Converse of the Toeplitz-Hausdorff Theorem for the Joint Numerical Range.

Question

Let $\mathbf{A}_1$ and $\mathbf{A}_2$ be two $N\times N$ hermitian matrices. Their Joint Numerical Range is defined as the 2-D set \begin{align} \mathbb{S}_2=\{[\textbf{u}^H\mathbf{A}_1\mathbf{u},\textbf{u}^H\mathbf{A}_2\mathbf{u}]\in\mathbb{R}^2, \mathbf{u}\in \mathbb{C}^{N\times 1},\mathbf{u}^H\mathbf{u}=1\} \end{align} By a famous theorem of Toeplitz-Hausdorff, $\mathbb{S}_2$ is a closed compact convex set. Does the converse hold? I mean, can every closed compact convex set in 2-D be the joint numerical range of any two hermitian matrices?.