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Affine sum-of-ranks minimization (ASRM) generalizes the affine rankminimization (ARM) problem from matrices to tensors. Here, the interest lies inthe ranks of a family $\mathcal{K}$ of different matricizations. Transferringour priorly discussed results on asymptotic log-det rank minimization, we showthat iteratively reweighted least squares with weight strength $p = 0$ remainsa, theoretically and practically, particularly viable method denoted as$\mathrm{IRLS}$-$0\mathcal{K}$. As in the matrix case, we prove globalconvergence of asymptotic minimizers of the log-det sum-of-ranks function todesired solutions. Further, we show local convergence of$\mathrm{IRLS}$-$0\mathcal{K}$ in dependence of the rate of decline of thetherein appearing regularization parameter $\gamma \searrow 0$. Forhierarchical families $\mathcal{K}$, we show how an alternating version($\mathrm{AIRLS}$-$0\mathcal{K}$, related to prior work under the name$\mathrm{SALSA}$) can be evaluated solely through tensor tree network basedoperations. The method can thereby be applied to high dimensions through theavoidance of exponential computational complexity. Further, the otherwisecrucial rank adaption process becomes essentially superfluous even forcompletion problems. In numerical experiments, we show that the thereforrequired subspace restrictions and relaxation of the affine constraint causeonly a marginal loss of approximation quality. On the other hand, wedemonstrate that $\mathrm{IRLS}$-$0\mathcal{K}$ allows to observe thetheoretical phase transition also for generic tensor recoverability inpractice. Concludingly, we apply $\mathrm{AIRLS}$-$0\mathcal{K}$ to largerscale problems.

Asymptotic Log-Det Sum-of-Ranks Minimization via Tensor (Alternating) Iteratively Reweighted Least Squares