LRTC-flow.tex

\documentclass[tikz,border={3cm 0.5cm 3cm 0.5cm}]{standalone}
\usepackage{amsmath,amsthm}
\usepackage{amssymb}
\usepackage{bbm}
\usepackage{amsfonts}
\usepackage[ruled,vlined]{algorithm2e}
\usetikzlibrary{positioning,matrix,fit,calc}
\pgfdeclarelayer{behind}
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{behind,background,main,foreground}

\begin{document}
\begin{tikzpicture}[T/.style={text width=12em,node font=\bfseries},
 A/.style={align=center},
 B/.style={A,draw,text width=14em,align=left},
 C/.style={text width=14em,align=right},
 L/.style={node font=\tiny,text=blue},
 F/.style={draw,dashed,fill=white},
 font=\sffamily]
 
 \matrix(mat1)[matrix of nodes,nodes={minimum width=12em}] at (0,0) {
  |[T]| \large{\color{orange!80}Incomplete tensor} \\[1em]
  |[A]| \pgfdeclareimage[width=4.8cm]{img}{input_tensor.pdf}
  \pgfuseimage{img} \\
  |[A]| Tensor $\boldsymbol{\mathcal{Y}}\in\mathbb{R}^{M\times N\times T}$ \\
 };

 \matrix(mat2)[matrix of nodes,nodes={minimum width=13em}] at (7,0) {
  |[T]| \large{\color{orange!80}Model} \\[1em]
  |[B]| Initialize $\boldsymbol{\mathcal{T}}^{1}=\boldsymbol{0}$, $\mathcal{P}_{\Omega}(\boldsymbol{\mathcal{M}}_{k}^{1}) = \mathcal{P}_{\Omega}(\boldsymbol{\mathcal{Y}})$, and set $\boldsymbol{\alpha},\rho,\theta$ and maximum iteration $L$. \\[1.5em]
  |[C]| \begin{algorithm}[H]
\For{$l = 1$ \KwTo $L$}{
  \For{$k = 1$ \KwTo  $3$}{

  Update $\boldsymbol{\mathcal{X}}_{k}^{l+1}$;
  
  }
  
  Update $\boldsymbol{\mathcal{M}}^{l+1}$;
  
  Update $\boldsymbol{\mathcal{T}}^{l+1}$;

}
\end{algorithm} \\
 };
 
  \matrix(mat3)[matrix of nodes,nodes={minimum width=12em}] at (14,0) {
  |[T]| \large{\color{orange!80}Recovered tensor}\\[1em]
  |[A]| \pgfdeclareimage[width=4.8cm]{img}{output_tensor.pdf}
  \pgfuseimage{img} \\
  |[A]| Tensor $\hat{\boldsymbol{\mathcal{Y}}}=\sum_{k=1}^{3}\alpha_k\boldsymbol{\mathcal{X}}_{k}^{L+1}$ \\
 };

 \begin{scope}
  \begin{pgfonlayer}{background}
  \node[F,fit=(mat1-1-1)(mat1-3-1),fill=gray!3](F1){};
  \node[F,fit=(mat2-1-1)(mat2-3-1),fill=gray!3](F2){};
  \node[F,fit=(mat3-1-1)(mat3-3-1),fill=gray!3](F3){};

  \end{pgfonlayer}
  \draw[-latex](mat2-2-1)--(mat2-3-1);
  \node[text width=2cm] (cdots) at (4.2,0) {{\color{gray}\LARGE$\Rightarrow$}};
  \node[text width=2cm] (cdots) at (11.2,0) {{\color{gray}\LARGE$\Rightarrow$}};
 \end{scope}
 \begin{scope}
  \begin{pgfonlayer}{behind}
  \end{pgfonlayer}
 \end{scope}
\end{tikzpicture}
\end{document}