The accurate segmentation of remotely sensed hyperspectral images has widespread attention in the Earth observation and remote sensing communities. In the past decade, most of the efforts focus on the development of different supervised methods for hyperspectral image classification. Recently, the computer vision community is developing unsupervised methods that can adapt to new conditions without leveraging expensive supervision. In general, among unsupervised classification methods, sparse subspace clustering (SSC) is a popular tool that achieves good clustering results on experiments with real data. However, for the specific case of hyperspectral clustering, the SSC model does not take into account the spatial information of such images, which limits its discrimination capability and hampering the spatial homogeneity of the clustering results. As a solution, we propose to incorporate a regularization term to the SSC model, which takes into account the neighboring spatial information of spectral pixels in the scene. Specifically, the proposed method uses a three-dimensionall (3D) Gaussian filter to perform a 3D convolution on the sparse coefficients, obtaining a piecewise-smooth representation matrix that enforces an averaging constraint in the SSC optimization program. Extensive simulations demonstrate the effectiveness of the proposed method, achieving an overall accuracy of up to 99% in the selected hyperspectral remote sensing datasets.
The snapshot colored compressive spectral imager (SCCSI) is a recent compressive spectral imaging (CSI) architecture that senses the spatial and spectral information of a scene in a single snapshot by means of a colored mosaic FPA detector and a dispersive element. Commonly, CSI architectures allow multiple snapshot acquisition, yielding improved reconstructions of spatially detailed and spectrally rich scenes. Each snapshot is captured employing a different coding pattern. In principle, SCCSI does not admit multiple snapshots since the pixelated tiling of optical filters is directly attached to the detector. This paper extends the concept of SCCSI to a system admitting multiple snapshot acquisition by rotating the dispersive element, so the dispersed spatio-spectral source is coded and integrated at different detector pixels in each rotation. Thus, a different set of coded projections is captured using the same optical components of the original architecture. The mathematical model of the multishot SCCSI system is presented along with several simulations. Results show that a gain up to 7 dB of peak signal-to-noise ratio is achieved when four SCCSI snapshots are compared to a single snapshot reconstruction. Furthermore, a gain up to 5 dB is obtained with respect to state-of-the-art architecture, the multishot CASSI.
Compressive spectral imaging (CSI) captures coded and dispersed projections of the spatio-spectral source rather than direct measurements of the voxels. Using the coded projections, an l1 minimization reconstruction algorithm is then used to reconstruct the underlying scene. An architecture known as the snapshot colored compressive spectral imager (SCCSI) exploits the compression capabilities of CSI techniques and efficiently senses a spectral image using a single snapshot by means of a colored mosaic FPA detector and a dispersive element. In CSI, different coding patterns are used to acquire multiple snapshots, yielding improved reconstructions of spatially detailed and spectrally rich scenes. SCCSI however, does not admit multiple coding patterns since the pixelated tiling of optical filters is directly attached to the detector. This paper extends the concept of SCCSI to a system admitting multiple measurement shots by rotating the dispersive element such that the dispersed spatio-spectral source is coded and integrated at different detector pixels in each rotation. This approach allows the acquisition of a different set of coded projections on each measurement shot. Simulations show that increasing the number of measurement snapshots results on improved reconstructions. More specifically, a gain up to 7 dB is obtained when results from four measurement shots are compared to the reconstruction from a single SCCSI snapshot.