Abstract
Blind source separation is a common processing tool to analyse the constitution of pixels of hyperspectral images. Such methods usually suppose that pure pixel spectra (endmembers) are the same in all the image for each class of materials. In the framework of remote sensing, such an assumption is no longer valid in the presence of intra-class variability due to illumination conditions, weathering, slight variations of the pure materials, etc. In this paper, we first describe the results of investigations highlighting intra-class variability measured in real images. Considering these results, a new formulation of the linear mixing model is presented leading to two new methods. Unconstrained pixel-by-pixel NMF (UP-NMF) is a new blind source separation method based on the assumption of a linear mixing model, which can deal with intra-class variability. To overcome the limitations of UP-NMF, an extended method is also proposed, named Inertia-constrained Pixel-by-pixel NMF (IP-NMF). For each sensed spectrum, these extended versions of NMF extract a corresponding set of source spectra. A constraint is set to limit the spreading of each source’s estimates in IP-NMF. The proposed methods are first tested on a semi-synthetic data set built with spectra extracted from a real hyperspectral image and then numerically mixed. We thus demonstrate the interest of our methods for realistic source variabilities. Finally, IP-NMF is tested on a real data set and it is shown to yield better performance than state of the art methods.
Highlights
Hyperspectral imaging is a common tool in the framework of remote sensing
Three matrices R (0) are tested: (i) M mixed signals randomly selected from the observations; (ii) the M purest signals extracted with a classical remote sensing blind source separation method (N-FINDR [39]); (iii) for each class m, the average of all P source signals in this class
Each of these figures shows the abundance maps of VCA + Fully Constrained Least Square (FCLS) unmixing (1st line), Nonnegative Matrix Factorisation (NMF) (2nd line), Inertia-constrained Pixel-by-pixel NMF (IP-NMF) initialised with VCA (3rd line) and IP-NMF manually initialised (4th line) applied with M equal to 3, 5 and 7 respectively in Figures 12–14.The results obtained with N-FINDR are not shown because they are very close to those obtained with VCA
Summary
Hyperspectral imaging is a common tool in the framework of remote sensing. Images provided by these sensors are spectrally highly resolved. Independent Component Analysis (ICA) methods are considered as one of the main classes of BSS methods, they require the source signals to be mutually statistically independent, which is a quite restrictive condition, that is not met in some application fields, including for the reflectance spectra and abundances faced in remote sensing: see e.g., [13] Even this source independence constraint is not sufficient for ensuring that ICA methods apply to general types of mixing models [14]. We present original unmixing methods which aim at combining the above two attractive features: (i) they are (semi-)blind in the sense that they aim at estimating both the considered source signals (reflectance spectra) and mixing model parameters while only requiring limited prior knowledge; and (ii) they handle intra-class variability, for very general variability patterns.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
