Efficient deconvolution and spatial resolution enhancement from continuous and oversampled observations in microwave imagery

In this paper, we develop efficient deconvolution and super-resolution methodologies and apply these techniques to reduce image blurring and distortion inherent in an aperture synthesis system. Such a system produces ringing at sharp edges and other transitions in the observed field. The conventional approach to suppressing sidelobes is to apply linear apodization, which has the undesirable side effect of degrading spatial resolution. We have developed an efficient total variation minimization technique based on Split Bregman deconvolution that reduces image ringing while sharpening the image and preserving information content. Furthermore, a proposed multiframe super-resolution method is presented that is robust to image noise and noise in the point spread function and leads to additional improvements in spatial resolution. Our super-resolution methodologies are based on current research in sparse optimization and compressed sensing, which lead to unprecedented efficiencies for solving image reconstruction problems.