Sampling high-dimensional bandlimited fields on low-dimensional manifolds.
Consider the problem of sampling a bandlimited spatial field using mobile sensors. Classical sampling theory commonly uses the spatial density of samples as the performance metric of a sampling scheme. We argue that in the mobile sensing paradigm, a more relevant metric is the path density, or total distance traveled by the sensors per unit spatial volume. We introduce the problem of designing sampling trajectories with minimal path density subject to the constraint that bandlimited spatial fields can be perfectly reconstructed using samples taken on these trajectories. We obtain partial solutions to this problem from certain restricted classes of trajectories. Our results for trajectories can be generalized to results for higher dimensional sampling manifolds. Our results have applications in environment monitoring with mobile sensors, and also in designing scanning schemes for Magnetic Resonance Imaging (MRI).
Posted by Runwei Zhang on Thursday 23 January 2014 at 13:13