lie in the zero level set of an annihilating polynomial, the continuous domain image restoration is based on the fact that the structured matrix (Hankel/Toeplitz matrix) constructed from the Fourier samples of piecewise constant images is low rank [@G.Ongie2018; @G.Ongie2015; @G.Ongie2016]. Hence, we can apply the following structured low rank matrix completion model [@Y.Chen2014; @G.Ongie2017] $$\begin{aligned}
\label{LRSMCompletion}
\min~~\rank\left(\bmH\left(\La\bsv\right)\right)~~~~~~~\text{subject to}~~\bmP_{\MM}\bsv=\bsf\end{aligned}$$ to restore the fully sampled k-space data (the discrete sample of the Fourier transform of a piecewise constant function). Here, $\bmH$ is an operator that constructs a so-called two-fold Hankel matrix, and $\La$ is a weight matrix derived from the Fourier transform of $\na$ (the detailed definitions will be postponed until \[Preliminaries\]). By restoring the k-space data first, we can directly utilize the property of the underlying function in the continuous domain, thus achieving the better restoration results over \[CSType\] by reducing the basis mismatch.

Though \[LRSMCompletion\] is an NP-hard problem in general [@E.J.Candes2009], numerous tractable relaxation approaches have been proposed in the literature. One of them is the convex nuclear norm relaxation method (e.g. [@J.F.Cai2016; @M.Fazel2013]), together with the theoretical restoration guarantees (e.g. [@G.Ongie2018]). In addition, the iterative reweighted least squares (IRLS) approaches for the Schatten $p$-norm minimization are proposed 