A data-adaptive regularization method for line spectrum estimation

We present a data-adaptive regularization method for estimation of line spectra. A Gaussian mixture is used as a suitable prior distribution and a different regularization term is associated to each component of the mixture. The regularized functional is minimized by applying an iterative procedure. The parameters of the mixture as well as the noise variance are updated at each iteration. In this way, the method can be applied even if accurate estimates of these parameters are not available. We apply the method to 1-D and 2-D problems showing its high-resolution ability and good performance.