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Ongoing microlensing surveys have already yielded more than five hundred microlensing events, most of which have been identified in real-time. In this review I present the basic theory and observational status of these surveys. I highlight…
Astronomical source deblending is the process of separating the contribution of individual stars or galaxies (sources) to an image comprised of multiple, possibly overlapping sources. Astronomical sources display a wide range of sizes and…
Dark matter cannot be observed directly, but its weak gravitational lensing slightly distorts the apparent shapes of background galaxies, making weak lensing one of the most promising probes of cosmology. Several observational studies have…
The {\it assumption of additive absorptivity} by different components in compound particles is a widely used method applied in the literature to the analysis of the chemical and structural properties of astronomical (circumstellar,…
Faraday tomography through broadband polarimetry can provide crucial information on magnetized astronomical objects, such as quasars, galaxies, or galaxy clusters. However, the limited wavelength coverage of the instruments requires that we…
Recent galaxy redshift surveys have brought in a large amount of accurate cosmological data out to redshift 0.3, and future surveys are expected to achieve a high degree of completeness out to a redshift exceeding 1. Consequently, a…
Weak gravitational lensing of distant galaxies can probe the total projected mass distribution of foreground gravitational structures on all scales and has been used successfully to map the projected mass distribution of rich intermediate…
Weak gravitational lensing surveys have the potential to directly probe mass density fluctuation in the universe. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by…
We survey a new paradigm in signal processing known as "compressive sensing". Contrary to old practices of data acquisition and reconstruction based on the Shannon-Nyquist sampling principle, the new theory shows that it is possible to…
The 21 cm radiation of neutral hydrogen provides crucial information for studying the early universe and its evolution. To advance this research, countries have made significant investments in constructing large low-frequency radio…
The exploration of the redshift drift, a direct measurement of cosmological expansion, is expected to take several decades of observation with stable, sensitive instruments. We introduced a new method to probe cosmology which bypasses the…
Cosmological weak lensing is the powerful probe of cosmology. Here we address one of the most fundamental, statistical questions inherent in weak lensing cosmology: whether or not we can recover the initial Gaussian information content of…
Ground-based astronomical observations at thermal infrared wavelengths face the problem of extracting the weak astronomical signal from the large and rapidly variable background flux. The observing strategy most commonly used, the so-called…
We propose a framework for compressive sensing of images with local distinguishable objects, such as stars, and apply it to solve a problem in celestial navigation. Specifically, let x be an N-pixel real-valued image, consisting of a small…
Observational data from the ESA astrometric mission Gaia determining the positions of celestial objects within an accuracy of few microarcseconds will be soon fully available. Other satellite-based space missions are currently planned to…
This paper presents a case study from a single, six-hour observing period to illustrate the application of techniques developed for interferometric radio telescopes to the spectral analysis of observations of ionospheric fluctuations with…
We consider the probe of astrophysical signals through radio interferometers with small field of view and baselines with non-negligible and constant component in the pointing direction. In this context, the visibilities measured essentially…
Gravitational microlensing provides a new technique for studying the surfaces of distant stars. Microlensing events are detected in real time and can be followed up with precision photometry and spectroscopy. This method is particularly…
On the scale of the cosmic horizon, signatures that are unique to general relativity are concealed within the statistics of the large scale distribution of galaxies. These were thought to be beyond the reach of all but the most ambitious…
An automated, rapid classification of transient events detected in the modern synoptic sky surveys is essential for their scientific utility and effective follow-up using scarce resources. This presents some unusual challenges: the data are…