| We study frames for robust transmission over the Internet. In our previous work, we used quantized nite-dimensional frames to achieve resilience to packet losses; here, we allow the input to be a sequence in`2 (Z) and focus on a lter-bank implementation of the system. We present results in parallel, R N or C N versus`2 (Z), and show that uniform tight frames, as well as newly introduced stron...

Frames which are tight might be considered optimally conditioned in the sense of their numerical stability. This leads to the question of perfect preconditioning of frames, i.e., modification of a given frame to generate a tight frame. In this paper, we analyze prefect preconditioning of frames by a diagonal operator. We derive various characterizations of functional analytic and geometric type...

Spline wavelet tight frames of [20] have been used widely in frame based image analysis and restorations (see, e.g. survey articles [15, 22]). However, except for the tight frame property and the approximation order of the truncated series (see [13,20]), there are few other properties of this family of spline wavelet tight frames to be known. This paper is to present a few new properties of thi...

In this article we introduce the notion of J-Parseval fusion frames in a Krein space K and characterize 1-uniform J-Parseval fusion frames with ζ = √ 2. We provide some results regarding construction of new J-tight fusion frame from given J-tight fusion frames. We also characterize an uniformly J-definite subspace of a Krein space K in terms of J-fusion frame. Finally we generalize the fundamen...

One of the major driven forces in the area of applied and computational harmonic analysis over the last decade or longer is the development of redundant systems that have sparse approximations of various classes of functions. Such redundant systems include framelet (tight wavelet frame), ridgelet, curvelet, shearlet and so on. This paper mainly focuses on a special class of such redundant syste...