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We propose a new imaging technique for radio and optical/infraredinterferometry. The proposed technique reconstructs the image from thevisibility amplitude and closure phase, which are standard data products ofshort-millimeter very long baseline interferometers such as the Event HorizonTelescope (EHT) and optical/infrared interferometers, by utilizing tworegularization functions: the $\ell_1$-norm and total variation (TV) of thebrightness distribution. In the proposed method, optimal regularizationparameters, which represent the sparseness and effective spatial resolution ofthe image, are derived from data themselves using cross validation (CV). As anapplication of this technique, we present simulated observations of M87 withthe EHT based on four physically motivated models. We confirm that $\ell_1$+TVregularization can achieve an optimal resolution of $\sim 20-30$% of thediffraction limit $\lambda/D_{\rm max}$, which is the nominal spatialresolution of a radio interferometer. With the proposed technique, the EHT canrobustly and reasonably achieve super-resolution sufficient to clearly resolvethe black hole shadow. These results make it promising for the EHT to providean unprecedented view of the event-horizon-scale structure in the vicinity ofthe super-massive black hole in M87 and also the Galactic center Sgr A*.

Imaging the Schwarzschild-radius-scale Structure of M87 with the Event Horizon Telescope using Sparse Modeling