Total Variation Spatial Regularization for Sparse Hyperspectral Unmixing

Abstract

Abstract-Spectral unmixing aims at estimating the fractional abundances of pure spectral signatures (also called endmembers) in each mixed pixel collected by a remote sensing hyperspectral imaging instrument. In recent work, the linear spectral unmixing problem has been approached in semisupervised fashion as a sparse regression one, under the assumption that the observed image signatures can be expressed as linear combinations of pure spectra, known a priori and available in a library. It happens, however, that sparse unmixing focuses on analyzing the hyperspectral data without incorporating spatial information. In this paper, we include the total variation (TV) regularization to the classical sparse regression formulation, thus exploiting the spatialcontextual information present in the hyperspectral images and developing a new algorithm called sparse unmixing via variable splitting augmented Lagrangian and TV. Our experimental results, conducted with both simulated and real hyperspectral data sets, indicate the potential of including spatial information (through the TV term) on sparse unmixing formulations for improved characterization of mixed pixels in hyperspectral imagery.Index Terms-Hyperspectral imaging, sparse regression, sparse unmixing, spectral unmixing, total variation (TV) regularization.

Double Reweighted Sparse Regression and Graph Regularization for Hyperspectral Unmixing

“…In general, two restrictions are imposed on the fractional abundances X in LMM due to physical constraints [5,21,24,26,33]. On the one hand, we often assume X ij 0 where X ij denotes the (i, j)-th entry of X, termed as the abundance non-negative constraint (ANC).…”

“…This simulated data cube contains 75 × 75 pixels generated from five randomly selected signature from A 2 . DC2 has 100 bands per pixel [5]. The true abundances of five endmembers are shown in Figure 4.…”

“…We use the portion corresponding to a 350 × 350-pixel subset with 188 spectral bands in this experiment (see [5] for more details). A mineral map produced in 1995 by USGS, in which the Tricorder 3.3 software product was used to map different minerals present in the Cuprite mining district (http://speclab.cr.usgs.gov/spectral.lib06).…”

“…The task of HU is to identify a set of endmembers, and to estimate their corresponding abundances in the formation of each hyperspectral image (HSI) pixel [5][6][7]. HU algorithms mainly depend on the expected type of mixing, which can be classified as either a nonlinear or linear model [8].…”

“…However, these methods do not exploit the spatial-contextual information of the hyperspectral images. In [5], Iordache et al proposed the SUnSAL-TV method, which utilizes the spatial information of the first-order pixel neighborhood system of the abundance map through total variation (TV) on sparse unmixing formulation. In [25], Zhao et al studied total variation regularization in deblurring and sparse unmixing of hyperspectral images and their method gets better performance than SUnSAL-TV.…”