Systematic Effects of Compressive Sensing for Time-Series Photometric Measurements for Space Observatories

Abstract

Natural phenomena may be sparse in some physical or temporal domain. If we exploit this sparsity by applying the technique of Compressive Sensing (CS) to obtain information about a phenomenon, how do our measurements change as a function of domain and measurement systematics? What are the specific implications for the science and for the sensing infrastructure? In this thesis, we directly address this issue by an in-depth study of the generalized systematic effects consequent to the application of CS to time-series photometric measurements. We will assess implications for observability, sparsification, and information loss in the detection, retrieval and reconstruction process. CS is a simultaneous data acquisition and compression technique, which can significantly reduce data samples at the detector front-end itself. To study time-series photometry, we explore the field of gravitational microlensing. A source star, typically in the galactic bulge, gets microlensed when there is a precise alignment of a lensing star and its planetary system with the source star. The microlensed source star changes in flux magnification as the lensing system crosses the precise path of alignment, resulting in a microlensing curve in thr time domain. A high-cadence, high-resolution system, which uses low power and bandwidth is essential to obtain valuable science measurements. Hence, we propose applying CS to gravitational microlensing data sets, which in turn can be generalized to any time-ordered photometric measurements. We develop a CS based architecture for acquiring and reconstructing transient astrophysical events. This architecture reconstructs a differenced image, eliminating the need for any sparse domain transforms otherwise required for traditional CS reconstruction. The resulting reconstructed differenced image is of importance as the information required for generating time-series photometric light curves is best obtained from an image differenced with a reference image. This architecture eliminates the need to 1.) transform an image to a sparse domain, 2.) reconstruct a dense field, and then apply differencing on the image to obtain the time-ordered photometry. Our results show that this architecture is able to reconstruct the light curve for magnification factors greater than 1 with error less than $2\%$ using only $10\%$ of the Nyquist rate samples for an ideal differenced image. To complete CS analysis for gravitational microlesning data, we simulate crowded stellar fields to obtain photometric light curves from the differenced images. We show through simulation modelling the error sensitivity for detecting microlensing event parameters. Particularly, we show the relation of 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 compressive sensing application. Our results conclude that for single and binary microlensing events we can obtain error less than 1% over a 3-pixel radius of the center of the microlensing star by using 25% Nyquist rate measurements. The CS error is well within the error caused by a 10% deviation of the microlensing parameters of interest. Hence, we can show CS accurately reconstructs gravitational microlensing curves within at least 10% statistical bounds of critical microlensing parameters. Our results are determined for both single and binary gravitational microlensing events. In addition, we show the effect of noise on such crowded stellar fields, where a star in the field is experiencing a microlensing event. We provide techniques to tune the CS measurement matrix in order to improve CS reconstruction in the presence of noise. We also study the effect of CS on gravitational microlensing parallax measurements for space-based observatories. Microlensing parallax breaks down degeneracy in the gravitational microlensing parameters, hence, providing additional information on the microlensing parameters of interest. Space observatory constellations provide an optimal platform for microlensing parallax measurements. The use of CS technology for small satellites (SmallSat) can be a game changing technology for obtaining valuable science parameters for gravitational microlensing. Using traditional detection methods on low-cost small satellites would not be very feasible for applications like these due to the limited on-board resource capacity of such satellites. Finally we combine together the modelled study with a potential implementation of a CS based detector system on a SmallSat instrument for obtaining gravitational microlensing light curves due to single and binary lensed events.