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 modeenables the reconstruction of lines from lowpass measurements, even in presence of a large amount onoise or blur. Furthermore, a Prony method performed on rows and columns of the restored imageprovides a spectral estimation of the line parameters, with subpixel accuracy.