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Leveraging recent advances in additive combinatorics, we exhibit explicit matrices satisfying the Restricted Isometry Property with better parameters. Namely, for $varepsilon=3.26cdot 10^{-7}$, large $k$ and $k^{2-varepsilon} le Nle k^{2+varepsilon}$, we construct $n times N$ RIP matrices of order $k$ with $k = Omega( n^{1/2+varepsilon/4} )$.
This letter analyzes the performances of a simple reconstruction method, namely the Projected Back-Projection (PBP), for estimating the direction of a sparse signal from its phase-only (or amplitude-less) complex Gaussian random measurements, i.e., a
A $t$-$(n,d,lambda)$ design over ${mathbb F}_q$, or a subspace design, is a collection of $d$-dimensional subspaces of ${mathbb F}_q^n$, called blocks, with the property that every $t$-dimensional subspace of ${mathbb F}_q^n$ is contained in the same
We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant operator. Speci
We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top conjecture${}^dagger$, Lieb permanent dominance conjecture, Bapat and
We consider the problem of learning a coefficient vector x_0in R^N from noisy linear observation y=Ax_0+w in R^n. In many contexts (ranging from model selection to image processing) it is desirable to construct a sparse estimator x. In this case, a p