Inertia-Constrained Pixel-by-Pixel Nonnegative Matrix Factorisation: a Hyperspectral Unmixing Method Dealing with Intra-class Variability

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 more valid in the presence of intra-class variabilities 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 UP-NMF limitations an extended method is 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 methods are 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

Opportunistic Sensing in Train Safety Systems

Train safety systems are complex and expensive, and changing them requires huge investments. Changes are evolutionary and small. Current developments, like faster - high speed - trains and a higher train density on the railway network, have initiated research on safety systems that can cope with the new requirements. This paper presents a novel approach for a safety subsystem that checks the composition of a train, based on opportunistic sensing with a wireless sensor network. Opportunistic sensing systems consist of changing constellations sensors that, for a limited amount of time, work together to achieve a common goal. Such constellations are selforganizing and come into being spontaneously. The proposed opportunistic sensing system selects a subset of sensor nodes from a larger set based on a common context.We show that it is possible to use a wireless sensor network to make a distinction between carriages from different trains. The common context is acceleration, which is used to select the subset of carriages that belong to the same train out of all the carriages from several trains in close proximity. Simulations based on a realistic set of sensor data show that the method is valid, but that the algorithm is too complex for implementation on simple wireless sensor nodes. Downscaling the algorithm reduces the number of processor execution cycles as well as memory usage, and makes it suitable for implementation on a wireless sensor node with acceptable loss of precision. Actual implementation on wireless sensor nodes confirms the results obtained with the simulations

SNR-Walls in Eigenvalue-based Spectrum Sensing

Various spectrum sensing approaches have been shown to suffer from a so-called SNR-wall, an SNR value below which a detector cannot perform robustly no matter how many observations are used. Up to now, the eigenvalue-based maximum-minimum-eigenvalue (MME) detector has been a notable exception. For instance, the model uncertainty of imperfect knowledge of the receiver noise power, which is known to be responsible for the energy detector's fundamental limits, does not adversely affect the MME detector's performance. While additive white Gaussian noise (AWGN) is a standard assumption in wireless communications, it is not a reasonable one for the MME detector. In fact, in this work we prove that uncertainty in the amount of noise coloring does lead to an SNR-wall for the MME detector. We derive a lower bound on this SNR-wall and evaluate it for example scenarios. The findings are supported by numerical simulations.Comment: 17 pages, 3 figures, submitted to EURASIP Journal on Wireless Communications and Networkin