Related papers: Approximate oblique duality for fusion frames

In representations using frames, oblique duality appears in situations where the analysis and the synthesis has to be done in different subspaces. In some cases, we cannot obtain an explicit expression for the oblique duals and in others…

We introduce and develop the concept of oblique duality for fusion frames. This concept provides a mathematical framework to deal with problems in distributed signal processing where the signals, considered as elements in a Hilbert space…

In this paper we extend the notion of approximate dual to fusion frames and present some approaches to obtain dual and approximate alternate dual fusion frames. Also, we study the stability of dual and approximate alternate dual fusion…

A new notion of dual fusion frame has been recently introduced by the authors. In this article that notion is further motivated and it is shown that it is suitable to deal with questions posed in a finite-dimensional real or complex Hilbert…

Functions or distributions used to sample and to reconstruct signals often occur in different domains, like the Dirac delta and a band-limited bump function in classical sampling. Oblique dual frames generalize this phenomenon. In this…

Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for…

The purpose of this work is to examine the structure of optimal dual fusion frames and get more exibility in the use of dual fusion frames for erasures of subspaces. We deal with optimal dual fusion frames with respect to different…

We discuss the concepts of pseudo-dual frames and approximately dual frames, and illuminate their relationship to classical frames. Approximately dual frames are easier to construct than the classical dual frames, and might be tailored to…

The definition of dual fusion frame presents technical problems related to the domain of the synthesis operator. The notion commonly used is the analogous to the canonical dual frame. Here a new concept of dual is studied in…

Frames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as well as interesting for theory. Some applications additionally require distributed…

Fusion frames are valuable generalizations of discrete frames. Most concepts of fusion frames are shared by discrete frames. However, the dual setting is so complicated. In particular, unlike discrete frames, two fusion frames are not dual…

Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…

We show that any two frames in a separable Hilbert space that are dual to each other have the same excess. Some new relations for the analysis resp. synthesis operators of dual frames are also derived. We then prove that pseudo-dual frames…

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…

Operator-valued frames (or g-frames) are generalizations of frames and fusion frames and have been used in packets encoding, quantum computing, theory of coherent states and more. In this paper, we give a new formula for operator-valued…

The ability to efficiently and accurately construct an inverse frame operator is critical for establishing the utility of numerical frame approximations. Recently, the admissible frame method was developed to approximate inverse frame…

Hilbert space fusion frames are a natural extension of Hilbert space frames, extending the notion from a set of vectors in a Hilbert space to a set of subspaces of a Hilbert space with analogous notions of overcompleteness and boundedness.…

Approximately dual frames as a generalization of duality notion in Hilbert spaces have applications in Gabor systems, wavelets, coorbit theory and sensor modeling. In recent years, the computing of the associated deviations of the canonical…

In this manuscript, the concept of dual and approximate dual for continuous frames in Hilbert spaces will be introduced. Some of its properties will be studied. Also, the relations between two continuous Riesz bases in Hilbert spaces will…

This paper demonstrates that random, independently chosen equi-dimensional subspaces with a unitarily invariant distribution in a real Hilbert space provide nearly tight, nearly equiangular fusion frames. The angle between a pair of…