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Article
Frame dimension functions and phase retrievability
The frame dimension function of a frame \({{\mathcal {F}}}= \{f_j\}_{j=1}^{n}\) F ...
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Article
The Uniqueness of Phase Retrieval of Analytic Signals from Very Few STFT Measurements
Analytic signals constitute a class of signals that are widely applied in time–frequency analysis such as extracting instantaneous frequency (IF) or phase derivative in the characterization of ultrashort laser...
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Article
Quantum injectivity of multi-window Gabor frames in finite dimensions
Finite Gabor frames for \({\mathbb {C}}^N\) C ...
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Article
Nonuniform sampling and approximation in Sobolev space from perturbation of the framelet system
The Sobolev space Hς (ℝd), where ς > d/2, is an important function space that has many applications in various areas of research. Attributed to the inertia of a measurement instrument, it is desirable in sampling...
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Article
Injective continuous frames and quantum detections
A quantum injective frame is a frame that can be used to distinguish density operators (states) from their frame measurements, and the frame quantum detection problem asks to characterize all such frames. This...
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Article
Structural Properties of Homomorphism Dilation Systems
Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras, the...
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Article
Frames and Finite-Rank Integral Representations of Positive Operator-Valued Measures
Discrete and continuous frames can be considered as positive operator-valued measures (POVMs) that have integral representations using rank-one operators. However, not every POVM has an integral representation...
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Article
Frame Phase-Retrievability and Exact Phase-Retrievable Frames
A phase-retrievable frame \(\{f_{i}\}_{i}^{N}\){fi}iN for an n-dimensional Hilbert space is exact if it fails to be phase-retrievable when removing any element from the frame sequence. Unlike exact frames, exact ...
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Article
Functional Matrix Multipliers for Parseval Gabor Multi-frame Generators
We consider the problem of characterizing the bounded linear operator multipliers on ...
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Article
Phase Retrievable Projective Representation Frames for Finite Abelian Groups
We consider the problem of characterizing projective representations that admit frame vectors with the maximal span property, a property that allows for an algebraic recovering for the phase-retrieval problem....
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Article
Stable recovery of signals from frame coefficients with erasures at unknown locations
In an earlier work, we proposed a frame-based kernel analysis approach to the problem of recovering erasures from unknown locations. The new approach led to the stability question on recovering a signal from n...
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Article
Dilation of Dual Frame Pairs in Hilbert C*-Modules
We investigate the geometric properties for Hilbert C*-modular frames. We show that any dual frame pair in a Hilbert C*-module is an orthogonal compression of a Riesz basis and its canonical dual for some larger ...
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Article
Orthogonal projection decomposition of matrices and construction of fusion frames
We investigate decompositions of positive matrices as weighted sums of orthogonal projections, and apply them to the construction of fusion frames when fusion frame operators are prescribed. Examples are provi...
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Article
Operator valued frames and structured quantum channels
Operator-valued frames are natural generalization of frames that have been used in many applied areas such as quantum computing, packets encoding and sensor networks. We focus on develo** the theory about op...
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Article
Frames and their associated \(\emph{H}_{{\kern-2pt}\emph{F}}^{\emph{p}}\) -subspaces
Given a frame F = {f j } for a separable Hilbert space H, we introduce the linear subspace ...
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Chapter
Unitary Systems and Bessel Generator Multipliers
A Bessel generator multiplier for a unitary system is a bounded linear operator that sends Bessel generator vectors to Bessel generator vectors. We characterize some special (but useful) Bessel generator multi...
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Article
Constructing super Gabor frames: the rational time-frequency lattice case
For a time-frequency lattice Λ = Aℤ d × Bℤ d , it is known that an orthonormal super Gabor frame of length L exists with respect to this lattic...
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Article
Preface
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Preface
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Article
On the Orthogonality of Frames and the Density and Connectivity of Wavelet Frames
We examine some recent results of Bownik on density and connectivity of the wavelet frames. We use orthogonality (strong disjointness) properties of frame and Bessel sequences, and also properties of Bessel mu...
