Several concepts for the localization of a frame are studied. The intrinsic localization of a frame is defined by the decay properties of its Gramian matrix. Our main result asserts that the canonical dual frame possesses the same intrinsic localization as the original frame. The proof relies heavily on Banach algebra techniques, in particular on recent spectral invariance properties for certai...

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...

This paper describes a uniform transform domain Video Codec where the motion estimation/compensation (ME) is performed in the transform domain. The estimation technique discussed here is a subpixel transform domain ME based on the Dual Tree Complex Wavelet Transform (DT CWT) and a maximum phase correlation technique. The DT CWT is a multiresolution fine-to-coarse bandpass filtered decomposition...

A dimension invariance property of finite frames of translates and Gabor frames is discussed. Under appropriate support conditions among the frame and dual frame generating functions, we show that a pair of dual frames evaluated in a given space remains a valid dual set if they are naturally embedded in the underlying space of almost arbitrarily enlarged dimension. Consequently, the evaluation ...

2-D mesh-based motion compensation preserves neighboring relations (through connectivity of the mesh) as well as allowing warping transformations between pairs of frames; thus, it eeectively eliminates blocking artifacts that are common in motion compensation by block matching. However , available 2-D mesh models, whether uniform or nonuniform, enforce connectivity everywhere within a frame, wh...

The central topic of this paper is the linear, redundant encoding of vectors using frames for the purpose of loss-insensitive data transmission. Our goal is to minimize the reconstruction error when frame coefficients are accidentally erased. Two-uniform frames are known to be optimal for handling up to two erasures, in the sense that they minimize the largest Euclidean error norm when up to tw...

this paper is an attempt at providing a systematic presentation of Quantified Modal Logics (with constant domains and rigid designators). We present a set of modular, uniform, normalizing, sound and complete labelled sequent calculi for all QMLs whose frame properties can be expressed as a finite set of first-order sentences with equality. We first present CQK, a calculus for the logic QK, and ...

An extended meniscus of a ferrofluid solution on a silicon surface is subjected to axisymmetric, non-uniform magnetic field resulting in significant forward movement of the thin liquid film. Image analyzing interferometry is used for accurate measurement of the film thickness profile, which in turn, is used to determine the instantaneous slope and the curvature of the moving film. The recorded ...

In this study, constant-ductility optimization algorithm under a family of earthquake ground motions is utilized to achieve uniform damage distribution over the height of steel moment resisting frames (SMRFs). SMRF structures with stiffness-degrading hysteric behavior are modeled as single-bay generic frame in which the plastic hinge is confined only at the beam ends and the bottom of the first...