Euclidean Distance to Convex Polyhedra and Application to Class Representation in Spectral Images

With the aim of estimating the abundance map from observations only, linear unmixing approaches are not always suitable to spectral images, especially when the number of bands is too small or when the spectra of the observed data are too correlated. To address this issue in the general case, we present a novel approach which provides an adapted spatial density function based on any arbitrary linear classifier. A robust mathematical formulation for computing the Euclidean distance to polyhedral sets is presented, along with an efficient algorithm that provides the exact minimum-norm point in a polyhedron. An empirical evaluation on the widely-used Samson hyperspectral dataset demonstrates that the proposed method surpasses state-of-the-art approaches in reconstructing abundance maps. Furthermore, its application to spectral images of a Lithium-ion battery, incompatible with linear unmixing models, validates the method's generality and effectiveness.

Energy Concerns with HPC Systems and Applications

For various reasons including those related to climate changes, {\em energy} has become a critical concern in all relevant activities and technical designs. For the specific case of computer activities, the problem is exacerbated with the emergence and pervasiveness of the so called {\em intelligent devices}. From the application side, we point out the special topic of {\em Artificial Intelligence}, who clearly needs an efficient computing support in order to succeed in its purpose of being a {\em ubiquitous assistant}. There are mainly two contexts where {\em energy} is one of the top priority concerns: {\em embedded computing} and {\em supercomputing}. For the former, power consumption is critical because the amount of energy that is available for the devices is limited. For the latter, the heat dissipated is a serious source of failure and the financial cost related to energy is likely to be a significant part of the maintenance budget. On a single computer, the problem is commonly considered through the electrical power consumption. This paper, written in the form of a survey, we depict the landscape of energy concerns in computer activities, both from the hardware and the software standpoints.