| Input: Observed data |$\mathcal{Y}$|, sampling operator |$\mathcal{P}$|, estimated rank |$({{R}_1},{{R}_2},{{R}_3})$| of the mode-|${{{{\bf j}}}_n}$| unfolding matrix, hyperparameters |$\lambda $|; Output: Reconstructed data |$\mathcal{X}$|; 1. Randomly initialize matrices |${{{{\bf U}}}_n}$| and |${{{{\bf V}}}_n}$|, set parameters |$k = 1,\mu = 0.01,\rho = 1.2,{{\mu }_{\max }} = {{10}^7}$|. 2. If the stopping criterion is met |$k \le 30$|, repeat step 2; if not, proceed to step 3. The detailed process for the k-th iteration is as follows: a) Update matrix |${{{{\hat{\bf V}}}}_n}$| using Equation (12); b) Update factor matrix |${{{{\bf U}}}_n}$| using Equation (8); c) Update factor matrix |${{{{\bf V}}}_n}$| using Equation (10); d) Update tensor |$\rm {X} $| using Equation (15); e) Update matrices |${{{{\bf D}}}_n}$| and |${{{{\bf F}}}_n}$| using Equations (16) and (17); |$\mu = \max ( {\rho \mu ,{{\mu }_{\max }}} )$|; |$k = k + 1$|; 3. Output the reconstructed data |$\rm {X} $|. |
| Input: Observed data |$\mathcal{Y}$|, sampling operator |$\mathcal{P}$|, estimated rank |$({{R}_1},{{R}_2},{{R}_3})$| of the mode-|${{{{\bf j}}}_n}$| unfolding matrix, hyperparameters |$\lambda $|; Output: Reconstructed data |$\mathcal{X}$|; 1. Randomly initialize matrices |${{{{\bf U}}}_n}$| and |${{{{\bf V}}}_n}$|, set parameters |$k = 1,\mu = 0.01,\rho = 1.2,{{\mu }_{\max }} = {{10}^7}$|. 2. If the stopping criterion is met |$k \le 30$|, repeat step 2; if not, proceed to step 3. The detailed process for the k-th iteration is as follows: a) Update matrix |${{{{\hat{\bf V}}}}_n}$| using Equation (12); b) Update factor matrix |${{{{\bf U}}}_n}$| using Equation (8); c) Update factor matrix |${{{{\bf V}}}_n}$| using Equation (10); d) Update tensor |$\rm {X} $| using Equation (15); e) Update matrices |${{{{\bf D}}}_n}$| and |${{{{\bf F}}}_n}$| using Equations (16) and (17); |$\mu = \max ( {\rho \mu ,{{\mu }_{\max }}} )$|; |$k = k + 1$|; 3. Output the reconstructed data |$\rm {X} $|. |
| Input: Observed data |$\mathcal{Y}$|, sampling operator |$\mathcal{P}$|, estimated rank |$({{R}_1},{{R}_2},{{R}_3})$| of the mode-|${{{{\bf j}}}_n}$| unfolding matrix, hyperparameters |$\lambda $|; Output: Reconstructed data |$\mathcal{X}$|; 1. Randomly initialize matrices |${{{{\bf U}}}_n}$| and |${{{{\bf V}}}_n}$|, set parameters |$k = 1,\mu = 0.01,\rho = 1.2,{{\mu }_{\max }} = {{10}^7}$|. 2. If the stopping criterion is met |$k \le 30$|, repeat step 2; if not, proceed to step 3. The detailed process for the k-th iteration is as follows: a) Update matrix |${{{{\hat{\bf V}}}}_n}$| using Equation (12); b) Update factor matrix |${{{{\bf U}}}_n}$| using Equation (8); c) Update factor matrix |${{{{\bf V}}}_n}$| using Equation (10); d) Update tensor |$\rm {X} $| using Equation (15); e) Update matrices |${{{{\bf D}}}_n}$| and |${{{{\bf F}}}_n}$| using Equations (16) and (17); |$\mu = \max ( {\rho \mu ,{{\mu }_{\max }}} )$|; |$k = k + 1$|; 3. Output the reconstructed data |$\rm {X} $|. |
| Input: Observed data |$\mathcal{Y}$|, sampling operator |$\mathcal{P}$|, estimated rank |$({{R}_1},{{R}_2},{{R}_3})$| of the mode-|${{{{\bf j}}}_n}$| unfolding matrix, hyperparameters |$\lambda $|; Output: Reconstructed data |$\mathcal{X}$|; 1. Randomly initialize matrices |${{{{\bf U}}}_n}$| and |${{{{\bf V}}}_n}$|, set parameters |$k = 1,\mu = 0.01,\rho = 1.2,{{\mu }_{\max }} = {{10}^7}$|. 2. If the stopping criterion is met |$k \le 30$|, repeat step 2; if not, proceed to step 3. The detailed process for the k-th iteration is as follows: a) Update matrix |${{{{\hat{\bf V}}}}_n}$| using Equation (12); b) Update factor matrix |${{{{\bf U}}}_n}$| using Equation (8); c) Update factor matrix |${{{{\bf V}}}_n}$| using Equation (10); d) Update tensor |$\rm {X} $| using Equation (15); e) Update matrices |${{{{\bf D}}}_n}$| and |${{{{\bf F}}}_n}$| using Equations (16) and (17); |$\mu = \max ( {\rho \mu ,{{\mu }_{\max }}} )$|; |$k = k + 1$|; 3. Output the reconstructed data |$\rm {X} $|. |
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