For a given class F of uniform frames of fixed redundancy we define a Grassmannian frame as one that minimizes the maximal correlation |〈fk, fl〉| among all frames {fk}k∈I ∈ F . We first analyze finite-dimensional Grassmannian frames. Using links to packings in Grassmannian spaces and antipodal spherical codes we derive bounds on the minimal achievable correlation for Grassmannian frames. These ...

A fruitful approach for solving signal deconvolution problems consists of resorting to a framebased convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have become popular optimization techniques to approximate iteratively the desired solution. Until now, in most of these methods, either Lipschitz differentiabili...

A semiempirical approach for calculating the bulk and surface stress is developed and presented in this work. It is based on the tight-binding method with Chadi’s total energy model. A strained system is treated as a perturbation of an unstrained system; the corresponding stress can be calculated by the resolvent Green function method. This approach is applied to an arsenic terminated Si(001)23...

An important tool for the construction of tight wavelet frames is the Unitary Extension Principle first formulated in the Fourierdomain by Ron and Shen. We show that the time-domain analogue of this principle provides a unified approach to the construction of tight frames based on many variations of multiresolution analyses, e.g., regular refinements of bounded L-shaped domains, refinements of ...

We study tight wavelet frame systems in Lp(R), and prove that such systems (under mild hypotheses) give atomic decompositions of L p(R) for 1 < p < . We also characterize Lp(R) and Sobolev space norms by the analysis coefficients for the frame. We consider Jackson inequalities for best mterm approximation with the systems in Lp(R) and prove that such inequalities exist. Moreover, it is proved t...

We prove that pointwise and global Hölder regularity can be characterized using the coefficients on Haar tight frame obtained by a finite union of shifted bases, despite fact elements composing are discontinuous.

This paper proves that every frame of windowed exponentials satisfies a Strong Homogeneous Approximation Property with respect to its canonical dual frame, and a Weak Homogeneous Approximation Property with respect to an arbitrary dual frame. As a consequence, a simple proof of the Nyquist density phenomenon satisfied by frames of windowed exponentials with one or finitely many generators is ob...

We introduce a new class of frames with strong symmetry properties called geometrically uniform frames (GU), that are defined over an abelian group of unitary matrices and are generated by a single generating vector. The notion of GU frames is then extended to compound GU (CGU) frames which are generated by an abelian group of unitary matrices using multiple generating vectors. The dual frame v...