The Experts below are selected from a list of 3009 Experts worldwide ranked by ideXlab platform
Jwoyuh Wu - One of the best experts on this subject based on the ideXlab platform.
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an improved rip based performance guarantee for sparse signal recovery via orthogonal matching pursuit
IEEE Transactions on Information Theory, 2014Co-Authors: Linghua Chang, Jwoyuh WuAbstract:A sufficient Condition reported very recently for perfect recovery of a K-sparse vector via orthogonal matching pursuit (OMP) in K iterations (when there is no noise) is that the restricted isometry constant (RIC) of the sensing matrix satisfies δ K+1 <; (1/√(K) + 1). In the noisy case, this RIC upper bound along with a requirement on the minimal signal entry magnitude is known to guarantee exact support identification. In this paper, we show that, in the presence of noise, a relaxed RIC upper bound δ K+1 <; (√(4K + 1) - 1/2K) together with a relaxed requirement on the minimal signal entry magnitude suffices to achieve perfect support identification using OMP. In the noiseless case, our result asserts that such a relaxed RIC upper bound can ensure exact support recovery in K iterations: this narrows the gap between the so far best known bound δ K+1 <; (1/√(K( + 1)) and the ultimate performance guarantee δ K+1 = (1/(K)). Our approach relies on a newly established near Orthogonality Condition, characterized via the achievable angles between two orthogonal sparse vectors upon compression, and, thus, better exploits the knowledge about the geometry of the compressed space. The proposed near Orthogonality Condition can be also exploited to derive less restricted sufficient Conditions for signal reconstruction in two other compressive sensing problems, namely, compressive domain interference cancellation and support identification via the subspace pursuit algorithm.
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an improved rip based performance guarantee for sparse signal recovery via orthogonal matching pursuit
International Symposium on Communications Control and Signal Processing, 2014Co-Authors: Linghua Chang, Jwoyuh WuAbstract:A sufficient Condition reported very recently for perfect recovery of a K-sparse vector via orthogonal matching pursuit in K iterations is that the restricted isometry constant of the sensing matrix satisfies δ K+1 <; 1/(√K + 1). By exploiting a “near Orthogonality” Condition specified in terms of the achievable angles between two orthogonal sparse vectors upon compression, this paper shows that the requirement on δ K+1 can be further relaxed to δ k+1 <; √4k+1 - 1\2K. This result thus narrows the gap between the so far best known bound and the ultimate performance guarantee δ K+1 <; 1/√K that is conjectured by Dai and Milenkovic in 2009.
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an improved rip based performance guarantee for sparse signal recovery via orthogonal matching pursuit
arXiv: Information Theory, 2014Co-Authors: Linghua Chang, Jwoyuh WuAbstract:A sufficient Condition reported very recently for perfect recovery of a K-sparse vector via orthogonal matching pursuit (OMP) in K iterations is that the restricted isometry constant of the sensing matrix satisfies delta_K+1<1/(sqrt(delta_K+1)+1). By exploiting an approximate Orthogonality Condition characterized via the achievable angles between two orthogonal sparse vectors upon compression, this paper shows that the upper bound on delta can be further relaxed to delta_K+1<(sqrt(1+4*delta_K+1)-1)/(2K).This result thus narrows the gap between the so far best known bound and the ultimate performance guarantee delta_K+1<1/(sqrt(delta_K+1)) that is conjectured by Dai and Milenkovic in 2009. The proposed approximate Orthogonality Condition is also exploited to derive less restricted sufficient Conditions for signal reconstruction in several compressive sensing problems, including signal recovery via OMP in a noisy environment, compressive domain interference cancellation, and support identification via the subspace pursuit algorithm.
Amedeo Primo - One of the best experts on this subject based on the ideXlab platform.
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adaptive integrand decomposition in parallel and orthogonal space
Journal of High Energy Physics, 2016Co-Authors: Pierpaolo Mastrolia, Tiziano Peraro, Amedeo PrimoAbstract:We present the integrand decomposition of multiloop scattering amplitudes in parallel and orthogonal space-time dimensions, d = d ∥ + d ⊥, being d ∥ the dimension of the parallel space spanned by the legs of the diagrams. When the number n of external legs is n ≤ 4,thecorrespondingrepresentationofmultiloopintegralsexposesasubsetofintegration variables which can be easily integrated away by means of Gegenbauer polynomials Orthogonality Condition. By decomposing the integration momenta along parallel and orthogonal directions, the polynomial division algorithm is drastically simplified. Moreover, the Orthogonality Conditions of Gegenbauer polynomials can be suitably applied to integrate the decomposed integrand, yielding the systematic annihilation of spurious terms. Consequently, multiloop amplitudes are expressed in terms of integrals corresponding to irreducible scalar products of loop momenta and external ones. We revisit the one-loop decomposition, which turns out to be controlled by the maximum-cut theorem in different dimensions, and we discuss the integrand reduction of two-loop planar and non-planar integrals up to n = 8 legs, for arbitrary external and internal kinematics. The proposed algorithm extends to all orders in perturbation theory.
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Adaptive Integrand Decomposition in parallel and orthogonal space
Journal of High Energy Physics, 2016Co-Authors: Pierpaolo Mastrolia, Tiziano Peraro, Amedeo PrimoAbstract:We present the integrand decomposition of multiloop scattering amplitudes in parallel and orthogonal space-time dimensions, $d=d_\parallel+d_\perp$, being $d_\parallel$ the dimension of the parallel space spanned by the legs of the diagrams. When the number $n$ of external legs is $n\le 4$, the corresponding representation of the multiloop integrals exposes a subset of integration variables which can be easily integrated away by means of Gegenbauer polynomials Orthogonality Condition. By decomposing the integration momenta along parallel and orthogonal directions, the polynomial division algorithm is drastically simplified. Moreover, the Orthogonality Conditions of Gegenbauer polynomials can be suitably applied to integrate the decomposed integrand, yielding the systematic annihilation of spurious terms. Consequently, multiloop amplitudes are expressed in terms of integrals corresponding to irreducible scalar products of loop momenta and external momenta. We revisit the one-loop decomposition, which turns out to be controlled by the maximum-cut theorem in different dimensions, and we discuss the integrand reduction of two-loop planar and non-planar integrals up to $n=8$ legs, for arbitrary external and internal kinematics. The proposed algorithm extends to all orders in perturbation theory.
Ichiro Hagiwara - One of the best experts on this subject based on the ideXlab platform.
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Development of a new mode-superposition technique for modal frequency response analysis of coupled acoustic-structural systems
Finite Elements in Analysis and Design, 1993Co-Authors: Ichiro HagiwaraAbstract:Abstract A new formulation is derived for obtaining the modal frequency response (MFR) of a coupled acoustic-structural system, by using an Orthogonality Condition of a coupled system which is presented in this journal. An improved technique is then proposed to compensate the effect of truncated modes, which are the lower and higher modes beyond the frequency domain of an MFR analysis. A coupled acoustic-box model is used in the analysis to confirm the applicability of the proposed method to actual coupled analysis problems. It is demonstrated that the use of this technique greatly improves convergence, and makes it possible to determine the frequency response with better accuracy than the mode-displacement method, the mode-acceleration method or Hansteen-Bell's method. Moreover, it does not increase the computational effort.
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improved mode superposition technique for modal frequency response analysis of coupled acoustic structural systems
AIAA Journal, 1991Co-Authors: Ichiro HagiwaraAbstract:A new formulation is derived by using an Orthogonality Condition of a coupled system. An improved compensation technique is then proposed for compensating for the effect of truncated modes, which are the lower and/or higher modes beyond the frequency domain of an MFR analysis
Linghua Chang - One of the best experts on this subject based on the ideXlab platform.
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an improved rip based performance guarantee for sparse signal recovery via orthogonal matching pursuit
IEEE Transactions on Information Theory, 2014Co-Authors: Linghua Chang, Jwoyuh WuAbstract:A sufficient Condition reported very recently for perfect recovery of a K-sparse vector via orthogonal matching pursuit (OMP) in K iterations (when there is no noise) is that the restricted isometry constant (RIC) of the sensing matrix satisfies δ K+1 <; (1/√(K) + 1). In the noisy case, this RIC upper bound along with a requirement on the minimal signal entry magnitude is known to guarantee exact support identification. In this paper, we show that, in the presence of noise, a relaxed RIC upper bound δ K+1 <; (√(4K + 1) - 1/2K) together with a relaxed requirement on the minimal signal entry magnitude suffices to achieve perfect support identification using OMP. In the noiseless case, our result asserts that such a relaxed RIC upper bound can ensure exact support recovery in K iterations: this narrows the gap between the so far best known bound δ K+1 <; (1/√(K( + 1)) and the ultimate performance guarantee δ K+1 = (1/(K)). Our approach relies on a newly established near Orthogonality Condition, characterized via the achievable angles between two orthogonal sparse vectors upon compression, and, thus, better exploits the knowledge about the geometry of the compressed space. The proposed near Orthogonality Condition can be also exploited to derive less restricted sufficient Conditions for signal reconstruction in two other compressive sensing problems, namely, compressive domain interference cancellation and support identification via the subspace pursuit algorithm.
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an improved rip based performance guarantee for sparse signal recovery via orthogonal matching pursuit
International Symposium on Communications Control and Signal Processing, 2014Co-Authors: Linghua Chang, Jwoyuh WuAbstract:A sufficient Condition reported very recently for perfect recovery of a K-sparse vector via orthogonal matching pursuit in K iterations is that the restricted isometry constant of the sensing matrix satisfies δ K+1 <; 1/(√K + 1). By exploiting a “near Orthogonality” Condition specified in terms of the achievable angles between two orthogonal sparse vectors upon compression, this paper shows that the requirement on δ K+1 can be further relaxed to δ k+1 <; √4k+1 - 1\2K. This result thus narrows the gap between the so far best known bound and the ultimate performance guarantee δ K+1 <; 1/√K that is conjectured by Dai and Milenkovic in 2009.
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an improved rip based performance guarantee for sparse signal recovery via orthogonal matching pursuit
arXiv: Information Theory, 2014Co-Authors: Linghua Chang, Jwoyuh WuAbstract:A sufficient Condition reported very recently for perfect recovery of a K-sparse vector via orthogonal matching pursuit (OMP) in K iterations is that the restricted isometry constant of the sensing matrix satisfies delta_K+1<1/(sqrt(delta_K+1)+1). By exploiting an approximate Orthogonality Condition characterized via the achievable angles between two orthogonal sparse vectors upon compression, this paper shows that the upper bound on delta can be further relaxed to delta_K+1<(sqrt(1+4*delta_K+1)-1)/(2K).This result thus narrows the gap between the so far best known bound and the ultimate performance guarantee delta_K+1<1/(sqrt(delta_K+1)) that is conjectured by Dai and Milenkovic in 2009. The proposed approximate Orthogonality Condition is also exploited to derive less restricted sufficient Conditions for signal reconstruction in several compressive sensing problems, including signal recovery via OMP in a noisy environment, compressive domain interference cancellation, and support identification via the subspace pursuit algorithm.
Pierpaolo Mastrolia - One of the best experts on this subject based on the ideXlab platform.
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adaptive integrand decomposition in parallel and orthogonal space
Journal of High Energy Physics, 2016Co-Authors: Pierpaolo Mastrolia, Tiziano Peraro, Amedeo PrimoAbstract:We present the integrand decomposition of multiloop scattering amplitudes in parallel and orthogonal space-time dimensions, d = d ∥ + d ⊥, being d ∥ the dimension of the parallel space spanned by the legs of the diagrams. When the number n of external legs is n ≤ 4,thecorrespondingrepresentationofmultiloopintegralsexposesasubsetofintegration variables which can be easily integrated away by means of Gegenbauer polynomials Orthogonality Condition. By decomposing the integration momenta along parallel and orthogonal directions, the polynomial division algorithm is drastically simplified. Moreover, the Orthogonality Conditions of Gegenbauer polynomials can be suitably applied to integrate the decomposed integrand, yielding the systematic annihilation of spurious terms. Consequently, multiloop amplitudes are expressed in terms of integrals corresponding to irreducible scalar products of loop momenta and external ones. We revisit the one-loop decomposition, which turns out to be controlled by the maximum-cut theorem in different dimensions, and we discuss the integrand reduction of two-loop planar and non-planar integrals up to n = 8 legs, for arbitrary external and internal kinematics. The proposed algorithm extends to all orders in perturbation theory.
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Adaptive Integrand Decomposition in parallel and orthogonal space
Journal of High Energy Physics, 2016Co-Authors: Pierpaolo Mastrolia, Tiziano Peraro, Amedeo PrimoAbstract:We present the integrand decomposition of multiloop scattering amplitudes in parallel and orthogonal space-time dimensions, $d=d_\parallel+d_\perp$, being $d_\parallel$ the dimension of the parallel space spanned by the legs of the diagrams. When the number $n$ of external legs is $n\le 4$, the corresponding representation of the multiloop integrals exposes a subset of integration variables which can be easily integrated away by means of Gegenbauer polynomials Orthogonality Condition. By decomposing the integration momenta along parallel and orthogonal directions, the polynomial division algorithm is drastically simplified. Moreover, the Orthogonality Conditions of Gegenbauer polynomials can be suitably applied to integrate the decomposed integrand, yielding the systematic annihilation of spurious terms. Consequently, multiloop amplitudes are expressed in terms of integrals corresponding to irreducible scalar products of loop momenta and external momenta. We revisit the one-loop decomposition, which turns out to be controlled by the maximum-cut theorem in different dimensions, and we discuss the integrand reduction of two-loop planar and non-planar integrals up to $n=8$ legs, for arbitrary external and internal kinematics. The proposed algorithm extends to all orders in perturbation theory.
