We consider the sparse recovery problem on Euclidean Jordan algebra (SREJA), which includes sparse signal recovery and low-rank symmetric matrix recovery as special cases. We introduce the restricted isometry property, null space property (NSP), and s-goodness for linear transformations in s-sparse element recovery on Euclidean Jordan algebra (SREJA), all of which provide sufficient conditions ...

We study the recovery conditions of weighted mixed l2/lp (0 < p ≤ 1) minimization for block sparse signal reconstruction from compressed measurements when partial block support information is available. We show that the block p-restricted isometry property (RIP) can ensure the robust recovery. Moreover, we present the sufficient and necessary condition for the recovery by using weighted block p...

We study the recovery conditions of weighted `1 minimization for real signal reconstruction from phaseless compressed sensing measurements when partial support information is available. A Strong Restricted Isometry Property (SRIP) condition is provided to ensure the stable recovery. Moreover, we present the weighted null space property as the sufficient and necessary condition for the success o...

Oracle inequalities and variable selection properties for the Lasso in linear models have been established under a variety of different assumptions on the design matrix. We show in this paper how the different conditions and concepts relate to each other. The restricted eigenvalue condition (Bickel et al., 2009) or the slightly weaker compatibility condition (van de Geer, 2007) are sufficient f...

We consider the problem of constructing a linear map from a Hilbert space H (possibly infinite dimensional) to R that satisfies a restricted isometry property (RIP) on an arbitrary signal model S ⊂ H. We present a generic framework that handles a large class of low-dimensional subsets but also unstructured and structured linear maps. We provide a simple recipe to prove that a random linear map ...

A theorem proved by Hrushovski for graphs and extended by Solecki and Vershik (independently from each other) to metric spaces leads to a stronger version of ultrahomogeneity of the infinite random graph R, the universal Urysohn metric space U, and other related objects. We propose a new proof of the result and show how it can be used to average out uniform and coarse embeddings of U (and its v...

‎in this paper‎, ‎first we develop the duality concept for $g$-bessel sequences‎ ‎and bessel fusion sequences in hilbert spaces‎. ‎we obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎we also expand every $g$-bessel ‎sequence to a frame by summing some elements‎. ‎we define the restricted isometry property for ‎$g$-frames and generalize some resu...

We examine some peculiarities of the subset of lattice preserving elements in a pseudo-Euclidean group, when the lattice under consideration contains a lightlike vector, or more generally, when the restriction of a pseudo-Euclidean metric to the real linear enveloppe of the lattice is not definite. For the case of a Lorentzian metric, it is shown in detail that the isometry group of the spaceti...

We give necessary and sufficient conditions for an integral polynomial without linear factors to be the characteristic of isometry some even, unimodular lattice given signature. This gives rise Hasse principle questions, which we answer in a more general setting. As application, prove signatures knots.

The purpose of this note is to study the bounded isometry conjecture proposed by Lalonde and Polterovich [11]. In particular, we show that the conjecture holds for the Kodaira-Thurston manifold with the standard symplectic form and for the 4-torus with all linear symplectic forms.