A Convex Approach to Superresolution and Regularization of Lines in Images

We present a new convex formulation for the problem of recovering lines in degraded images. Following the recent paradigm of superresolution, we formulate a dedicated atomic norm penalty and we solve this optimization problem by means of a primal-dual algorithm. This parsimonious model enables the reconstruction of lines from lowpass measurements, even in presence of a large amount of noise or blur. Furthermore, a Prony method performed on rows and columns of the restored image, provides a spectral estimation of the line parameters, with subpixel accuracy.