Controlled K−g−Fusion Frames in Hilbert C∗−Modules

Controlled frames have been the subject of interest because of its ability to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we introduce the concepts of controlled g−fusion frame and controlled K−g−fusion frame in Hilbert C∗−modules and we give some properties. Also, we study the perturbation problem of controlled K−g−fusion frame. Moreover, an illustrative example is presented to support the obtained results.

K-g-fusion frames in Hilbert C∗-modules

In this paper, we introduce the concepts of g-fusion frame and K-g-fusion frame in Hilbert C∗-modules and we give some properties. Also, we study the stability problem of g-fusion frame. The presented results extend, generalize and improve many existing results in the literature.

Controlled g-fusion frame in Hilbert space

Fusion frame is a generalization of frame, which can analyze signals by projecting them onto multidimensional subspaces. Controlled fusion frame as generalization of fusion frame, it can improve the numerical efficiency of iterative algorithms for inverting the fusion frame operators. In this paper, we first introduce the notion of controlled g-fusion frame, discuss several properties of controlled g-fusion Bessel sequence. Then, we present some sufficient conditions and some characterizations of controlled g-fusion frames. Finally, we study the sum of controlled g-fusion frames.

Perturbations on K-fusion frames

Fusion frames are widely studied for their applications in recovering signals from large data. These are proved to be very useful in many areas, for example, wireless sensor networks. In this paper, we discuss a generalization of fusion frames, K-fusion frames. K-fusion frames provide decompositions of a Hilbert space into atomic subspaces with respect to a bounded linear operator. This article studies various kinds of properties of K-fusion frames. Several perturbation results on K-fusion frames are formulated and analyzed.

Controlled K-Fusion Frame for Hilbert Spaces

K-fusion frames are a generalization of fusion frames in frame theory. In this paper, we extend the concept of controlled fusion frames to controlled K-fusion frames, and we develop some results on the controlled K-fusion frames for Hilbert spaces, which generalize some well known results of controlled fusion frame case. Also we discuss some characterizations of controlled Bessel K-fusion sequences and of controlled K-fusion frames. Further, we analyze stability conditions of controlled K-fusion frames under perturbation.

G-frame representations with bounded operators

Dynamical sampling, as introduced by Aldroubi et al., deals with frame properties of sequences of the form [Formula: see text], where [Formula: see text] belongs to Hilbert space [Formula: see text] and [Formula: see text] belongs to certain classes of bounded operators. Christensen et al. studied frames for [Formula: see text] with index set [Formula: see text] (or [Formula: see text]), that has representations in the form [Formula: see text] (or [Formula: see text]). As frames of subspaces, fusion frames and generalized translation invariant systems are the special cases of [Formula: see text]-frames, the purpose of this paper is to study and get sufficient conditions for [Formula: see text]-frames [Formula: see text] (or [Formula: see text] having the form [Formula: see text] [Formula: see text] (or [Formula: see text] [Formula: see text]). Also, we get the relation between representations of dual [Formula: see text]-frames with index set [Formula: see text]. Finally, we study stability of [Formula: see text]-frame representations under some perturbations.

High-order low-bit Sigma-Delta quantization for fusion frames

We construct high-order low-bit Sigma-Delta [Formula: see text] quantizers for the vector-valued setting of fusion frames. We prove that these [Formula: see text] quantizers can be stably implemented to quantize fusion frame measurements on subspaces [Formula: see text] using [Formula: see text] bits per measurement. Signal reconstruction is performed using a version of Sobolev duals for fusion frames, and numerical experiments are given to validate the overall performance.