| 1. |
- Andersson, Fredrik, et al.
(författare)
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A method for 3D direction of arrival estimation for general arrays using multiple frequencies
- 2016
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Ingår i: 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015. - 9781479919635 ; , s. 325-328
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Konferensbidrag (refereegranskat)abstract
- We develop a novel high-resolution method for the estimation of the direction of incidence of energy emitted by sources in 3D space from wideband measurements collected by a planar array of sensors. We make use of recent generalizations of Kronecker's theorem and formulate the direction of arrival estimation problem as an optimization problem in the space of sequences generating so called general domain Hankel matrices of fixed rank. The unequal sampling at different wavelengths is handled by using appropriate interpolation operators. The algorithm is operational for general array geometries (i.e., not restricted to, e.g., rectangular arrays) and for equidistantly as well as unequally spaced receivers. Numerical simulations for different sensor arrays and various signal-to-noise ratios are provided and demonstrate its excellent performance.
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| 2. |
- Andersson, Fredrik, et al.
(författare)
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A New Frequency Estimation Method for Equally and Unequally Spaced Data
- 2014
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Ingår i: IEEE Transactions on Signal Processing. - 1053-587X. ; 62:21, s. 5761-5774
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Tidskriftsartikel (refereegranskat)abstract
- Spectral estimation is an important classical problem that has received considerable attention in the signal processing literature. In this contribution, we propose a novel method for estimating the parameters of sums of complex exponentials embedded in additive noise from regularly or irregularly spaced samples. The method relies on Kronecker's theorem for Hankel operators, which enables us to formulate the nonlinear least squares problem associated with the spectral estimation problem in terms of a rank constraint on an appropriate Hankel matrix. This matrix is generated by sequences approximating the underlying sum of complex exponentials. Unequally spaced sampling is accounted for through a proper choice of interpolation matrices. The resulting optimization problem is then cast in a form that is suitable for using the alternating direction method of multipliers (ADMM). The method can easily include either a nuclear norm or a finite rank constraint for limiting the number of complex exponentials. The usage of a finite rank constraint makes, in contrast to the nuclear norm constraint, the method heuristic in the sense that the problem is non-convex and convergence to a global minimum can not be guaranteed. However, we provide a large set of numerical experiments that indicate that usage of the finite rank constraint nevertheless makes the method converge to minima close to the global minimum for reasonably high signal to noise ratios, hence essentially yielding maximum-likelihood parameter estimates. Moreover, the method does not seem to be particularly sensitive to initialization and performs substantially better than standard subspace-based methods.
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| 3. |
- Andersson, Fredrik, et al.
(författare)
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Frequency Estimation Based on Hankel Matrices and the Alternating Direction Method of Multipliers
- 2013
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Ingår i: 2013 Proceedings of the 21st European Signal Processing Conference (Eusipco).
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Konferensbidrag (refereegranskat)abstract
- We develop a parametric high-resolution method for the estimation of the frequency nodes of linear combinations of complex exponentials with exponential damping. We use Kronecker's theorem to formulate the associated nonlinear least squares problem as an optimization problem in the space of vectors generating Hankel matrices of fixed rank. Approximate solutions to this problem are obtained by using the alternating direction method of multipliers. Finally, we extract the frequency estimates from the con-eigenvectors of the solution Hankel matrix. The resulting algorithm is simple, easy to implement and can be applied to data with equally spaced samples with approximation weights, which for instance allows cases of missing data samples. By means of numerical simulations, we analyze and illustrate the excellent performance of the method, attaining the Cramer-Rao bound.
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| 4. |
- Andersson, Fredrik, et al.
(författare)
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Multi-scale discrete approximation of Fourier integral operators
- 2012
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Ingår i: Multiscale Modeling & Simulation. - : Society for Industrial & Applied Mathematics (SIAM). - 1540-3459 .- 1540-3467. ; 10:1, s. 111-135
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Tidskriftsartikel (refereegranskat)abstract
- Abstract in UndeterminedWe develop a discretization and computational procedures for approximation of the action of Fourier integral operators the canonical relations of which are graphs. Such operators appear, for instance, in the formulation of imaging and inverse scattering of seismic reflection data. Our discretization and algorithms are based on a multiscale low-rank expansion of the action of Fourier integral operators using the dyadic parabolic decomposition of phase space and on explicit constructions of low-rank separated representations using prolate spheroidal wave functions, which directly reflect the geometry of such operators. The discretization and computational procedures connect to the discrete almost symmetric wave packet transform. Numerical wave propagation and imaging examples illustrate our computational procedures.
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| 5. |
- Andersson, Fredrik, et al.
(författare)
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Multiscale Reverse-Time-Migration-Type Imaging Using the Dyadic Parabolic Decomposition of Phase Space
- 2015
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Ingår i: SIAM Journal of Imaging Sciences. - 1936-4954. ; 8:4, s. 2383-2411
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Tidskriftsartikel (refereegranskat)abstract
- We develop a representation of reverse-time migration (RTM) in terms of Fourier integral operators, the canonical relations of which are graphs. Through the dyadic parabolic decomposition of phase space, we obtain the solution of the wave equation with a boundary source and homogeneous initial conditions using wave packets. On this basis, we develop a numerical procedure for the reverse-time continuation from the boundary of scattering data and for RTM. The algorithms are derived from those we recently developed for the discrete approximate evaluation of the action of Fourier integral operators and inherit their conceptual and numerical properties.
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| 6. |
- Andersson, Fredrik, et al.
(författare)
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On a fixed-point algorithm for structured low-rank approximation and estimation of half-life parameters
- 2016
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Ingår i: 2016 24th European Signal Processing Conference, EUSIPCO. - 9780992862657 ; , s. 326-330
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Konferensbidrag (refereegranskat)abstract
- We study the problem of decomposing a measured signal as a sum of decaying exponentials. There is a direct connection to sums of these types and positive semi-definite (PSD) Hankel matrices, where the rank of these matrices equals the number of exponentials. We propose to solve the identification problem by forming an optimization problem with a misfit function combined with a rank penalty function that also ensures the PSD-constraint. This problem is non-convex, but we show that it is possible to compute the minimum of an explicit closely related convexified problem. Moreover, this minimum can be shown to often coincide with the minimum of the original non-convex problem, and we provide a simple criterion that enables to verify if this is the case.
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| 7. |
- Carlsson, Marcus, et al.
(författare)
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Unbiased Group-Sparsity Sensing Using Quadratic Envelopes
- 2019
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Ingår i: 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2019 - Proceedings. - 9781728155494 ; , s. 425-429
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Konferensbidrag (refereegranskat)abstract
- This paper investigates a new regularization of the group-sparsity estimation problem based on a quadratic envelope operator. The resulting estimator is shown to have a reduced bias when compared to the classical LASSO estimator and is characterized by a simple hyperparameter selection. Numerical results show that the quadratic envelope regularization yields estimates equal to an oracle solution with high probability. The robustness of the proposed hyperparameter selection rule is also analyzed.
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| 8. |
- Duchkov, Anton A., et al.
(författare)
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Sparse wave-packet representations and seismic imaging
- 2010
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Ingår i: SEG Technical Program Expanded Abstracts. - : Society of Exploration Geophysicists. - 1052-3812. ; 29:1, s. 3318-3322
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Konferensbidrag (refereegranskat)abstract
- In this paper we introduce a new algorithm for seismic imaging based on the flow out of Gaussian wave packets. We follow the standard strategy of decomposing data into wave packets and flowing them out along rays to approximate the downward wavefield extrapolation, and finally applying an imaging condition. We revisit each computational step to gain efficiency. Furthermore, we develop procedure for seismic data decomposition in order to obtain highly sparse representations with Gaussian wave packets. As a result we get fast algorithm heavily exploiting sparse data representation and analytic description of Gaussian wave packets. We tests our algorithm on synthetic example of migrating common-shot gather.
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| 9. |
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| 10. |
- Wendt, Herwig, et al.
(författare)
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Multi-scale structured imaging using wave packets and prolate spheroidal wave functions
- 2010
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Ingår i: SEG Technical Program Expanded Abstracts. - : Society of Exploration Geophysicists. - 1052-3812. ; 29:1, s. 3359-3363
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Konferensbidrag (refereegranskat)abstract
- Imaging and inverse scattering of seismic reflection data can be formulated in terms of a certain class of Fourier integral operators. We present an approximation and discretization of such operators following a multiscale approach, based on wave packets as the quanta for representing seismic data. One of the key ingredients in our approach is the coupling of dyadic parabolic decomposition and prolate spheroidal wave functions. As an example, we detail our method for parametrices of evolution equations, and obtain a onestep algorithm wave- equation for imaging and inverse scattering, time and depth extrapolation, velocity continuation, and extended imaging
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