Bandlimited Signal Reconstruction From the Distribution of Unknown Sampling Locations

Abstract

We study the reconstruction of bandlimited fields from samples taken at unknown but statistically distributed sampling locations. The setup is motivated by distributed sampling where precise knowledge of sensor locations can be difficult. Periodic one-dimensional bandlimited fields are considered for sampling. Perfect samples of the field at independent and identically distributed locations are obtained. The statistical realization of sampling locations is not known. First, it is shown that a bandlimited field cannot be uniquely determined with samples taken at statistically distributed but unknown locations, even if the number of samples is infinite. Next, it is assumed that the order of sample locations is known. In this case, using insights from order-statistics, an estimate for the field with useful asymptotic properties is designed. Distortion (mean-squared error) and central-limit are established for this estimate.

Submitted to SampTA 2013 workshop

References in corpus (2)

• Sampling and Reconstruction of Spatial Fields using Mobile Sensors
• Performance of Linear Field Reconstruction Techniques with Noise and Uncertain Sensor Locations

Cited by in corpus (5)

• Sampling and Reconstruction of Bandlimited Signals with Multi-Channel Time Encoding
• Bandlimited Spatial Field Sampling with Mobile Sensors in the Absence of Location Information
• Bandlimited Field Reconstruction from Samples Obtained at Unknown Random Locations on a Grid
• Mobile Sensing of Two-Dimensional Bandlimited Fields on Random Paths
• Spatial Field estimation from Samples taken at Unknown Locations generated by an Unknown Autoregressive Process