Hyperspectral Image Unmixing With LiDAR Data-Aided Spatial Regularization

Abstract

Spectral unmixing methods incorporating spatial regularizations have demonstrated increasing interest. Although spatial regularizers which promote smoothness of the abundance maps have been widely used, they may overly smooth these maps and, in particular, may not preserve edges present in the hyperspectral image. Existing unmixing methods usually ignore these edge structures or use edge information derived from the hyperspectral image itself. However, this information may be affected by large amounts of noise or variations in illumination, leading to erroneous spatial information incorporated into the unmixing procedure. This paper proposes a simple, yet powerful, spectral unmixing framework which incorporates external data (i.e. LiDAR data). The LiDAR measurements can be easily exploited to adjust standard spatial regularizations applied to the unmixing process. The proposed framework is rigorously evaluated using two simulated datasets and a real hyperspectral image. It is compared with competing methods that rely on spatial information derived from a hyperspectral image. The resultsshow that the proposed framework can provide better abundance estimates and, more specifically, can significantly improve the abundance estimates for pixels affected by shadows.

Matrix Cofactorization for Joint Spatial–Spectral Unmixing of Hyperspectral Images

“…Due to the general ill-conditioning of the endmember matrix M, the objective function underlying (1) is often granted with additional regularizations promoting expected properties of the solution. In particular, numerous works exploited the expected spatial behavior of the mixing coefficients to introduce spatial regularizations enforcing piecewise-constant [5], [8] or smoothly varying [3], [19] abundance maps, possibly driven by external knowledge [20]. Conversely, this work does not consider spatial information as a prior knowledge but rather proposes a decomposition model dedicated to the image spatial content, paving the way towards the concept of spatial unmixing.…”

Matrix cofactorization for joint representation learning and supervised classification – Application to hyperspectral image analysis

“…The weights β m,n can be computed beforehand to adjust the penalizations with respect to expected spatial variations of the scene. They can be estimated directly from the image to be analyzed or extracted from a complementary dataset as in [47]. They will be specified during the experiments reported in Section 4.…”

Matrix Cofactorization for Joint Unmixing and Classification of Hyperspectral Images

“…The weighting coefficients β m,n are introduced to account for the natural boundaries present in the image. They are computed beforehand using external data containing information on the spatial structures, e.g., a panchromatic image or a LIDAR image [11]. An example of such weights is described in Section IV.…”