Algorithm 1. Gradient-based algorithm

Input: set of the positions of the missing samples: ${\mathbb{N}}_x$; measurement vector y;     Set $x^{(0)}(n)\leftarrow y(n)$ for $n\notin {\mathbb{N}}_x$     Set $x^{(0)}(n)\leftarrow 0$ for $n\in {\mathbb{N}}_x$     $m\leftarrow 0$     Set $\Delta \leftarrow \max \left|x^{(0)}(n)\right|$     repeat         repeat             $x^{(m+1)}(n)\leftarrow x^{(m)}(n)$, for each n             for $n_i\in {\mathbb{N}}_x$ do        $\begin{array}{l}{X}^{+}(k)\leftarrow \mathit{\Im }\{x^{(m)}(n)+\mathsf{\Delta }\mathit{\delta }(n-n_i)\},\\ X^{-}(k)\leftarrow \mathit{\Im }\{x^{(m)}(n)-\mathsf{\Delta }\mathit{\delta }(n-n_i)\},\hspace{1em}\left(\mathsf{\Im }\hspace{1em}-\mathrm{transformation}\right)\end{array}$                     $g(n_i)\leftarrow \frac{1}{N}{\displaystyle \sum _{k=0}^{N-1}\left({\Vert X^{+}(k)\Vert }_1-{\Vert X^{-}(k)\Vert }_1\right),}$     $x^{(m+1)}(n_i)\leftarrow x^{(m)}(n_i)-g(n_i)$     end for     $m\leftarrow m+1$     until stopping criterion is satisfied     $\mathsf{\Delta }\leftarrow \mathsf{\Delta }/3$     until required precision is achieved Output: reconstructed signal $x^{(m)}(n)$