Snapshot mosaic multispectral imagery acquires an undersampled data cube by acquiring a single spectral measurement per spatial pixel. Sensors which acquire p frequencies, therefore, suffer from severe 1/p undersampling of the full data cube. We show that the missing entries can be accurately imputed using non-convex techniques from sparse approximation and matrix completion initialised with traditional demosaicing algorithms. In particular, we observe the peak signalto-noise ratio can typically be improved by 2 dB to 5 dB over current state-of-the-art methods when simulating a p = 16 mosaic sensor measuring both high and low altitude urban and rural scenes as well as ground-based scenes.

Low Earth Orbit is becoming crowded with satellites. Updating estimates of collision probabilities is important as new deployments are authorised but is difficult because only limited information is given. This report investigates developing analytic estimates of collision probabilities. A survey of approaches reported in the literature is carried out. A collision involving a satellite from the Iridium cluster is reviewed. A simple analytic expression for the collision probability between two satellites is derived using the smallness of several dimensionless ratios appearing in the problem. Single collision probabilities are then extended to orbital planes populated by n satellites with the aim of finding the optimal point at which to traverse such an orbit. This report demonstrates that analytic estimates relevant to the problem can be made. Further work should focus on: making these estimates rigorous by using a formal asymptotic approach, considering multiple orbital planes and introducing time dependence

This report is a summary of the work performed during 145th European Industrial Study Group on the topic of Simultaneous Transmission and Reception of electromagnetic signals presented by Dstl. We establish that the solution to this problem lies in estimating the reflected signals caused by the outgoing signal. We define the problem mathematically using an integral equation to represent the received signal. From this we derive Cramer-Rao bounds which give lower bounds for the error when estimating the signal based upon error in the calculation of the reflected signal. We perform numerical simulations for a simple example to demonstrate some techniques that can be used in the solving of this problem.