  Direct inversion of incomplete visibility samples in VLBI (Very Large
Baseline Interferometry) radio telescopes produces images with convolutive
artifacts. Since proper analysis and interpretations of astronomical radio
sources require a non-distorted image, and because filling all of sampling
points in the uv-plane is an impossible task, image deconvolution has been one
of central issues in the VLBI imaging. Up to now, the most widely used
deconvolution algorithms are based on least-squares-optimization and maximum
entropy method. In this paper, we propose a new algorithm that is based on an
emerging paradigm called compressive sensing (CS). Under the sparsity
condition, CS capable to exactly reconstructs a signal or an image, using only
a few number of random samples. We show that CS is well-suited with the VLBI
imaging problem and demonstrate that the proposed method is capable to
reconstruct a simulated image of radio galaxy from its incomplete visibility
samples taken from elliptical trajectories in the uv-plane. The effectiveness
of the proposed method is also demonstrated with an actual VLBI measured data
of 3C459 asymmetric radio-galaxy observed by the VLA (Very Large Array).
