems and the inherent NP-hardness of the integer optimization associated. We extend the Segmentation via the Constraint Split Augmented Lagrangian Shrinkage (SegSALSA) algorithm by generalizing the vectorial total variation prior using a structure tensor prior constructed from a patch-based Jacobian. The resulting algorithm is convex, time-efficient and highly parallelizable. This shows the potential of combining hidden fields with convex optimization through the inclusion of different regularizers. The SegSALSA-STR algorithm is validated in the segmentation of real hyperspectral images.