Super-resolution imaging with radio interferometry using sparse modeling

We propose a new technique to obtain super-resolution images with radio interferometry using sparse modeling. In standard radio interferometry, sampling of (u, v) is quite often incomplete and thus obtaining an image from observed visibilities becomes an underdetermined problem, and a technique of so-called zero-padding is often used to fill up unsampled grids in the (u, v) plane, resulting in image degradation by finite beam size as well as numerous side-lobes. In this paper we show that directly solving such an underdetermined problem based on sparse modeling (in this paper, Least Absolute Shrinkage and Selection Operator, known as LASSO) avoids the above problems introduced by zero-padding, leading to super-resolution images in which structure finer than the standard beam size (diffraction limit) can be reproduced. We present results of one-dimensional and two-dimensional simulations of interferometric imaging, and discuss its implications for super-resolution imaging, particularly focusing on imaging of black hole shadows with millimeter VLBI (Very Long Baseline Interferometry).