The Experts below are selected from a list of 243 Experts worldwide ranked by ideXlab platform
Haichao Wang - One of the best experts on this subject based on the ideXlab platform.
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phase retrieval of real valued signals in a shift Invariant Space
Applied and Computational Harmonic Analysis, 2018Co-Authors: Yang Chen, Cheng Cheng, Haichao WangAbstract:Abstract In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living in a shift-Invariant Space from their phaseless samples taken either on the whole line or on a discrete set with finite sampling density. We characterize all phase retrievable signals in a real-valued shift-Invariant Space using their nonseparability. For nonseparable signals generated by some function with support length L, we show that they can be well approximated, up to a sign, from their noisy phaseless samples taken on a discrete set with sampling density 2 L − 1 . In this paper, we also propose an algorithm with linear computational complexity to reconstruct nonseparable signals in a shift-Invariant Space from their phaseless samples corrupted by bounded noises.
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phase retrieval of real valued signals in a shift Invariant Space
arXiv: Information Theory, 2016Co-Authors: Yang Chen, Cheng Cheng, Haichao WangAbstract:Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living in a shift-Invariant Space from its phaseless samples taken either on the whole line or on a set with finite sampling rate. We find the equivalence between nonseparability of signals in a linear Space and its phase retrievability with phaseless samples taken on the whole line. For a spline signal of order $N$, we show that it can be well approximated, up to a sign, from its noisy phaseless samples taken on a set with sampling rate $2N-1$. We propose an algorithm to reconstruct nonseparable signals in a shift-Invariant Space generated by a compactly supported continuous function. The proposed algorithm is robust against bounded sampling noise and it could be implemented in a distributed manner.
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Principal shift-Invariant Spaces with extra invariance nearest to observed data
Collectanea Mathematica, 2011Co-Authors: Akram Aldroubi, Ilya A. Krishtal, Romain Tessera, Haichao WangAbstract:Given a set of functions \({\mathcal{F}=\{f_1, \dots, f_m\}\subset L^2(\mathbb{R}),}\) we construct a principal shift-Invariant Space V nearest to \({\mathcal{F}}\) in the sense that V minimizes the expression $$\sum_{i=1}^{m}\|f_i-P_{V}f_i\|^2,$$ among all the principal shift-Invariant Spaces with an orthonormal generator which are also translation Invariant, or among all the principal shift-Invariant Spaces with an orthonormal generator which are also \({\frac{1}{n}\mathbb{Z}}\) -Invariant for some fixed \({n\in\mathbb{N}}\) .
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Uncertainty Principles and Balian-Low type Theorems in Principal Shift-Invariant Spaces
Applied and Computational Harmonic Analysis, 2011Co-Authors: Akram Aldroubi, Haichao WangAbstract:Abstract In this paper, we consider the time-frequency localization of the generator of a principal shift-Invariant Space on the real line which has additional shift-invariance. We prove that if a principal shift-Invariant Space on the real line is translation-Invariant then any of its orthonormal (or Riesz) generators is non-integrable. However, for any n ⩾ 2 , there exist principal shift-Invariant Spaces on the real line that are also 1 n Z -Invariant with an integrable orthonormal (or a Riesz) generator ϕ, but ϕ satisfies ∫ R | ϕ ( x ) | 2 | x | 1 + ϵ d x = ∞ for any ϵ > 0 and its Fourier transform ϕ ˆ cannot decay as fast as ( 1 + | ξ | ) − r for any r > 1 2 . Examples are constructed to demonstrate that the above decay properties for the orthonormal generator in the time domain and in the frequency domain are optimal.
Ayman F Abouraddy - One of the best experts on this subject based on the ideXlab platform.
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classification of propagation Invariant Space time wave packets in free Space theory and experiments
arXiv: Optics, 2018Co-Authors: Murat Yessenov, Esat H Kondakci, Basanta Bhaduri, Ayman F AbouraddyAbstract:Introducing correlations between the spatial and temporal degrees of freedom of a pulsed optical beam (or wave packet) can profoundly alter its propagation in free Space. Indeed, appropriate spatio-temporal spectral correlations can render the wave packet propagation-Invariant: the spatial and temporal profiles remain unchanged along the propagation axis. The spatio-temporal spectral locus of any such wave packet lies at the intersection of the light-cone with tilted spectral hyperplanes. We investigate (2+1)D 'Space-time' propagation-Invariant light sheets, and identify 10 classes categorized according to the magnitude and sign of their group velocity and the nature of their spatial spectrum - whether the low spatial frequencies are physically allowed or forbidden according to their compatibility with causal excitation and propagation. We experimentally synthesize and characterize all 10 classes using an experimental strategy capable of synthesizing Space-time wave packets that incorporate arbitrary spatio-temporal spectral correlations.
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synthesizing broadband propagation Invariant Space time wave packets using transmissive phase plates
Optics Express, 2018Co-Authors: Esat H Kondakci, Murat Yessenov, Monjurul Meem, Danielle Reyes, Daniel J Thul, Shermineh Rostami Fairchild, Martin Richardson, Rajesh Menon, Ayman F AbouraddyAbstract:Space-time wave packets are a class of pulsed optical beams that are diffraction-free and dispersion-free in free Space by virtue of introducing a tight correlation between the spatial and temporal degrees of freedom of the field. Such wave packets have been recently synthesized in a novel configuration that makes use of a spatial light modulator to realize the required spatio-temporal correlations. This arrangement combines pulse-modulation and beam-shaping to assign one spatial frequency to each wavelength according to a prescribed correlation function. Relying on a spatial light modulator results in several limitations by virtue of their pixelation, small area, and low energy-handling capability. Here we demonstrate the synthesis of Space-time wave packets with one spatial dimension kept uniform – that is, light sheets – using transparent transmissive phase plates produced by a gray-scale lithography process. We confirm the diffraction-free behavior of wave packets having a bandwidth of 0.25 nm (filtered from a typical femtosecond Ti:sapphire laser) and 30 nm (a multi-terawatt femtosecond laser). This work paves the way for developing versatile high-energy light bullets for applications in nonlinear optics and laser machining.
Cesar Cadena - One of the best experts on this subject based on the ideXlab platform.
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empty cities image inpainting for a dynamic object Invariant Space
International Conference on Robotics and Automation, 2019Co-Authors: Berta Bescos, Jose L Neira, Roland Siegwart, Cesar CadenaAbstract:In this paper we present an end-to-end deep learning framework to turn images that show dynamic content, such as vehicles or pedestrians, into realistic static frames. This objective encounters two main challenges: detecting all the dynamic objects, and inpainting the static occluded background with plausible imagery. The former challenge is addressed by the use of a convolutional network that learns a multiclass semantic segmentation of the image. The second problem is approached with a conditional generative adversarial model that, taking as input the original dynamic image and its dynamic/static binary mask, is capable of generating the final static image. These generated images can be used for applications such as augmented reality or vision-based robot localization purposes. To validate our approach, we show both qualitative and quantitative comparisons against other state-of-the-art inpainting methods by removing the dynamic objects and hallucinating the static structure behind them. Furthermore, to demonstrate the potential of our results, we carry out pilot experiments that show the benefits of our proposal for visual place recognition 1.1All our code has been made available on https://github.com/bertabescos/EmptyCities.
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empty cities image inpainting for a dynamic object Invariant Space
arXiv: Computer Vision and Pattern Recognition, 2018Co-Authors: Berta Bescos, Jose L Neira, Roland Siegwart, Cesar CadenaAbstract:In this paper we present an end-to-end deep learning framework to turn images that show dynamic content, such as vehicles or pedestrians, into realistic static frames. This objective encounters two main challenges: detecting all the dynamic objects, and inpainting the static occluded background with plausible imagery. The second problem is approached with a conditional generative adversarial model that, taking as input the original dynamic image and its dynamic/static binary mask, is capable of generating the final static image. The former challenge is addressed by the use of a convolutional network that learns a multi-class semantic segmentation of the image. These generated images can be used for applications such as augmented reality or vision-based robot localization purposes. To validate our approach, we show both qualitative and quantitative comparisons against other state-of-the-art inpainting methods by removing the dynamic objects and hallucinating the static structure behind them. Furthermore, to demonstrate the potential of our results, we carry out pilot experiments that show the benefits of our proposal for visual place recognition.
Esat H Kondakci - One of the best experts on this subject based on the ideXlab platform.
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classification of propagation Invariant Space time wave packets in free Space theory and experiments
arXiv: Optics, 2018Co-Authors: Murat Yessenov, Esat H Kondakci, Basanta Bhaduri, Ayman F AbouraddyAbstract:Introducing correlations between the spatial and temporal degrees of freedom of a pulsed optical beam (or wave packet) can profoundly alter its propagation in free Space. Indeed, appropriate spatio-temporal spectral correlations can render the wave packet propagation-Invariant: the spatial and temporal profiles remain unchanged along the propagation axis. The spatio-temporal spectral locus of any such wave packet lies at the intersection of the light-cone with tilted spectral hyperplanes. We investigate (2+1)D 'Space-time' propagation-Invariant light sheets, and identify 10 classes categorized according to the magnitude and sign of their group velocity and the nature of their spatial spectrum - whether the low spatial frequencies are physically allowed or forbidden according to their compatibility with causal excitation and propagation. We experimentally synthesize and characterize all 10 classes using an experimental strategy capable of synthesizing Space-time wave packets that incorporate arbitrary spatio-temporal spectral correlations.
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synthesizing broadband propagation Invariant Space time wave packets using transmissive phase plates
Optics Express, 2018Co-Authors: Esat H Kondakci, Murat Yessenov, Monjurul Meem, Danielle Reyes, Daniel J Thul, Shermineh Rostami Fairchild, Martin Richardson, Rajesh Menon, Ayman F AbouraddyAbstract:Space-time wave packets are a class of pulsed optical beams that are diffraction-free and dispersion-free in free Space by virtue of introducing a tight correlation between the spatial and temporal degrees of freedom of the field. Such wave packets have been recently synthesized in a novel configuration that makes use of a spatial light modulator to realize the required spatio-temporal correlations. This arrangement combines pulse-modulation and beam-shaping to assign one spatial frequency to each wavelength according to a prescribed correlation function. Relying on a spatial light modulator results in several limitations by virtue of their pixelation, small area, and low energy-handling capability. Here we demonstrate the synthesis of Space-time wave packets with one spatial dimension kept uniform – that is, light sheets – using transparent transmissive phase plates produced by a gray-scale lithography process. We confirm the diffraction-free behavior of wave packets having a bandwidth of 0.25 nm (filtered from a typical femtosecond Ti:sapphire laser) and 30 nm (a multi-terawatt femtosecond laser). This work paves the way for developing versatile high-energy light bullets for applications in nonlinear optics and laser machining.
Carlos Cabrelli - One of the best experts on this subject based on the ideXlab platform.
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Frames by Iterations in Shift-Invariant Spaces
2019 13th International conference on Sampling Theory and Applications (SampTA), 2019Co-Authors: Alejandra Aguilera, Carlos Cabrelli, Diana Carbajal, Victoria PaternostroAbstract:In this note we solve the dynamical sampling problem for a class of shift-preserving (SP) operators, acting on a finitely generated shift-Invariant Space (FSIS). We find conditions on the operator and on a finite set of functions in the FSIS in order that the iterations of the operator on the functions produce a frame generator set. That is, the integer translations of the frame generator set is a frame of the FSIS. In order to obtain these results, we study the structure of SP operators and obtain a generalized finite dimensional spectral theorem.
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Shift-modulation Invariant Spaces on LCA groups
arXiv: Classical Analysis and ODEs, 2011Co-Authors: Carlos Cabrelli, Victoria PaternostroAbstract:A $(K,\Lambda)$ shift-modulation Invariant Space is a subSpace of $L^2(G)$, that is Invariant by translations along elements in $K$ and modulations by elements in $\Lambda$. Here $G$ is a locally compact abelian group, and $K$ and $\Lambda$ are closed subgroups of $G$ and the dual group $\hat G$, respectively. In this article we provide a characterization of shift-modulation Invariant Spaces in this general context when $K$ and $\Lambda$ are uniform lattices. This extends previous results known for $L^2(\R^d)$. We develop fiberization techniques and suitable range functions adapted to LCA groups needed to provide the desired characterization.
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Extra invariance of shift-Invariant Spaces on LCA groups
Journal of Mathematical Analysis and Applications, 2010Co-Authors: Magali Anastasio, Carlos Cabrelli, Victoria PaternostroAbstract:Abstract This article generalizes recent results in the extra invariance for shift-Invariant Spaces to the context of LCA groups. Let G be a locally compact abelian (LCA) group and K a closed subgroup of G. A closed subSpace of L 2 ( G ) is called K-Invariant if it is Invariant under translations by elements of K. Assume now that H is a countable uniform lattice in G and M is any closed subgroup of G containing H. In this article we study necessary and sufficient conditions for an H-Invariant Space to be M-Invariant. As a consequence of our results we prove that for each closed subgroup M of G containing the lattice H, there exists an H-Invariant Space S that is exactly M-Invariant. That is, S is not Invariant under any other subgroup M ′ containing H. We also obtain estimates on the support of the Fourier transform of the generators of the H-Invariant Space, related to its M-invariance.
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invariance of a shift Invariant Space
Journal of Fourier Analysis and Applications, 2010Co-Authors: Akram Aldroubi, Carlos Cabrelli, Christopher Heil, Keri Kornelson, Ursula MolterAbstract:A shift-Invariant Space is a Space of functions that is Invariant under integer translations. Such Spaces are often used as models for Spaces of signals and images in mathematical and engineering applications. This paper characterizes those shift-Invariant subSpaces S that are also Invariant under additional (non-integer) translations. For the case of finitely generated Spaces, these Spaces are characterized in terms of the generators of the Space. As a consequence, it is shown that principal shift-Invariant Spaces with a compactly supported generator cannot be Invariant under any non-integer translations.
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Extra Invariance of Shift-Invariant Spaces on LCA Groups
arXiv: Classical Analysis and ODEs, 2009Co-Authors: Magali Anastasio, Carlos Cabrelli, Victoria PaternostroAbstract:Let G be an LCA group and K a closed subgroup of G. A closed subSpace of L^2(G) is called K-Invariant if it is Invariant under translations by elements of K. Assume now that H is a countable uniform lattice in G and M is any closed subgroup of G containing H. In this article we study necessary and sufficient conditions for an H-Invariant Space to be M-Invariant. As a consequence of our results we prove that for each closed subgroup M of G containing the lattice H, there exists an H-Invariant Space S that is exactly M-Invariant. That is, S is not Invariant under any other subgroup M' containing M. We also obtain estimates on the support of the Fourier transform of the generators of the H-Invariant Space, related to its M-invariance.
