Compressive sensing (CS) is a mathematical technique for simultaneous data acquisition and compression. In this work, we show 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 timeseries 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. We study the case of gravitational microlensing in which a distant source star in a crowded field is briefly magnified by the passage of a mass through the line of sight between the source star and observer. 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.
Compressive Sensing is an emerging technology for data compression and simultaneous data acquisition. This is an enabling technique for significant reduction in data bandwidth, and transmission power and hence, can greatly benefit space-flight instruments. We apply this process to detect exoplanets via gravitational microlensing. We experiment with various impact parameters that describe microlensing curves to determine the effectiveness and uncertainty caused by Compressive Sensing. Finally, we describe implications for space-flight missions.
Compressive sensing is a simultaneous data acquisition and compression technique, which can significantly reduce data bandwidth, data storage volume, and power. We apply this technique for transient photometric events. In this work, we analyze the effect of noise on the detection of these events using compressive sensing (CS). We show numerical results on the impact of source and measurement noise on the reconstruction of transient photometric curves, generated due to gravitational microlensing events. In our work, we define source noise as background noise, or any inherent noise present in the sampling region of interest. For our models, measurement noise is defined as the noise present during data acquisition. These results can be generalized for any transient photometric CS measurements with source noise and CS data acquisition measurement noise. Our results show that the CS measurement matrix properties have an effect on CS reconstruction in the presence of source noise and measurement noise. We provide potential solutions for improving the performance by tuning some of the properties of the measurement matrices. For source noise applications, we show that choosing a measurement matrix with low mutual coherence can lower the amount of error caused due to CS reconstruction. Similarly, for measurement noise addition, we show that by choosing a lower expected value of the binomial measurement matrix, we can lower the amount of error due to CS reconstruction.
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