12 problems

The NTG is a component of the registration process for hyperspectral super-resolution, and the fused image produced by NTG-Hysure is observed to exhibit pronounced color inconsiste…

Let $N_{\lambda}$ denote the size of the uniform grid used to choose the decimation parameter, let $N_b$ denote the number of histogram bins, let $\Omega$ be the bandwidth paramete…

Optimal separation conjecture. The optimal separation for convex methods is

Let $N$ observations of a signal be collected from the model, with each observation sampled at $L$ equally spaced locations; let $M$ denote the number of grid points and let…

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…

The paper considers Proposition … is not optimal, so its bound can be improved. The authors leave the improvement for future work; the source provides no resolution of this conject…

The paper considers discrete prolate spheroidal wave functions (DPSWFs) and the asymptotic criteria imposed on the kernel $g_{\sigma,N}(\cdot)$ as $N=2f_C+1\to\infty$, namely Crite…

Finite-rank convergence conjecture. If the data $\mathbf{a}$ and $\mathbf{b}$ in problem … is satisfied.

Let $\mathcal{S}=\{\omega_j:j\in\mathbb{Z}\}$ be a periodic support set on a lattice of spacing $\Delta$, with Rayleigh index $R_*$. Define … and let $\smin^2(\Phi^L)$ denote the c…

Let $x_i$ be an original spike location for a non-dyadic measure, and consider the neighboring grid points relevant to the discrete minimal-norm certificate. Immediate-neighbor con…

Consider a non-dyadic measure and a sufficiently fine grid, in a regime where there is at most one pair of spikes at consecutive grid points in the neighborhood of each original sp…

Let $m$ be a discrete complex measure on the torus, with minimum separation distance … Suppose identifiability is guaranteed whenever $\Delta(m)\geq C/f_c$, where $f_c$ is the cuto…