10 problems

Third-moment finite-candidate conjecture. Moments up to degree three should generically restrict the solution set to finitely many candidates.

Heterogeneous orbit-recovery conjecture. A phenomenon analogous to the single-signal model should hold: the orbits of multiple signals can be estimated simultaneously from the aver…

Multi-reference alignment moment recovery conjecture. Suppose that the $q$-th moment of $y$ determines $x$ uniquely, possibly up to some intrinsic symmetries. Then $x$ is determine…

Heterogeneous multi-reference alignment is a natural extension of the multi-reference alignment model in which the observations may arise from different underlying signals. A compu…

In the projected multi-reference alignment model, let $L$ and $L'$ tend to infinity with $L'\leq L$ and $L'=\omega(\log L)$, and scale the noise according to … Write…

Let $K$ signals be observed through averaged mean, power-spectrum, and bispectrum measurements, and let $L$ denote the signal length. Statistical-computational gap conjecture. The…

Let $K$ signals be represented through their averaged mean, power spectrum, and bispectrum, and let $G_{\Pi,L}x$ denote the orbit of the underlying signal under the parameterized s…

Let $x$ be a signal, let $M$ be the number of grid points, let $L$ be the number of equally spaced samples per observation, and let $\mathcal{P}(L)$ be the quantity defined in the…

Let $\sigma>.1$, let $\varepsilon>0$, and consider generic heterogeneous mixtures in the multi-reference alignment problem, perhaps with only a constant number of components, in we…

The phase shift model is considered for signals in the classes $\mathcal{T}_s$, with noise level $\sigma$ and sample size $n$. The upper bound contains a remainder term of the form…