| 1. |
- Elvander, Filip, et al.
(författare)
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Interpolation and Extrapolation of Toeplitz Matrices via Optimal Mass Transport
- 2018
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Ingår i: IEEE Transactions on Signal Processing. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 1053-587X .- 1941-0476. ; 66:20, s. 5285-5298
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Tidskriftsartikel (refereegranskat)abstract
- In this work, we propose a novel method for quantifying distances between Toeplitz structured covariance matrices. By exploiting the spectral representation of Toeplitz matrices, the proposed distance measure is defined based on an optimal mass transport problem in the spectral domain. This may then be interpreted in the covariance domain, suggesting a natural way of interpolating and extrapolating Toeplitz matrices, such that the positive semi-definiteness and the Toeplitz structure of these matrices are preserved. The proposed distance measure is also shown to be contractive with respect to both additive and multiplicative noise, and thereby allows for a quantification of the decreased distance between signals when these are corrupted by noise. Finally, we illustrate how this approach can be used for several applications in signal processing. In particular, we consider interpolation and extrapolation of Toeplitz matrices, as well as clustering problems and tracking of slowly varying stochastic processes.
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| 2. |
- Elvander, Filip, et al.
(författare)
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Multi-dimensional grid-less estimation of saturated signals
- 2018
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Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684. ; 145, s. 37-47
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Tidskriftsartikel (refereegranskat)abstract
- This work proposes a multi-dimensional frequency and amplitude estimator tailored for noise corrupted signals that have been clipped. Formulated as a sparse reconstruction problem, the proposed algorithm estimates the signal parameters by solving an atomic norm minimization problem. The estimator also exploits the waveform information provided by the clipped samples, incorporated in the form of linear constraints that have been augmented by slack variables as to provide robustness to noise. Numerical examples indicate that the algorithm offers preferable performance as compared to methods not exploiting the saturated samples.
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| 3. |
- Elvander, Filip, et al.
(författare)
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Tracking and sensor fusion in direction of arrival estimation using optimal mass transport
- 2018
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Ingår i: 2018 26th European Signal Processing Conference (EUSIPCO). - : European Signal Processing Conference, EUSIPCO. - 9789082797015 ; , s. 1617-1621
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Konferensbidrag (refereegranskat)abstract
- In this work, we propose new methods for information fusion and tracking in direction of arrival (DOA) estimation by utilizing an optimal mass transport framework. Sensor array measurements in DOA estimation may not be consistent due to misalignments and calibration errors. By using optimal mass transport as a notion of distance for combining the information obtained from all the sensor arrays, we obtain an approach that can prevent aliasing and is robust to array misalignments. For the case of sequential tracking, the proposed method updates the DOA estimate using the new measurements and an optimal mass transport prior. In the case of sensor fusion, information from several, individual, sensor arrays is combined using a barycenter formulation of optimal mass transport.
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| 4. |
- Elvander, Filip, et al.
(författare)
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USING OPTIMAL MASS TRANSPORT FOR TRACKING AND INTERPOLATION OF TOEPLITZ COVARIANCE MATRICES
- 2018
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Ingår i: 2018 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP). - : IEEE. - 9781538646588 ; , s. 4469-4473
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Konferensbidrag (refereegranskat)abstract
- In this work, we propose a novel method for interpolation and extrapolation of Toeplitz structured covariance matrices. By considering a spectral representation of Toeplitz matrices, we use an optimal mass transport problem in the spectral domain in order to define a notion of distance between such matrices. The obtained optimal transport plan naturally induces a way of interpolating, as well as extrapolating, Toeplitz matrices. The constructed covariance matrix interpolants and extrapolants preserve the Toeplitz structure, as well as the positive semi-definiteness and the zeroth covariance of the original matrices. We demonstrate the proposed method's ability to model locally linear shifts of spectral power for slowly varying stochastic processes, illustrating the achievable performance using a simple tracking problem.
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| 5. |
- Juhlin, Maria, et al.
(författare)
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Fast Gridless Estimation of Damped Modes
- 2018
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Ingår i: 2018 International Symposium on Intelligent Signal Processing and Communication Systems.
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Konferensbidrag (refereegranskat)
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| 6. |
- Jälmby, Martin, et al.
(författare)
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Computationally Efficient Estimation of Multi-dimensional Damped Modes using Sparse Wideband Dictionaries
- 2018
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Ingår i: 26th European Signal Processing Conference, EUSIPCO 2018. - 9789082797015 ; , s. 1759-1763
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Konferensbidrag (refereegranskat)abstract
- Estimating the parameters of non-uniformly sampled multi-dimensional damped modes is computationally cumbersome, especially if the model order of the signal is not assumed to be known a priori. In this work, we examine the possibility of using the recently introduced wideband dictionary framework to formulate a computationally efficient estimator that iteratively refines the estimates of the candidate frequency and damping coefficients for each component. The proposed wideband dictionary allows for the use of a coarse initial grid without increasing the risk of not identifying closely spaced components, resulting in a substantial reduction in computational complexity. The performance of the proposed method is illustrated using both simulated and real spectroscopy data, clearly showing the improved performance as compared to previous techniques.
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| 7. |
- Swärd, Johan, et al.
(författare)
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Designing sampling schemes for multi-dimensional data
- 2018
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Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684. ; 150, s. 1-10
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Tidskriftsartikel (refereegranskat)abstract
- In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the sum of the Cramér–Rao lower bounds for the parameters of interest, given a desired number of sampling points. The proposed framework allows for selecting an arbitrary subset of the parameters detailing the model, as well as weighing the importance of the different parameters. Also presented is a scheme for incorporating any imprecise a priori knowledge of the locations of the parameters, as well as defining estimation performance bounds for the parameters of interest. Numerical examples illustrate the efficiency of the proposed scheme.
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