  We propose a new technique to obtain super-resolution images with radio
interferometer 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
so-called "zero-padding" is often used to fill up unsampled grids in ($u$, $v$)
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 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 to
super-resolution imaging, particularly focusing on imaging of black hole
shadows with millimeter VLBI.
