Semi-supervised linear spectral unmixing using a hierarchical Bayesian model for hyperspectral imagery

This paper proposes a hierarchical Bayesian model that can be used for semi-supervised hyperspectral image unmixing. The model assumes that the pixel reflectances result from linear combinations of pure component spectra contaminated by an additive Gaussian noise. The abundance parameters appearing in this model satisfy positivity and additivity constraints. These constraints are naturally expressed in a Bayesian context by using appropriate abundance prior distributions. The posterior distributions of the unknown model parameters are then derived. A Gibbs sampler allows one to draw samples distributed according to the posteriors of interest and to estimate the unknown abundances. An extension of the algorithm is finally studied for mixtures with unknown numbers of spectral components belonging to a know library. The performance of the different unmixing strategies is evaluated via simulations conducted on synthetic and real data

Key Information Retrieval in Hyperspectral Imagery through Spatial-Spectral Data Fusion

Hyperspectral (HS) imaging is measuring the radiance of materials within each pixel area at a large number of contiguous spectral wavelength bands. The key spatial information such as small targets and border lines are hard to be precisely detected from HS data due to the technological constraints. Therefore, the need for image processing techniques is an important field of research in HS remote sensing. A novel semisupervised spatial-spectral data fusion method for resolution enhancement of HS images through maximizing the spatial correlation of the endmembers (signature of pure or purest materials in the scene) using a superresolution mapping (SRM) technique is proposed in this paper. The method adopts a linear mixture model and a fully constrained least squares spectral unmixing algorithm to obtain the endmember abundances (fractional images) of HS images. Then, the extracted endmember distribution maps are fused with the spatial information using a spatial-spectral correlation maximizing model and a learning-based SRM technique to exploit the subpixel level data. The obtained results validate the reliability of the technique for key information retrieval. The proposed method is very efficient and is low in terms of computational cost which makes it favorable for real-time applications

Endmember extraction algorithms from hyperspectral images

During the last years, several high-resolution sensors have been developed for hyperspectral remote sensing applications. Some of these sensors are already available on space-borne devices. Space-borne sensors are currently acquiring a continual stream of hyperspectral data, and new efficient unsupervised algorithms are required to analyze the great amount of data produced by these instruments. The identification of image endmembers is a crucial task in hyperspectral data exploitation. Once the individual endmembers have been identified, several methods can be used to map their spatial distribution, associations and abundances. This paper reviews the Pixel Purity Index (PPI), N-FINDR and Automatic Morphological Endmember Extraction (AMEE) algorithms developed to accomplish the task of finding appropriate image endmembers by applying them to real hyperspectral data. In order to compare the performance of these methods a metric based on the Root Mean Square Error (RMSE) between the estimated and reference abundance maps is used

A Stepwise Analytical Projected Gradient Descent Search for Hyperspectral Unmixing and Its Code Vectorization

We present, in this paper, a new methodology for spectral unmixing, where a vector of fractions, corresponding to a set of endmembers (EMs), is estimated for each pixel in the image. The process first provides an initial estimate of the fraction vector, followed by an iterative procedure that converges to an optimal solution. Specifically, projected gradient descent (PGD) optimization is applied to (a variant of) the spectral angle mapper objective function, so as to significantly reduce the estimation error due to amplitude (i.e., magnitude) variations in EM spectra, caused by the illumination change effect. To improve the computational efficiency of our method over a commonly used gradient descent technique, we have analytically derived the objective function's gradient and the optimal step size (used in each iteration). To gain further improvement, we have implemented our unmixing module via code vectorization, where the entire process is ''folded'' into a single loop, and the fractions for all of the pixels are solved simultaneously. We call this new parallel scheme vectorized code PGD unmixing (VPGDU). VPGDU has the advantage of solving (simultaneously) an independent optimization problem per image pixel, exactly as other pixelwise algorithms, but significantly faster. Its performance was compared with the commonly used fully constrained least squares unmixing (FCLSU), the generalized bilinear model (GBM) method for hyperspectral unmixng, and the fast state-of-the-art methods, sparse unmixing by variable splitting and augmented Lagrangian (SUnSAL) and collaborative SUnSAL (CLSUnSAL) based on the alternating direction method of multipliers. Considering all of the prospective EMs of a scene at each pixel (i.e., without a priori knowledge which/how many EMs are actually present in a given pixel), we demonstrate that the accuracy due to VPGDU is considerably higher than that obtained by FCLSU, GBM, SUnSAL, and CLSUnSAL under varying illumination, and is, otherwise, comparable with respect to these methods. However, while our method is significantly faster than FCLSU and GBM, it is slower than SUnSAL and CLSUnSAL by roughly an order of magnitude.Israel Science Ministry Scientific Infrastructure Research Grant Scheme, Helen Norman Asher Space Research Grant Scheme, Technion PhD Scholarship, new England fund Technion, Environmental Mapping and Monitoring of Iceland by Remote Sensing EMMIRS projectPeer Reviewe