| 1. |
- Carlström, Göran, et al.
(författare)
-
Rapid NMR Relaxation Rate Measurements Using Optimal Non-Uniform Sampling of Multi-Dimensional Accordion Data Analyzed by a Sparse Reconstruction Method
- 2019
-
Ingår i: The Journal of Physical Chemistry Part A: Molecules, Spectroscopy, Kinetics, Environment and General Theory. - : American Chemical Society (ACS). - 1089-5639. ; 123:27, s. 5718-5723
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Tidskriftsartikel (refereegranskat)abstract
- Nonuniform sampling (NUS) of multidimensional NMR data offers significant time savings while improving spectral resolution or increasing sensitivity per unit time. However, NUS has not been widely used for quantitative analysis because of the nonlinearity of most methods used to model NUS data, which leads to problems in estimating signal intensities, relaxation rate constants, and their error bounds. Here, we present an approach that avoids these limitations by combining accordion spectroscopy and NUS in the indirect dimensions of multidimensional spectra and then applying sparse exponential mode analysis, which is well suited for analyzing accordion-type relaxation data in a NUS context. By evaluating the Cramér-Rao lower bound of the variances of the estimated relaxation rate constants, we achieve a robust benchmark for the underlying reconstruction model. Furthermore, we design NUS schemes optimized with respect to the information theoretical lower bound of the error in the parameters of interest, given a specified number of sampling points. The accordion-NUS method compares favorably with conventional relaxation experiments in that it produces identical results, within error, while shortening the length of the experiment by an order of magnitude. Thus, our approach enables rapid acquisition of NMR relaxation data for optimized use of spectrometer time or accurate measurements on samples of limited lifetime.
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| 2. |
- Elvander, Filip, et al.
(författare)
-
An Adaptive Penalty Multi-Pitch Estimator with Self-Regularization
- 2016
-
Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684. ; 127, s. 56-70
-
Tidskriftsartikel (refereegranskat)abstract
- This work treats multi-pitch estimation, and in particular the common misclassification issue wherein the pitch at half the true fundamental frequency, the sub-octave, is chosen instead of the true pitch. Extending on current group LASSO-based methods for pitch estimation, this work introduces an adaptive total variation penalty, which enforces both group- and block sparsity, as well as deals with errors due to sub-octaves. Also presented is a scheme for signal adaptive dictionary construction and automatic selection of the regularization parameters. Used together with this scheme, the proposed method is shown to yield accurate pitch estimates when evaluated on synthetic speech data. The method is shown to perform as good as, or better than, current state-of-the-art sparse methods while requiring fewer tuning parameters than these, as well as several con- ventional pitch estimation methods, even when these are given oracle model orders. When evaluated on a set of ten musical pieces, the method shows promising results for separating multi-pitch signals.
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| 3. |
- Elvander, Filip, et al.
(författare)
-
Convex Clustering for Multistatic Active Sensing via Optimal Mass Transport
- 2021
-
Ingår i: 2021 29th European Signal Processing Conference (EUSIPCO). - : European Signal Processing Conference, EUSIPCO. ; , s. 1730-1734
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Konferensbidrag (refereegranskat)abstract
- In multistatic active sensing, such as active sonar, exploiting the spatial diversity provided by the use of several transmitting and receiving units can lead to increased resolution and target localization performance. For multi-target scenarios, the success of the task depends on correctly identifying the subsets of measurements associated with each target, a problem of combinatorial nature. In this paper, we propose to address this problem using a convex relaxation. In particular, we propose a method inspired by the concept of optimal mass transport capable of jointly performing the measurement clustering and target localization. We show that this method may be interpreted as maximum likelihood estimation on a grid, allowing for local post-processing achieving statistical efficiency. The behavior of the proposed method is illustrated using simulated 2D examples.
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| 4. |
- Elvander, Filip, et al.
(författare)
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Defining Fundamental Frequency for Almost Harmonic Signals
- 2020
-
Ingår i: IEEE Transactions on Signal Processing. - 1053-587X. ; , s. 6453-6466
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Tidskriftsartikel (refereegranskat)abstract
- In this work, we consider the modeling of signals that are almost, but not quite, harmonic, i.e., composed of sinusoids whose frequencies are close to being integer multiples of a common frequency. Typically, in applications, such signals are treated as perfectly harmonic, allowing for the estimation of their fundamental frequency, despite the signals not actually being periodic. Herein, we provide three different definitions of a concept of fundamental frequency for such inharmonic signals and study the implications of the different choices for modeling and estimation. We show that one of the definitions corresponds to a misspecified modeling scenario, and provides a theoretical benchmark for analyzing the behavior of estimators derived under a perfectly harmonic assumption. The second definition stems from optimal mass transport theory and yields a robust and easily interpretable concept of fundamental frequency based on the signals‘ spectral properties. The third definition interprets the inharmonic signal as an observation of a randomly perturbed harmonic signal. This allows for computing a hybrid information theoretical bound on estimation performance, as well as for finding an estimator attaining the bound. The theoretical findings are illustrated using numerical examples.
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| 5. |
- Elvander, Filip, et al.
(författare)
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Grid-less estimation of saturated signals
- 2017
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Ingår i: 2017 51st Asilomar Conference on Signals, Systems, and Computers. - 9781538618233 ; , s. 372-376
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Konferensbidrag (refereegranskat)abstract
- This work proposes a 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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| 6. |
- Elvander, Filip, et al.
(författare)
-
Interpolation and Extrapolation of Toeplitz Matrices via Optimal Mass Transport
- 2018
-
Ingår i: IEEE Transactions on Signal Processing. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 1053-587X .- 1941-0476. ; 66:20, s. 5285-5298
-
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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| 7. |
- Elvander, Filip, et al.
(författare)
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Mismatched Estimation of Polynomially Damped Signals
- 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. 246-250
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Konferensbidrag (refereegranskat)abstract
- In this work, we consider the problem of estimating the parameters of polynomially damped sinusoidal signals, commonly encountered in, for instance, spectroscopy. Generally, finding the parameter values of such signals constitutes a high-dimensional problem, often further complicated by not knowing the number of signal components or their specific signal structures. In order to alleviate the computational burden, we herein propose a mismatched estimation procedure using simplified, approximate signal models. Despite the approximation, we show that such a procedure is expected to yield predictable results, allowing for statistically and computationally efficient estimates of the signal parameters.
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| 8. |
- Elvander, Filip
(författare)
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Modeling and Sampling of Spectrally Structured Signals
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of five papers concerned with the modeling of stochastic signals, as well as deterministic signals in stochastic noise, exhibiting different kinds of structure. This structure is manifested as the existence of finite-dimensional parameterizations, and/or in the geometry of the signals' spectral representations. The two first papers of the thesis, Papers A and B, consider the modeling of differences, or distances, between stochastic processes based on their second-order statistics, i.e., covariances. By relating the covariance structure of a stochastic process to spectral representations, it is proposed to quantify the dissimilarity between two processes in terms of the cost associated with morphing one spectral representation to the other, with the cost of morphing being defined in terms of the solutions to optimal mass transport problems. The proposed framework allows for modeling smooth changes in the frequency characteristics of stochastic processes, which is shown to yield interpretable and physically sensible predictions when used in applications of temporal and spatial spectral estimation. Also presented are efficient computational tools, allowing for the framework to be used in high-dimensional problems.Paper C considers the modeling of so-called inharmonic signals, i.e., signals that are almost, but not quite, harmonic. Such signals appear in many fields of signal processing, not least in audio. Inharmonicity may be interpreted as a deviation from a parametric structure, as well as from a particular spectral structure. Based on these views, as well as on a third, stochastic interpretation, Paper C proposes three different definitions of the concept of fundamental frequency for inharmonic signals, and studies the estimation theoretical implications of utilizing either of these definitions. Paper D then considers deliberate deviations from a parametric signal structure arising in spectroscopy applications. With the motivation of decreasing the computational complexity of parameter estimation, the paper studies the implications of estimating the parameters of the signal in a sequential fashion, starting out with a simplified model that is then refined step by step.Lastly, Paper E studies how parametric descriptions of signals can be leveraged as to design optimal, in an estimation theoretical sense, schemes for sampling or collecting measurements from the signal. By means of a convex program, samples are selected as to minimize bounds on estimator variance, allowing for efficiently measuring parametric signals, even when the parametrization is only partially known.
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| 9. |
- Elvander, Filip, et al.
(författare)
-
Multi-dimensional grid-less estimation of saturated signals
- 2018
-
Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684. ; 145, s. 37-47
-
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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| 10. |
- Elvander, Filip, et al.
(författare)
-
Multi-marginal optimal transport using partial information with applications in robust localization and sensor fusion
- 2020
-
Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684 .- 1872-7557. ; 171
-
Tidskriftsartikel (refereegranskat)abstract
- During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, a common setup in many inverse problems in, e.g., remote sensing and imaging. By considering an entropy regularized approximation of the original transport problem, we propose an algorithm corresponding to a block-coordinate ascent of the dual problem, where Newton’s algorithm is used to solve the sub-problems. In order to make this computationally tractable for large-scale settings, we utilize the tensor structure that arises in practical problems, allowing for computing projections of the multi-marginal transport plan using only matrix-vector operations of relatively small matrices. As illustrating examples, we apply the resulting method to tracking and barycenter problems in spatial spectral estimation. In particular, we show that the optimal mass transport framework allows for fusing information from different time steps, as well as from different sensor arrays, also when the sensor arrays are not jointly calibrated. Furthermore, we show that by incorporating knowledge of underlying dynamics in tracking scenarios, one may arrive at accurate spectral estimates, as well as faithful reconstructions of spectra corresponding to unobserved time points.
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| 11. |
- Elvander, Filip, et al.
(författare)
-
NON-COHERENT SENSOR FUSION VIA ENTROPY REGULARIZED OPTIMAL MASS TRANSPORT
- 2019
-
Ingår i: 2019 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP). - : IEEE. - 9781479981311 ; , s. 4415-4419
-
Konferensbidrag (refereegranskat)abstract
- This work presents a method for information fusion in source localization applications. The method utilizes the concept of optimal mass transport in order to construct estimates of the spatial spectrum using a convex barycenter formulation. We introduce an entropy regularization term to the convex objective, which allows for low-complexity iterations of the solution algorithm and thus makes the proposed method applicable also to higher-dimensional problems. We illustrate the proposed method's inherent robustness to misalignment and miscalibration of the sensor arrays using numerical examples of localization in two dimensions.
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| 12. |
- Elvander, Filip, et al.
(författare)
-
Offline Noise Reduction Using Optimal Mass Transport Induced Covariance Interpolation
- 2019
-
Ingår i: 27th European Signal Processing Conference, EUSIPCO 2019. - 9781538673003 - 9789082797039
-
Konferensbidrag (refereegranskat)abstract
- In this work, we propose to utilize a recently developed covariance matrix interpolation technique in order to improve noise reduction in multi-microphone setups in the presence of a moving, localized noise source. Based on the concept of optimal mass transport, the proposed method induces matrix interpolants implying smooth spatial displacement of the noise source, allowing for physically reasonable reconstructions of the noise source trajectory. As this trajectory is constructed as to connect two observed, or estimated, covariance matrices, the proposed method is suggested for offline applications. The performance of the proposed method is demonstrated using simulations of a speech enhancement scenario.
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| 13. |
- Elvander, Filip, et al.
(författare)
-
On Harmonic Approximations of Inharmonic Signals
- 2020
-
Ingår i: 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings. - 1520-6149. - 9781509066315 ; 2020-May, s. 5360-5364
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Konferensbidrag (refereegranskat)abstract
- In this work, we present the misspecified Gaussian Cramér-Rao lower bound for the parameters of a harmonic signal, or pitch, when signal measurements are collected from an almost, but not quite, harmonic model. For the asymptotic case of large sample sizes, we present a closed-form expression for the bound corresponding to the pseduo-true fundamental frequency. Using simulation studies, it is shown that the bound is sharp and is attained by maximum likelihood estimators derived under the misspecified harmonic assumption. It is shown that misspecified harmonic models achieve a lower mean squared error than correctly specified unstructured models for moderately inharmonic signals. Examining voices from a speech database, we conclude that human speech belongs to this class of signals, verifying that the use of a harmonic model for voiced speech is preferable.
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| 14. |
- Elvander, Filip, et al.
(författare)
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Online Estimation of Multiple Harmonic Signals
- 2017
-
Ingår i: IEEE/ACM Transactions on Audio, Speech, and Language Processing. - 2329-9290. ; 25:2, s. 273-284
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, we propose a time-recursive multipitch estimation algorithm using a sparse reconstruction framework, assuming that only a few pitches from a large set of candidates are active at each time instant. The proposed algorithm does not require any training data, and instead utilizes a sparse recursive least-squares formulation augmented by an adaptive penalty term specifically designed to enforce a pitch structure on the solution. The amplitudes of the active pitches are also recursively updated, allowing for a smooth and more accurate representation. When evaluated on a set of ten music pieces, the proposed method is shown to outperform other general purpose multipitch estimators in either accuracy or computational speed, although not being able to yield performance as good as the state-of-the art methods, which are being optimally tuned and specifically trained on the present instruments. However, the method is able to outperform such a technique when used without optimal tuning, or when applied to instruments not included in the training data.
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| 15. |
- Elvander, Filip, et al.
(författare)
-
Robust Non-Negative Least Squares Using Sparsity
- 2016
-
Ingår i: 2016 24th European Signal Processing Conference (EUSIPCO). - 2076-1465. - 9780992862657 ; , s. 61-65
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Konferensbidrag (refereegranskat)abstract
- Sparse, non-negative signals occur in many applications. To recover such signals, estimation posed as non-negative least squares problems have proven to be fruitful. Efficient algorithms with high accuracy have been proposed, but many of them assume either perfect knowledge of the dictionary generating the signal, or attempts to explain deviations from this dictionary by attributing them to components that for some reason is missing from the dictionary. In this work, we propose a robust non-negative least squares algorithm that allows the generating dictionary to differ from the assumed dictionary, introducing uncertainty in the setup. The proposed algorithm enables an improved modeling of the measurements, and may be efficiently implemented using a proposed ADMM implementation. Numerical examples illustrate the improved performance as compared to the standard non-negative LASSO estimator.
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| 16. |
- Elvander, Filip
(författare)
-
Sparse Modeling of Harmonic Signals
- 2017
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis considers sparse modeling and estimation of multi-pitch signals, i.e., signals whose frequency content can be described by superpositions of harmonic, or close-to-harmonic, structures, characterized by a set of fundamental frequencies. As the number of fundamental frequencies in a given signal is in general unknown, this thesis casts the estimation as a sparse reconstruction problem, i.e., estimates of the fundamental frequencies are produced by finding a sparse representation of the signal in a dictionary containing an over-complete set of pitch atoms. This sparse representation is found by using convex modeling techniques, leading to highly tractable convex optimization problems from whose solutions the estimates of the fundamental frequencies can be deduced.In the first paper of this thesis, a method for multi-pitch estimation for stationary signal frames is proposed. Building on the heuristic of spectrally smooth pitches, the proposed method produces estimates of the fundamental frequencies by minimizing a sequence of penalized least squares criteria, where the penalties adapt to the signal at hand. An efficient algorithm building on the alternating direction method of multipliers is proposed for solving these least squares problems.The second paper considers a time-recursive formulation of the multi-pitch estimation problem, allowing for the exploiting of longer-term correlations of the signal, as well as fundamental frequency estimates with a sample-level time resolution. Also presented is a signal-adaptive dictionary learning scheme, allowing for smooth tracking of frequency modulated signals.In the third paper of this thesis, robustness to deviations from the harmonic model in the form of inharmonicity is considered. The paper proposes a method for estimating the fundamental frequencies by, in the frequency domain, mapping each found spectral line to a set of candidate fundamental frequencies. The optimal mapping is found as the solution to a minimimal transport problem, wherein mappings leading to sparse pitch representations are promoted. The presented formulation is shown to yield robustness to varying degrees of inharmonicity without requiring explicit knowledge of the structure or scope of the inharmonicity.In all three papers, the performance of the proposed methods are evaluated using simulated signals as well as real audio.
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| 17. |
- Elvander, Filip, et al.
(författare)
-
Time Recursive Multi-Pitch Estimation Using Group Sparse Recursive Least Squares
- 2017
-
Ingår i: 50th Asilomar Conference on Signals, Systems, and Computers, 2016. - 9781538639542 ; , s. 369-373
-
Konferensbidrag (refereegranskat)abstract
- In this work, we propose a time-recursive multi-pitch estimation algorithm, using a sparse reconstruction framework, assuming only a few pitches from a large set of candidates to be active at each time instant. The proposed algorithm utilizes a sparse recursive least squares formulation augmented by an adaptive penalty term specifically designed to enforce a pitch structure on the solution. When evaluated on a set of ten music pieces, the proposed method is shown to outperform state-of-the-art multi-pitch estimators in either accuracy or computational spe
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| 18. |
- Elvander, Filip, et al.
(författare)
-
Tracking and sensor fusion in direction of arrival estimation using optimal mass transport
- 2018
-
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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| 19. |
- Elvander, Filip, et al.
(författare)
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USING OPTIMAL MASS TRANSPORT FOR TRACKING AND INTERPOLATION OF TOEPLITZ COVARIANCE MATRICES
- 2018
-
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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| 20. |
- Elvander, Filip, et al.
(författare)
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Using optimal transport for estimating inharmonic pitch signals
- 2017
-
Ingår i: 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). - : Institute of Electrical and Electronics Engineers (IEEE). - 9781509041176 ; , s. 331-335
-
Konferensbidrag (refereegranskat)abstract
- In this work, we propose a novel multi-pitch estimation technique that is robust with respect to the inharmonicity commonly occurring in many applications. The method does not require any a priori knowledge of the number of signal sources, the number of harmonics of each source, nor the structure or scope of any possibly occurring inharmonicity. Formulated as a minimum transport distance problem, the proposed method finds an estimate of the present pitches by mapping any found spectral line to the closest harmonic structure. The resulting optimization is a convex and highly tractable linear programming problem. The preferable performance of the proposed method is illustrated using both simulated and real audio signals.
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| 21. |
- Elvander, Filip, et al.
(författare)
-
Variance Analysis of Covariance and Spectral Estimates for Mixed-Spectrum Continuous-Time Signals
- 2023
-
Ingår i: IEEE Transactions on Signal Processing. - : Institute of Electrical and Electronics Engineers (IEEE). - 1053-587X .- 1941-0476. ; 71, s. 1395-1407
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Tidskriftsartikel (refereegranskat)abstract
- The estimation of the covariance function of a stochastic process, or signal, is of integral importance for a multitude of signal processing applications. In this work, we derive closed-form expressions for the covariance of covariance estimates for mixed-spectrum continuous-time signals, i.e., spectra containing both absolutely continuous and singular parts. The results cover both finite-sample and asymptotic regimes, allowing for assessing the exact speed of convergence of estimates to their expectations, as well as their limiting behavior. As is shown, such covariance estimates may converge even for non-ergodic processes. Furthermore, we consider approximating signals with arbitrary spectral densities by sequences of singular spectrum, i.e., sinusoidal, processes, and derive the limiting behavior of covariance estimates as both the sample size and the number of sinusoidal components tend to infinity. We show that the asymptotic-regime variance can be described by a time-frequency resolution product, with dramatically different behavior depending on how the sinusoidal approximation is constructed. In numerical examples, we illustrate the theory and its implications for signal and array processing applications.
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| 22. |
- Elvander, Filip, et al.
(författare)
-
Worst-Case Uncertainty Bounds in Covariance Interpolation
- 2022
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Ingår i: 2022 30TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO 2022). - : IEEE. ; , s. 2256-2260
-
Konferensbidrag (refereegranskat)abstract
- In this work, we establish and compute worst case bounds in covariance interpolation for continuous-time stationary stochastic processes, a problem that appears in applications such as broad-band direction-of-arrival estimation and optimal sensor placement. More specifically, for two such stochastic processes whose covariance functions agree on a finite discrete set of time-lags, we would like to compute the maximal possible discrepancy of the covariance functions for real-valued time-lags outside this discrete grid. In array processing, this difference quantifies the inherent uncertainty pertaining to the discrete sampling of space determined by the array geometry. Computing this uncertainty corresponds to solving an infinite-dimensional non-convex problem. However, we herein prove that the maximal objective value may be bounded from above by a finite-dimensional convex optimization problem, allowing for efficient computation by standard methods. Furthermore, we empirically observe that for the case of signals whose spectra are supported on an interval, this upper bound is sharp, i.e., provides an exact quantification of the covariance uncertainty.
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| 23. |
- Jansson, Andreas, et al.
(författare)
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Range-based radar model structure selection
- 2021
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Ingår i: 28th European Signal Processing Conference, EUSIPCO 2020 - Proceedings. - 2219-5491. - 9789082797053 ; 2021-January, s. 2269-2273
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Konferensbidrag (refereegranskat)abstract
- In this work, we study under which circumstances it is appropriate to use simplified models for range determination using radar. Typically, pulsed radar systems result in the backscattered, demodulated, and matched signal having a chirp signal structure, with the frequency rate being related to the range to the reflecting target and the relative velocity of the transmitter and reflector. Far from the target, and at low relative velocities, one may achieve preferable location estimates by neglecting the frequency rate, treating the received signal as being purely sinusoidal, whereas at close range, neglecting the frequency rate notably reduces the achievable performance. Using misspecified estimation theory, we derive a lower bound of the achievable performance when neglecting the true signal structure, and show at which ranges one model is preferable to the other. Numerical results from a mm-wave radar system illustrate the results.
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| 24. |
- Juhlin, Maria, et al.
(författare)
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Defining Graph Signal Distances Using an Optimal Mass Transport Framework
- 2019
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Ingår i: 2019 27th European Signal Processing Conference, EUSIPCO 2019. - 9789082797039 - 9781538673003 ; 2019
-
Konferensbidrag (refereegranskat)abstract
- In this work, we propose a novel measure of distance for quantifying dissimilarities between signals observed on a graph. Building on a recently introduced optimal mass transport framework, the distance measure is formed using the second-order statistics of the graph signals, allowing for comparison of graph processes without direct access to the signals themselves, while explicitly taking the dynamics of the underlying graph into account. The behavior of the proposed distance notion is illustrated in a graph signal classification scenario, indicating attractive modeling properties as compared to the standard Euclidean metric.
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| 25. |
- 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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| 26. |
- Jälmby, Martin, et al.
(författare)
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Computationally Efficient Estimation of Multi-dimensional Damped Modes using Sparse Wideband Dictionaries
- 2018
-
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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| 27. |
- Kronvall, Ted, et al.
(författare)
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An Adaptive Penalty Approach to Multi-Pitch Estimation
- 2015
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Ingår i: Signal Processing Conference (EUSIPCO), 2015 23rd European. - 2076-1465. - 9780992862633
-
Konferensbidrag (refereegranskat)abstract
- This work treats multi-pitch estimation, and in particular the common misclassification issue wherein the pitch at half of the true fundamental frequency, here referred to as a sub-octave, is chosen instead of the true pitch. Extending on current methods which use an extension of the Group LASSO for pitch estimation, this work introduces an adaptive total variation penalty, which both enforce group- and block sparsity, and deal with errors due to sub-octaves. The method is shown to outperform current state-of-the-art sparse methods, where the model orders are unknown, while also requiring fewer tuning parameters than these. The method is also shown to outperform several conventional pitch estimation methods, even when these are virtued with oracle model orders.
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| 28. |
- Kronvall, Ted, et al.
(författare)
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Multi-pitch estimation via fast group sparse learning
- 2016
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Ingår i: 2016 24th European Signal Processing Conference (EUSIPCO). - 2076-1465. - 9780992862657 ; , s. 1093-1097
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Konferensbidrag (refereegranskat)abstract
- In this work, we consider the problem of multi-pitch estimation using sparse heuristics and convex modeling. In general, this is a difficult non-linear optimization problem, as the frequencies belonging to one pitch often overlap the frequencies belonging to other pitches, thereby causing ambiguity between pitches with similar frequency content. The problem is further complicated by the fact that the number of pitches is typically not known. In this work, we propose a sparse modeling framework using a generalized chroma representation in order to remove redundancy and lower the dictionary's block-coherency. The found chroma estimates are then used to solve a small convex problem, whereby spectral smoothness is enforced, resulting in the corresponding pitch estimates. Compared with previously published sparse approaches, the resulting algorithm reduces the computational complexity of each iteration, as well as speeding up the overall convergence.
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| 29. |
- Lei, Shiwen, et al.
(författare)
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Computationality efficient multi-pitch estimation using sparsity
- 2016
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Ingår i: 11th IMA International Conference on Mathematics in Signal Processing.
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Konferensbidrag (refereegranskat)abstract
- In this work, we introduce a computationally efficient multi-pitch estimation algorithm making use of an approximative frequency domain reformulation of a recent block-sparse multi-pitch estimator. Different to most other pitch estimators, the proposed method does not require a prior knowledge of the number of sources present, nor the number of overtones of each such source. Evaluated on measured audio signals, the estimator is shown to offer excellent performance at a low computational cost.
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| 30. |
- Sundstrom, David, et al.
(författare)
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Optimal Transport Based Impulse Response Interpolation in the Presence of Calibration Errors
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Ingår i: IEEE Transactions on Signal Processing. - 1053-587X.
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Tidskriftsartikel (refereegranskat)abstract
- Acoustic impulse responses (IRs) are widely used to model sound propagation between two points in space. Being a point-to-point description, IRs are generally estimated based on input-output pairs for source and sensor positions of interest. Alternatively, the IR at an arbitrary location in space may be constructed based on interpolation techniques, thus alleviating the need of densely sampling the space. The resulting IR interpolation problem is of general interest, e.g., for imaging of subsurface structures based on seismic waves, rendering of audio and radar IRs, as well as for numerous spatial audio applications. A commonly used model represents the acoustic reflections as image sources, often being determined using a sparse reconstruction framework employing spatial dictionaries. However, in the presence of calibration errors, such spatial dictionaries tend to inaccurately represent the actual propagation, limiting the use of these methods in practical applications. Instead of explicitly assuming an image source model, we here introduce a trade-off between minimizing the distance to an image source model and fitting the data by means of a multi-marginal optimal transport problem. The proposed method is evaluated on the early part of real acoustic IRs from the MeshRIR data set, illustrating its preferable performance as compared to state-of-the-art spatial dictionary-based IR interpolation approaches.
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| 31. |
- Svedberg, David, et al.
(författare)
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Determining joint periodicities in multi-time data with sampling uncertainties
- 2022
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Ingår i: 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). - : Institute of Electrical and Electronics Engineers (IEEE). - 1520-6149. - 9781665405409 - 9781665405416 ; , s. 5737-5741
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Konferensbidrag (refereegranskat)abstract
- In this work, we introduce a novel approach for determining a joint sparse spectrum from several non-uniformly sampled data sets, where each data set is assumed to have its own, and only partially known, sampling times. The problem originates in paleoclimatology, where each data point derives from a separate ice core measurement, resulting in that even though all measurements reflect the same periodicities, the sampling times and phases differ among the data sets, with the sampling times being only approximately known. The proposed estimator exploits all available data using a sparse reconstruction framework allowing for a reliable and robust estimation of the underlying periodicities. The performance of the method is illustrated using both simulated and measured ice core data sets.
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| 32. |
- Svedberg, David, et al.
(författare)
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Determining joint periodicities in multi-time data with sampling uncertainties
- 2023
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Ingår i: Signal Processing. - : Elsevier. - 0165-1684 .- 1872-7557. ; 213
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Tidskriftsartikel (refereegranskat)abstract
- In this work, we introduce a novel approach for determining a joint sparse spectrum from several non-uniformly sampled data sets, where each data set is assumed to have its own, possibly disjoint, and only partially known, sampling times. The potential of the proposed approach is illustrated using a spectral estimation problem in paleoclimatology. In this problem, each data point derives from a separate ice core measurement, resulting in that even though all measurements reflect the same periodicities, the sampling times and phases differ among the data sets. In addition, sampling times are only approximately known. The resulting joint estimate exploiting all available data is formulated using a sparse reconstruction framework allowing for a reliable and robust estimate of the underlying periodicities. The corresponding misspecified Cramer-Rao lower bound, accounting for the expected sampling uncertainties, is derived and the proposed method is shown to attain the resulting bound when the signal to noise ratio is sufficiently high. The performance of the proposed method is illustrated as compared to other commonly used approaches using both simulated and measured ice core data sets.
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| 33. |
- Swärd, Johan, et al.
(författare)
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Designing optimal sampling schemes
- 2017
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Ingår i: 25th European Signal Processing Conference, EUSIPCO 2017. - 9780992862671 ; 2017-January, s. 912-916
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Konferensbidrag (refereegranskat)abstract
- In this work, we propose a method for finding an optimal, non-uniform, sampling scheme for a general class of signals in which the signal measurements may be non-linear functions of the parameters to be estimated. Formulated as a convex optimization problem reminiscent of the sensor selection problem, the method determines an optimal sampling scheme given a suitable estimation bound on the parameters of interest. The formulation also allows for putting emphasis on a particular set of parameters of interest by scaling the optimization problem in such a way that the bound to be minimized becomes more sensitive to these parameters. For the case of imprecise a priori knowledge of these parameters, we present a framework for customizing the sampling scheme to take such uncertainty into account. Numerical examples illustrate the efficiency of the proposed scheme.
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| 34. |
- Swärd, Johan, et al.
(författare)
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Designing optimal sampling schemes for multi-dimensional data
- 2017
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Ingår i: 2017 51st Asilomar Conference on Signals, Systems, and Computers. - 9781538618233 ; , s. 850-852
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Konferensbidrag (refereegranskat)abstract
- In this work, we propose a method for determining an optimal, non-uniform, sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The optimal sampling scheme is determined given a suitable estimation bound on the parameters of interest, as well as incorporating any imprecise a priori knowledge of the locations of the parameters. Numerical examples illustrate the efficiency of the proposed scheme.
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| 35. |
- 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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