5 problems

Let $\boldsymbol{A}$ be a sensing matrix with restricted isometry constant $\delta_{K+1}$, and let $\boldsymbol{x}$ be a $K$-sparse signal. Dai–Milenkovic conjecture. There exist a…

Let $\mathbf{x}$ be a $K$-sparse signal, let $\mathbf{y}$ be its noisy measurements, and run OMP for $K$ iterations. Write … for the support-recovery error rate, and let…

Dai and Mo's conjecture. There exist a matrix $\boldsymbol{A}$ with

Let $s$ denote the sparsity level, let $\bar{k}$ denote the relevant support-size parameter, and let $\rho_+(\bar{k})$ and $\rho_-(s)$ be the corresponding upper and lower restrict…

Rauhut's conjecture. For $M\leq \widetilde c_n K^{2-1/n}$, with $n\in\mathbb N$, with high probability there exists a $K$-sparse signal $x\in\mathbb R^N$ that cannot be recovered v…