126 citations · 348 across the 94 of their papers we have counts for
96 papers · 1 filter
A Survey of Fusion Frames in Hilbert Spaces
Lukas Köhldorfer, Peter Balazs, Pete Casazza +4
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 pro…
Classifying weak phase retrieval
P. G. Casazza, F. Akrami
We will give several surprising equivalences and consequences of weak phase retrieval. These results give a complete understanding of the difference between weak phase retrieval an…
Remarks on scalable frames
Peter G. Casazza, Laura De Carli, Tin T. Tran
This paper investigates scalable frame in . We define the reduced diagram matrix of a frame and use it to classify scalability of the frame under some conditions. We…
New characterizations of the unit vector basis of or
Peter G. Casazza, Stephen J. Dilworth, Denka Kutzarova +1
Motivated by Altshuler's famous characterization of the unit vector basis of or among symmetric bases, we obtain similar characterizations among democratic bases and…
Piecewise scalable frames
Peter G. Casazza, Laura De Carli, Tin T. Tran
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…
The core of a Grassmannian frame
Peter G. Casazza, Ian Campbell, Tin T. Tran
Let be a set of unit vectors in $\RR^n$. The coherence of is $\coh(X):=\max_{i\not=j}|\langle x_i, x_j\rangle|$. A vector is said to be isolable if…
Bases equivalent to the unit vector basis of or
P. G. Casazza
We will show that an unconditional basis in a Banach space is equivalent to the unit vector basis of or for if and only if all finitely supported b…
On uniqueness and plentitude of subsymmetric sequences
Peter G. Casazza, Stephen J. Dilworth, Denka Kutzarova +1
We explore the diversity of subsymmetric basic sequences in spaces with a subsymmetric basis. We prove that the subsymmetrization of Tsirelson's original Banach space pro…
A note on (weak) phase and norm retrievable Real Hilbert space frames and projections
P. G. Casazza, F. Akrami, A. Rahimi +2
\begin{abstract} In this manuscript, we answer a list of longstanding open problems on weak phase retrieval including: (1) A complete classification of the vectors $\{x_i\}_{i=1}^2…
A note on phase (norm) retrievable Real Hilbert space (fusion) frames
F. Akrami, P. G. Casazza, M. A. Hasankhani Fard +1
In this manuscript, we present several new results in finite and countable dimensional real Hilbert space phase retrieval and norm retrieval by vectors and projections. We make a d…
Phase retrieval by projections in R^n requires 2n-2 projections (This paper has a gap)
Peter G. Casazza, Dorsa Ghoreishi
We will answer the most significant open problem in real phase retrieval by projections by showing it requires at least projections to do phase retrieval in $\RR^n$.
An elementary proof of a fundamental result in phase retrieval
Peter G. Casazza, Janet C. Tremain
Edidin [3] proved a fundamental result in phase retrieval: Theorem: A family of orthogonal projections does phase retrieval in if and only if for e…
Controlled scaling of Hilbert space frames for R^2
Peter Casazza, Shang Xu
A Hilbert space frame on is {\it scalable} if we can scale the vectors to make them a tight frame. There are known classifications of scalable frames. There are two basic que…
A notion of optimal packings of subspaces with mixed-rank and solutions
Peter G. Casazza, John I. Haas, Joshua Stueck +1
We resolve a longstanding open problem by reformulating the Grassmannian fusion frames to the case of mixed dimensions and show that this satisfies the proper properties for the pr…
Optimal Parseval frames: Total coherence and total volume
Jameson Cahill, Peter G. Casazza
We introduce three quantities called total coherence, total volume, and nuclear energy, and we show that equiangular Parseval frames maximize all three of these quantities over the…
Regular two distance sets
Peter G. Casazza, Tin T. Tran, Janet C. Tremain
This paper makes a deep study of regular two-distance sets. A set of unit vectors in Euclidean space $\RR^n$ is said to be regular two-distance set if the inner product of any…
Constructions and properties of optimally spread subspace packings via symmetric and affine block designs and mutually unbiased bases
Peter G. Casazza, John I. Haas, Joshua Stueck +1
We continue the study of optimal chordal packings, with emphasis on packing subspaces of dimension greater than one. Following a principle outlined in a previous work, where the au…
Phase Retrieval in $\ell_2(\RR)$
Sara Botelho-Andrade, Peter G. Casazza, Desai Cheng +2
We will review the major results in finite dimensional real phase retrieval for vectors and projections. We then (1)prove that many of these theorems hold in infinite dimensions, (…
The Solution to the Frame Quantum Detection Problem
Sara Bothelho-Andrade, Peter G. Casazza, Desai Cheng +1
We will give a complete solution to the frame quantum detection problem. We will solve both cases of the problem: the quantum injectivity problem and quantum state estimation probl…
The exact constant for the norm inequality
Sara Botelho-Andrade, Peter G. Casazza, Desai Cheng +1
A fundamental inequality for Hilbert spaces is the -norm inequality which gives that for any , But this is a strict inequali…
Phase retrieval by hyperplanes
Sara Botelho-Andrade, Peter G. Casazza, Desai Cheng +4
We show that a scalable frame does phase retrieval if and only if the hyperplanes of its orthogonal complements do phase retrieval. We then show this result fails in general by giv…
Associating vectors in $\CC^n$ with rank 2 projections in $\RR^{2n}$: with applications
Peter G. Casazza, Desai Cheng
We will see that vectors in $\CC^n$ have natural analogs as rank 2 projections in $\RR^{2n}$ and that this association transfers many vector properties into properties of rank two…
Constructions of biangular tight frames and their relationships with equiangular tight frames
John I. Haas, Jameson Cahill, Janet Tremain +1
We study several interesting examples of Biangular Tight Frames (BTFs) - basis-like sets of unit vectors admitting exactly two distinct frame angles (ie, pairwise absolute inner pr…
On the structures of Grassmannian frames
John I. Haas, Peter G. Casazza
A common criterion in the design of finite Hilbert space frames is minimal coherence, as this leads to error reduction in various signal processing applications. Frames that achiev…