Feichtinger's conjecture for Hilbert-space frames

Let $\{\tau_n\}_n$ be a frame for a Hilbert space $\mathcal{H}$ such that

$$0<\inf_{n\in\mathbb{N}}\|\tau_n\|.$$

Feichtinger conjecture. The sequence $\{\tau_n\}_n$ can be partitioned into a finite union of Riesz sequences for $\mathcal{H}$. This conjecture was proved by Marcus, Spielman and Srivastava; it is therefore a theorem rather than an open conjecture.