7 problems

Generic sparse phase retrieval conjecture. The signal $x$ is uniquely determined, up to unavoidable ambiguities, as long as

Support-recovery conjecture. If $|S-S|=|S'-S'|\geq K$, then $I_{S,S'}$ has dimension strictly less than $K$. This would imply that a generic vector supported on $S$ cannot share it…

Known-support recovery conjecture. If $|S-S|>|S|$, then $I_S$ has dimension $|S|$ and degree $2|D_S|$. This is the signal-recovery step for generic signals whose support is known;…

Let $S\subset[0,N-1]$ and let $L_S$ be the subspace of signals supported in $S$. Let $D_S$ be the subgroup of intrinsic symmetries $D$ that preserves $L_S$. Generic signal-recovery…

Let $K$ be the sparsity level and let $a_x$ denote the periodic auto-correlation of a $K$-sparse signal $x$. Measure-zero conjecture. If $K/N<1/2$, then the set of $K$-sparse signa…

Let $N$ be even, let $K$ be the sparsity, and let $x$ be a $K$-sparse generic signal whose periodic auto-correlation is $a_x$. An intrinsic symmetry is an element of the group $D$…

Let $\Theta_1(k_n,\zeta_n)$ be the parameter space of vectors $\theta\in\mathbb{R}^n$ with at most $k_n=n^\beta$ nonzero coordinates and satisfying…