Title :
Sampling trajectories for mobile sensing
Author :
Unnikrishnan, Jayakrishnan ; Vetterli, Martin
Author_Institution :
Sch. of Comput. & Commun. Sci., Ecole Polytech. Fed. de Lausanne (EPFL), Lausanne, Switzerland
Abstract :
Classical sampling theory for sampling and reconstructing bandlimited fields in ℝd addresses the problem of sampling on lattice points. We consider a generalization of this problem, in which one samples the field along 1-dimensional spatial trajectories in ℝd rather than at points. The process of sampling records the value of the field at all points on the sampling trajectories. Such a sampling setup is relevant in the problem of spatial sampling using mobile sensors. We study various possible designs of sampling trajectories and discuss necessary and sufficient conditions for perfect reconstruction. We introduce a density metric for trajectories which we call path density, that quantifies the total length of these trajectories per unit volume in ℝd. We formulate the problem of identifying optimal sampling trajectories that admit perfect reconstruction of bandlimited fields and are minimal in terms of the path density metric. We identify optimal sampling trajectories from a restricted class of trajectories.
Keywords :
mobile communication; sampling methods; 1-dimensional spatial trajectories; bandlimited fields; classical sampling theory; lattice points; mobile sensing; mobile sensors; necessary conditions; path density metric; sampling trajectories; spatial sampling; sufficient conditions; Image reconstruction; Lattices; Measurement; Mobile communication; Sensors; Trajectory; Vectors;
Conference_Titel :
Communication, Control, and Computing (Allerton), 2011 49th Annual Allerton Conference on
Conference_Location :
Monticello, IL
Print_ISBN :
978-1-4577-1817-5
DOI :
10.1109/Allerton.2011.6120308