To date, frames have established themselves as a standard notion in applied mathematics,
computer science, and engineering as a means to derive redundant, yet stable …

Tight fusion frames are an emerging concept of frame theory with applications in distributed
processing and communications. However, very little has been determined about the …

Finite unit norm tight frames provide Parseval-like decompositions of vectors in terms of
redundant components of equal weight. They are known to be robust against additive noise …

Fusion frame theory is an emerging mathematical theory that provides a natural framework
for performing hierarchical data processing. A fusion frame can be regarded as a frame-like …

Fusion frames enable signal decompositions into weighted linear subspace components.
For positive integers p, we introduce p-fusion frames, a sharpening of the notion of fusion …

We introduce probabilistic frames to study finite frames whose elements are chosen at
random. While finite tight frames generalize orthonormal bases by allowing redundancy …

In this paper we study the fusion frame potential that is a generalization of the Benedetto-
Fickus (vectorial) frame potential to the finite-dimensional fusion frame setting. We study the …

Naimark complements for Hilbert space Parseval frames are one of the most fundamental
and useful results in the field of frame theory. We will show actually all Hilbert space frames …

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 …

Given a finite sequence of vectors 𝓕 0 \mathcalF_0 in ℂ d we describe the spectral and
geometrical structure of optimal frame completions of 𝓕 0 \mathcalF_0 obtained by …