Abstract Phase retrieval in dynamical sampling is a novel research direction, where an unknown signal has to be recovered from the phaseless measurements with respect frame, i.e., sequence of vectors constructed by repeated action operator. The loss phase here turns well-posed into severe ill-posed inverse problem. In existing literature, involved operator usually completely known. this paper, ...

Given a discrete group and a unitary representation on a Hilbert space H, we prove that the notions of operator Bracket map and Gramian coincide on a dense set of H. As a consequence, combining this result with known frame theory, we can recover in a simple way all previous Bracket characterizations of Riesz and frame sequences generated by a single element under a unitary representation.

We prove fourteen equivalent conditions for a set of time-frequency shifts on a lattice Λ, {e2g(t − λ1) : (λ1, λ2) ∈ Λ} ⊆ L (R), to be a frame for L(R). Remarkably, several of these conditions can be formulated without an inequality. In particular, instead of checking the invertibility of the frame operator on L(R), it suffices to verify that it is one-to-one on a certain subspace of tempered d...

In this article, teleoperation over Internet is considered. A significant problem in teleoperations occurs if data is lost or late. This can lead to the fatal error in command decisions made by operator. Since operator must decide based on data on the client side of the link, modifications presented here are on the client side of the teleoperation system. Visual data was of particular concern. ...

Building models are conventionally reconstructed by measuring their vertices point-by-point in a digital photogrammetric workstation (DPW), which is time and labor consuming process. Although aerial photos implicitly provide 3D information of buildings, LiDAR systems directly provide high density and accurate point cloud coordinates. However, LiDAR data cannot accurately represent the building ...

We apply the theory of Weyl-Heisenberg frames (WHFs) to oversampled FIR and IIR DFT filter banks (FBs). We show that the polyphase matrices provide a matrix representation of the frame operator, and we find conditions on a DFT FB to provide a WHF expansion. We also show that paraunitary and biorthogonal DFT FBs correspond to tight and exact WHFs, respectively, and that the frame bounds can be o...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

In this paper we show that any shift-invariant Bessel sequence with an at most countable number of generators can be extended to a tight frame for its closed linear span by adding another shift-invariant system with at most the same number of generators. We show that in general this result is optimal, by providing examples where it is impossible to obtain a tight frame by adding a smaller numbe...

This paper presents a POCS-based algorithm for consistent reconstruction of a signal x 2 R from any subset of quantized coe cients y 2 R in an N K overcomplete frame expansion y = Fx, N = 2K. By choosing the frame operator F to be the concatenation of two K K invertible transforms, the projections may be computed in R using only the transforms and their inverses, rather than in the larger space...

This paper is concerned with adaptive numerical frame methods for elliptic operator equations. We show how specific non-canonical frame expansions on domains can be constructed. Moreover, we study the approximation order of best n-term frame approximation which serves as the benchmark for the performance of adaptive schemes. We also discuss numerical experiments for second order elliptic bounda...