Application of compressive sensing for gravitational microlensing events

Abstract

Compressive sensing (CS) is a unique mathematical technique for simultaneous data acquisition and compression. This technique is particularly apt for time-series photometric measurements; we apply CS to time-series photometric measurements specifically obtained due to gravitational microlensing events. We show the error sensitivity in detecting microlensing event parameters through simulation modeling. Particularly, we show the relation of both the amount of error and its impact on the microlensing parameters of interest. We derive statistical error bounds to apply those as a baseline for analyzing the effectiveness of CS application. Our results of single and binary microlensing events conclude that we can obtain error less than 1% over a three-pixel radius of the center of the microlensing star by using 25% Nyquist rate measurements.