10 problems

Let $p\equiv 1\pmod{4}$ be prime, let $\Phi_p$ be the Paley equiangular tight frame, and let $\delta_K=\delta_K(\Phi_p)$ denote its RIP constant of order $K$. Paley ETF RIP-constan…

Let $\{\Phi_n\}$ be the family of Paley equiangular tight frames, with $\Phi_n$ an $m\times n$ matrix and $m=m(n)\in[0.01n,0.99n]$. A matrix family is a restricted isometry for an…

Fourier RIP conjecture. For the discrete Fourier transform, $q=\mathcal{O}(K\log N)$ measurements should suffice to obtain an RIP matrix, in the sense needed for recovery of $K$-sp…

Restricted-isometry conjecture. If $A$ has restricted 2-isometry property of order $tk$ with

Let $\mathbf \Phi\in\mathbb R^{m\times n}$ satisfy the $2s$-restricted isometry property with constant $\delta_{2s}$, and consider the stable reconstruction result requiring…

Lower restricted isometry conjecture. The restriction to small $y$ is not needed for these bounds to hold. This would extend the quantitative control of the lower restricted isomet…

A measurement map ${\mathcal A}:\mathcal H_d\to\mathbb R^m$ is called Gaussian when its entries are independent normal random variables with mean zero and variance $1/m$. For a hie…

Let $s$ be the sparsity level, let $A$ be a sampling matrix satisfying the restricted isometry property, and let ${\rm OMMP}(2)$ denote orthogonal multi-matching pursuit selecting…

Let $A$ be an $m\times n$ random Fourier measurement matrix obtained by choosing $m$ rows independently and uniformly from the $n\times n$ discrete Fourier transform matrix, and le…

Conjecture on the measurement bound. The trailing logarithmic factors to the right of $S\log N$ are unnecessary; equivalently, the required number of measurements should be bounded…