Optimal stopping times for estimating Bernoulli parameters with applications to active imaging
Files
Accepted manuscript
Date
2018-01-01
Authors
Medin, Safa C.
Murray-Bruce, John
Goyal, Vivek K.
Version
Accepted manuscript
OA Version
Citation
Safa C Medin, John Murray-Bruce, Vivek K Goyal. 2018. "OPTIMAL STOPPING TIMES FOR ESTIMATING BERNOULLI PARAMETERS WITH APPLICATIONS TO ACTIVE IMAGING." 2018 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP). IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Calgary, CANADA, 2018-04-15 - 2018-04-20.
https://doi.org/10.1109/ICASSP.2018.8462676
Abstract
We address the problem of estimating the parameter of a Bernoulli process. This arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. We introduce a framework within which to minimize the mean-squared error (MSE) subject to an upper bound on the mean number of trials. This optimization has several simple and intuitive properties when the Bernoulli parameter has a beta prior. In addition, by exploiting typical spatial correlation using total variation regularization, we extend the developed framework to a rectangular array of Bernoulli processes representing the pixels in a natural scene. In simulations inspired by realistic active imaging scenarios, we demonstrate a 4.26 dB reduction in MSE due to the adaptive acquisition, as an average over many independent experiments and invariant to a factor of 3.4 variation in trial budget.