. 2021 Aug 13;4:687176. doi: 10.3389/frai.2021.687176

Algorithm 1.

Pseudo code of the proposed algorithm

INPUT: Incomplete image $\underline{X}$ , mask tensor $\underline{Ω}$ , vector of block sizes $p = [P_{1}, P_{2}, \dots, P_{L}]$ where L is number of stages, $t = [T_{1}, T_{2}]$ , rank vectors $r_{1}, \dots, r_{N}$ , error level ϵ, maximum value of the rank $R_{m a x}$ , internal iteration number $I_{i n t}$ , the rank increasing step ( $i n c$ ) and the threshold for selecting the core tensors for rank incremental in each iteration ( $t o l$ ).
OUTPUT: Completed image $\hat{\underline{X}}$ .
1: Initialize the missing elements of $\underline{X}$ by zero.
2: for $l = 1 : L$ do
3: Block Hankelize the input incomplete image ( $\underline{X}$ ) and the mask tensor ( $\underline{Ω}$ ) by block size $P_{l} \times P_{l}$ and window size $t = [T_{1}, T_{2}]$ which results in $\underline{H}$ and ${\underline{Ω}}_{H}$ .
4: Put $\tilde{\underline{H}} = \underline{H}$
5: while $max (r_{l}) < R_{m a x}$ (or the normalized approximation error is higher than the error level ϵ) do
6: for $j = 1 : I_{i n t}$ do
7: Compute the TR decomposition of $\tilde{\underline{H}}$ , i.e., $\hat{\underline{H}}$ with rank vector $r_{l}$ .
8: $\tilde{\underline{H}} = {\underline{Ω}}_{H} ⊛ \underline{H} + (\underline{1} - {\underline{Ω}}_{H}) ⊛ \hat{\underline{H}}$
9: end for
10: Increase the elements of the rank vector $r_{l}$ using the approach of (Sedighin et al., 2021).
11: Compute $\hat{\underline{X}}$ by de‐Hankelizing $\tilde{\underline{H}}$ (in noisy cases by de‐Hankelizing $\hat{\underline{H}}$ ).
12: $\hat{\underline{X}} = \underline{Ω} ⊛ \underline{X} + (\underline{1} - \underline{Ω}) ⊛ \hat{\underline{X}}$ .
13: Apply smoothing by replacing each estimated element (for $\underline{Ω} = 0$ ) by the average of its four neighbors in the frontal slice and keeping the observed elements fixed.
14: end while
15: Put $\underline{X} = \hat{\underline{X}}$ .
16: end for