Related papers: Fusion Frames and the Restricted Isometry Property

In this paper a new concept related to the frame theory is introduced; the notion of pair frame. By investigating some properties of such frames, it is shown that pair frames are a generalization of ordinary frames. Some classes of of them…

We propose two geometric versions of the bounded reduction property and find conditions for them to coincide. In particular, for the natural automatic structure on a hyperbolic group, the two notions are equivalent. We study endomorphisms…

We establish a packing dimension estimate on the exceptional sets of orthogonal projections of sets satisfying an almost dimension conservation law. In particular, the main result applies to homogeneous sets and to certain graph-directed…

We derive easily verifiable conditions which characterize when complex Seidel matrices containing cube roots of unity have exactly two eigenvalues. The existence of such matrices is equivalent to the existence of equiangular tight frames…

We consider existence and uniqueness of symmetric approximation of frames by normalized tight frames and of symmetric orthogonalization of bases by orthonormal bases in Hilbert spaces H . More precisely, we determine whether a given frame…

Naimark complements for Hilbert space Parseval frames are one of the most fundamental and useful results in the field of frame theory. We will show that actually all Hilbert space frames have Naimark complements which possess all the usual…

Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual…

We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space $\mathcal{H}$. We get sufficient conditions on an orthonormal basis of subspaces…

We make a trivial modification to the elegant analysis of Garg and Khandekar (\emph{Gradient Descent with Sparsification} ICML 2009) that replaces the standard Restricted Isometry Property (RIP), with another RIP-type property (which could…

We study some special almost complex structures on strictly pseudoconvex domains. They appear naturally as limits under a nonisotroping scaling procedure and play a role of model objects in the geometry of almost complex manifolds with…

In this paper, we investigate a novel form of approximate orthogonality that is based on integral orthogonality. Additionally, we establish the fundamental properties of this new approximate orthogonality and examine its capability to…

Compressed sensing is a new data acquisition paradigm enabling universal, simple, and reduced-cost acquisition, by exploiting a sparse signal model. Most notably, recovery of the signal by computationally efficient algorithms is guaranteed…

We propose a means of computing fitted frames on the boundary and in the interior of objects and using them to provide the basis for producing geometric features from them that are not only alignment-free but most importantly can be made to…

We prove that a PQ-symmetric homeomorphism between two complete metric spaces can be extended to a quasi-isometry between their hyperbolic approximations. This result is used to prove that two visual Gromov hyperbolic spaces are…

We demonstrate the existence of quasiconformal mappings on closed manifolds that cannot be decomposed as a composition of mappings with arbitrarily small conformal distortion.

Controlled frames which presented to improve the numerical output of iterative algorithms for inverting the frame operator, have been introduced by Balazs and et al. Also, these frames are used by Bogdanova and et al. for spherical…

Stellarator magnetic configurations need to be optimized in order to meet all the required properties of a fusion reactor. In this work, it is shown that a flat-mirror quasi-isodynamic configuration (i.e. a quasi-isodynamic configuration…

Frames provide redundant, stable representations of data which have important applications in signal processing. We introduce a connection between symplectic geometry and frame theory and show that many important classes of frames have…

Framelets (a.k.a. wavelet frames) are of interest in both theory and applications. Quite often, tight or dual framelets with high vanishing moments are constructed through the popular oblique extension principle (OEP). Though OEP can…

Orthogonal Matching Pursuit (OMP) has long been considered a powerful heuristic for attacking compressive sensing problems; however, its theoretical development is, unfortunately, somewhat lacking. This paper presents an improved Restricted…