Related papers: A Survey on Constructing Parseval Fusion Frames vi…
This article explores the problem of modifying the subspaces of a fusion frame in order to construct a Parseval fusion frame. In this respect, the notion of scalability is extended to the fusion frame setting. Then, scalable fusion Riesz…
In this paper we define "piecewise scalable frames". This new scaling process allows us to alter many frames to Parseval frames which is impossible by the previous standard scaling. We give necessary and sufficient conditions for a frame to…
Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the…
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…
A new notion in frame theory, so called weaving frames has been recently introduced to deal with some problems in signal processing and wireless sensor networks. Also, fusion frames are an important extension of frames, used in many areas…
A new notion in frame theory has been introduced recently that called woven frames. %From the perspective of others, Woven and weaving frames are powerful tools for pre-processing signals and distributed data processing. The purpose of…
Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Given a spectrum for a…
The recently introduced and characterized scalable frames can be considered as those frames which allow for perfect preconditioning in the sense that the frame vectors can be rescaled to yield a tight frame. In this paper we define…
A frame is scalable if each of its vectors can be rescaled in such a way that the resulting set becomes a Parseval frame. In this paper, we consider four different optimization problems for determining if a frame is scalable. We offer some…
In this paper, we introduce orthonoramal and Riesz bases for g-fusion frames and will show that the weights have basic roles. Next, we prove an effective theorem between frames and g-fusion frames by using an operator. Finally,…
Continuing the ideas from our previous paper, we construct Parseval frames of weighted exponential functions for self-affine measures.
Tight frames can be characterized as those frames which possess optimal numerical stability properties. In this paper, we consider the question of modifying a general frame to generate a tight frame by rescaling its frame vectors; a process…
In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly…
This article gives a procedure to convert a frame which is not a tight frame into a Parseval frame for the same space, with the requirement that each element in the resulting Parseval frame can be explicitly written as a linear combination…
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…
Fusion frames are widely studied for their applications in recovering signals from large data. These are proved to be very useful in many areas, such as, distributed processing, wireless sensor networks, packet encoding. Inspired by the…
We consider the problem of rescaling the lengths of a finite frame thereby transforming it into a tight one. Such frames are called scalable and have received a lot of attention in recent years. In this note we investigate the question in…
Computing the excess as a method of measuring the redundancy of frames was recently introduced to address certain issues in frame theory. In this paper, the concept of excess for fusion frames is studied. Then, several explicit methods are…
In this note we study frame-related properties of a sequence of functions multiplied by another function. In particular we study frame and Riesz basis properties. We apply these results to sets of irregular translates of a bandlimited…
Fusion frames are extensively studied due to their effectiveness in recovering signals from large-scale data. They are applicable in distributed processing, wireless sensor networks, and packet encoding systems due to their robustness and…