(1) **Input:** data tensor , and dimensions of all -mode signal subspaces. |

(2) **Initialization** : For to , calculate the projectors given by HOSVD-(): |

(a) -mode unfold into matrix ; |

(b) Compute the SVD of ; |

(c) Compute matrix formed by the eigenvectors associated with the largest singular values of |

. is the initial matrix of the -mode signal subspace orthogonal basis vectors; |

(d) Form the initial orthogonal projector on the -mode signal subspace; |

(e) Compute the HOSVD-() of tensor given by |

; |

(3) **ALS loop:** Repeat until convergence, that is, for example, while , being a prior |

fixed threshold, |

(a) For to : |

(i) Form : ; |

(ii) -mode unfold tensor into matrix ; |

(iii) Compute matrix ; |

(iv) Compute matrix composed of the eigenvectors associated with the largest eigenvalues |

of . is the matrix of the -mode signal subspace orthogonal basis vectors at the |

iteration; |

(v) Compute ; |

(b) Compute ; |

(c) Increment . |

(4) **Output:** the estimated signal tensor is obtained through . is |

the rank- approximation of , where is the index of the last iteration after the |

convergence of TUCKALS3 algorithm. |