A Low-Rank Model for Compressive Spectral Image Classification

Compressive sensing enables efficient acquisition of hyperspectral images (HSIs) by assuming high redundancy on natural scenes. Several reconstruction algorithms have been proposed to retrieve the underlying image, and most of them take advantage of the spatial and spectral correlations. However, reconstruction may not be necessary in certain applications such as land cover classification. Instead of knowing the full image, researchers are interested in features that could be extracted directly from the compressed measurements, which provide high inference capabilities. Low-rank (LR) matrix approximation has been widely used in feature extraction (FE), because it reduces the data dimension and computational cost. Therefore, in this paper, compressive hyperspectral imaging and FE are combined in a framework for HSI classification using an LR matrix approximation model. In the proposed framework, the compressed measurements are acquired from a single-pixel spectrometer. Instead of using the traditional high-complexity reconstruction model, an LR matrix factorization problem is formulated. The LR problem maximizes the posterior distribution with respect to the feature space and coefficients, and it is numerically solved based on an alternating optimization strategy. By incorporating spatial information, the numerical procedure minimizes the total variational of the feature coefficients subject to an orthogonality constraint for the feature space. Experiments on real HSIs show that the proposed approach can provide equally competitive classification results when compared to the traditional approach that performs FE and classification on the recovered images.