Comon's conjecture for Hankel tensors

Let $\mathcal{H}\in\operatorname{H}^m(\mathbb{C}^n)$ be any Hankel tensor, where $\operatorname{rank}(\mathcal{H})$ denotes its tensor rank and $\operatorname{rank}_S(\mathcal{H})$ its symmetric rank. Comon's conjecture for Hankel tensors. For all Hankel tensors,

$$\operatorname{rank}(\mathcal{H})=\operatorname{rank}_S(\mathcal{H}).$$

This is proposed as a restricted form of Comon's conjecture. The unrestricted assertion for all symmetric tensors is known to be false by a counterexample of Y. Shitov, while the Hankel-tensor case remains open.