| 1. |
- Adalbjörnsson, Stefan Ingi, et al.
(författare)
-
A Sparse Approach for Estimation of Amplitude Modulated Sinusoids
- 2014
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Konferensbidrag (refereegranskat)abstract
- We consider the problem of spectral analysis of signals composed of sums of multiple amplitude modulated, possibly harmonically related, sinusoids using a sparse approach. By separating the nonlinear frequency variables using a dictionary of possible frequency components as well as a spline basis for the amplitude modulation, results in a convex criterion which can be efficiently solved without worrisome local minima. The resulting method makes no model order assumption and automatically estimates both the signal parameters and their amplitude modulations
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| 2. |
- Adalbjörnsson, Stefan Ingi, et al.
(författare)
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Sparse Localization of Harmonic Audio Sources
- 2016
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Ingår i: IEEE/ACM Transactions on Audio, Speech, and Language Processing. - 2329-9290. ; 24:1, s. 117-129
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we propose a novel method for estimating the locations of near- and/or far-field harmonic audio sources impinging on an arbitrary, but calibrated, sensor array. Using a joint pitch and location estimation formed in two steps, we first estimate the fundamental frequencies and complex amplitudes under a sinusoidal model assumption, whereafter the location of each source is found by utilizing both the difference in phase and the relative attenuation of the magnitude estimates. As audio recordings often consist of multi-pitch signals exhibiting some degree of reverberation, where both the number of pitches and the source locations are unknown, we propose to use sparse heuristics to avoid the necessity of detailed a priori assumptions on the spectral and spatial model orders. The method’s performance is evaluated using both simulated and measured audio data, with the former showing that the proposed method achieves near-optimal performance, whereas the latter confirms the method’s feasibility when used with real recordings.
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| 3. |
- Elvander, Filip, et al.
(författare)
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An Adaptive Penalty Multi-Pitch Estimator with Self-Regularization
- 2016
-
Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684. ; 127, s. 56-70
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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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| 4. |
- Juhlin, Maria, et al.
(författare)
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Sparse Chroma Estimation for Harmonic Non-Stationary Audio
- 2015
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Ingår i: Signal Processing Conference (EUSIPCO), 2015 23rd European. ; , s. 26-30
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Konferensbidrag (refereegranskat)abstract
- In this work, we extend on our recently proposed block sparse chroma estimator, such that the method also allows for signals with time-varying envelopes. Using a spline-based amplitude modulation of the chroma dictionary, the refined estimator is able to model longer frames than our earlier approach, as well as to model highly time-localized signals, and signals containing sudden bursts, such as trumpet or trombone signals, thus retaining more signal information than other methods for chroma estimation. The performance of the proposed estimator is evaluated on a recorded trumpet signal, clearly illustrating the improved performance, as compared to other used techniques.
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| 5. |
- 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
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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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| 6. |
- Kronvall, Ted, et al.
(författare)
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Computationally Efficient Robust Widely Linear Beamforming for Improper Non-Stationary Signals
- 2013
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Ingår i: [Host publication title missing].
-
Konferensbidrag (refereegranskat)abstract
- In this work, we introduce a computationally efficient Kalman-filter based implementation of the robust widely linear (WL) minimum variance distortionless response (MVDR) beamformer. The beamformer is able to achieve the same performance as the recently derived robust WL MVDR beamformer, but avoids the computationally burdensome solution based on a second order cone programming (SOCP), and exploiting the recent Kalman-based regular robust MVDR beamformer, extends this to also allow for non-circular sources and interferences. Numerical simulations illustrate the achieved performance.
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| 7. |
- Kronvall, Ted, et al.
(författare)
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Group-Sparse Regression Using the Covariance Fitting Criterion
- 2017
-
Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684. ; 139, s. 116-130
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Tidskriftsartikel (refereegranskat)abstract
- In this work, we present a novel formulation for efficient estimation of group-sparse regression problems. By relaxing a covariance fitting criteria commonly used in array signal processing, we derive a generalization of the recent SPICE method for grouped variables. Such a formulation circumvents cumbersome model order estimation, while being inherently hyperparameter-free. We derive an implementation which iteratively decomposes into a series of convex optimization problems, each being solvable in closed-form. Furthermore, we show the connection between the proposed estimator and the class of LASSO-type estimators, where a dictionary-dependent regularization level is inherently set by the covariance fitting criteria. We also show how the proposed estimator may be used to form group-sparse estimates for sparse groups, as well as validating its robustness against coherency in the dictionary, i.e., the case of overlapping dictionary groups. Numerical results show preferable estimation performance, on par with a group-LASSO bestowed with oracle regularization, and well exceeding comparable greedy estimation methods.
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| 8. |
- Kronvall, Ted
(författare)
-
Group-Sparse Regression : With Applications in Spectral Analysis and Audio Signal Processing
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This doctorate thesis focuses on sparse regression, a statistical modeling tool for selecting valuable predictors in underdetermined linear models. By imposing different constraints on the structure of the variable vector in the regression problem, one obtains estimates which have sparse supports, i.e., where only a few of the elements in the response variable have non-zero values. The thesis collects six papers which, to a varying extent, deals with the applications, implementations, modifications, translations, and other analysis of such problems. Sparse regression is often used to approximate additive models with intricate, non-linear, non-smooth or otherwise problematic functions, by creating an underdetermined model consisting of candidate values for these functions, and linear response variables which selects among the candidates. Sparse regression is therefore a widely used tool in applications such as, e.g., image processing, audio processing, seismological and biomedical modeling, but is also frequently used for data mining applications such as, e.g., social network analytics, recommender systems, and other behavioral applications. Sparse regression is a subgroup of regularized regression problems, where a fitting term, often the sum of squared model residuals, is accompanied by a regularization term, which grows as the fit term shrinks, thereby trading off model fit for a sought sparsity pattern. Typically, the regression problems are formulated as convex optimization programs, a discipline in optimization where first-order conditions are sufficient for optimality, a local optima is also the global optima, and where numerical methods are abundant, approachable, and often very efficient. The main focus of this thesis is structured sparsity; where the linear predictors are clustered into groups, and sparsity is assumed to be correspondingly group-wise in the response variable. The first three papers in the thesis, A-C, concerns group-sparse regression for temporal identification and spatial localization, of different features in audio signal processing. In Paper A, we derive a model for audio signals recorded on an array of microphones, arbitrarily placed in a three-dimensional space. In a two-step group-sparse modeling procedure, we first identify and separate the recorded audio sources, and then localize their origins in space. In Paper B, we examine the multi-pitch model for tonal audio signals, such as, e.g., musical tones, tonal speech, or mechanical sounds from combustion engines. It typically models the signal-of-interest using a group of spectral lines, located at some integer multiple of a fundamental frequency. In this paper, we replace the regularizers used in previous works by a group-wise total variation function, promoting a smooth spectral envelope. The proposed combination of regularizers thereby avoids the common suboctave error, where the fundamental frequency is incorrectly classified using half of the fundamental frequency. In Paper C, we analyze the performance of group-sparse regression for classification by chroma, also known as pitch class, e.g., the musical note C, independent of the octave. The last three papers, D-F, are less application-specific than the first three; attempting to develop the methodology of sparse regression more independently of the application. Specifically, these papers look at model order selection in group-sparse regression, which is implicitly controlled by choosing a hyperparameter, prioritizing between the regularizer and the fitting term in the optimization problem. In Papers D and E, we examine a metric from array processing, termed the covariance fitting criterion, which is seemingly hyperparameter-free, and has been shown to yield sparse estimates for underdetermined linear systems. In the paper, we propose a generalization of the covariance fitting criterion for group-sparsity, and show how it relates to the group-sparse regression problem. In Paper F, we derive a novel method for hyperparameter-selection in sparse and group-sparse regression problems. By analyzing how the noise propagates into the parameter estimates, and the corresponding decision rules for sparsity, we propose selecting it as a quantile from the distribution of the maximum noise component, which we sample from using the Monte Carlo method.
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| 9. |
- Kronvall, Ted, et al.
(författare)
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Hyperparameter-free sparse regression of grouped variables
- 2017
-
Ingår i: Conference Record of the 50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016. - 9781538639542 ; , s. 394-398
-
Konferensbidrag (refereegranskat)abstract
- In this paper, we introduce a novel framework for semi-parametric estimation of an unknown number of signals, each parametrized by a group of components. Via a reformulation of the covariance fitting criteria, we formulate a convex optimization problem over a grid of candidate representations, promoting solutions with only a few active groups. Utilizing the covariance fitting allows for a hyperparameter-free estimation procedure, highly robust against coherency between candidates, while still allowing for a computationally efficient implementation. Numerical simulations illustrate how the proposed method offers a performance similar to the group-LASSO for incoherent dictionaries, and superior performance for coherent dictionaries.
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| 10. |
- Kronvall, Ted, et al.
(författare)
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Hyperparameter Selection for Group-Sparse Regression: A Probabilistic Approach
- 2018
-
Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684. ; 151, s. 107-118
-
Tidskriftsartikel (refereegranskat)abstract
- This work analyzes the effects on support recovery for different choices of the hyper- or regularization parameter in LASSO-like sparse and group-sparse regression problems. The hyperparameter implicitly selects the model order of the solution, and is typically set using cross-validation (CV). This may be computationally prohibitive for large-scale problems, and also often overestimates the model order, as CV optimizes for prediction error rather than support recovery. In this work, we propose a probabilistic approach to select the hyperparameter, by quantifying the type I error (false positive rate) using extreme value analysis. From Monte Carlo simulations, one may draw inference on the upper tail of the distribution of the spurious parameter estimates, and the regularization level may be selected for a specified false positive rate. By solving the e group-LASSO problem, the choice of hyperparameter becomes independent of the noise variance. Furthermore, the effects on the false positive rate caused by collinearity in the dictionary is discussed, including ways of circumventing them. The proposed method is compared to other hyperparameter-selection methods in terms of support recovery, false positive rate, false negative rate, and computational complexity. Simulated data illustrate how the proposed method outperforms CV and comparable methods in both computational complexity and support recovery.
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| 11. |
- Kronvall, Ted, et al.
(författare)
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Hyperparameter-selection for sparse regression : A probablistic approach
- 2018
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Ingår i: Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017. - 9781538618233 ; 2017-October, s. 853-857
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Konferensbidrag (refereegranskat)abstract
- The choice of hyperparameter(s) notably affects the support recovery in LASSO-like sparse regression problems, acting as an implicit model order selection. Parameters are typically selected using cross-validation or various ad hoc approaches. These often overestimates the resulting model order, aiming to minimize the prediction error rather than maximizing the support recovery. In this work, we propose a probabilistic approach to selecting hyperparameters in order to maximize the support recovery, quantifying the type I error (false positive rate) using extreme value analysis, such that the regularization level is selected as an appropriate quantile. By instead solving the scaled LASSO problem, the proposed choice of hyperparameter becomes almost independent of the noise variance. Simulation examples illustrate how the proposed method outperforms both cross-validation and the Bayesian Information Criterion in terms of computational complexity and support recovery.
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| 12. |
- Kronvall, Ted, et al.
(författare)
-
Joint DOA and Multi-Pitch Estimation Using Block Sparsity
- 2014
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Ingår i: Acoustics, Speech and Signal Processing (ICASSP), 2014 IEEE International Conference on. - 1520-6149. ; , s. 3958-3962
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Konferensbidrag (refereegranskat)abstract
- In this paper, we propose a novel method to estimate the fundamental frequencies and directions-of-arrival (DOA) of multi-pitch signals impinging on a sensor array. Formulating the estimation as a group sparse convex optimization problem, we use the alternating direction of multipliers method (ADMM) to estimate both temporal and spatial correlation of the array signal. By first jointly estimating both fundamental frequencies and time-of-arrivals (TOAs) for each sensor and sound source, we then form a non-linear least squares estimate to obtain the DOAs. Numerical simulations indcate the preferable performance of the proposed estimator as compared to current state-of-the-art methods.
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| 13. |
- Kronvall, Ted, et al.
(författare)
-
Joint DOA and Multi-Pitch Estimation Via Block Sparse Dictionary Learning
- 2014
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Ingår i: European Signal Processing Conference. - 2219-5491.
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Konferensbidrag (refereegranskat)abstract
- In this paper, we introduce a novel sparse method for joint estimation of the direction of arrivals (DOAs) and pitches of a set of multi-pitch signals impinging on a sensor array. Extending on earlier approaches, we formulate a novel dictionary learning framework from which an estimate is formed without making assumptions on the model orders. The proposed method alternatively uses a block sparse approach to estimate the pitches, using an alternating direction method of multipliers framework, and alternatively a nonlinear least squares approach to estimate the DOAs. The preferable performance of the proposed algorithm, as compared to earlier methods, is shown using numerical examples.
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| 14. |
- 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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| 15. |
- Kronvall, Ted, et al.
(författare)
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Non-Parametric Data-Dependent Estimation of Specroscopic Echo-Train Signals
- 2013
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Ingår i: Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on. - 1520-6149. ; , s. 6259-6263
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Konferensbidrag (refereegranskat)abstract
- This paper proposes a novel non-parametric estimator for spectroscopic echo-train signals, termed ETCAPA, to be used as a robust and reliable first-approach-technique for new, unknown, or partly disturbed substances. Exploiting the complete echo structure for the signal of interest, the method reliably estimates all parameters of interest, enabling initial estimates for the identification procedure to follow. Extending the recent dCapon and dAPES algorithms, ETCAPA exploits a data-dependent filter-bank formulation together with a non-linear minimization to give a hitherto unobtained non-parametric estimate of the echo train decay. The proposed estimator is evaluated on both simulated and measured NQR signals, clearly showing the excellent performance of the method, even in the case of strong interferences.
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| 16. |
- Kronvall, Ted, et al.
(författare)
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Online group-sparse estimation using the covariance fitting criterion
- 2017
-
Ingår i: 25th European Signal Processing Conference, EUSIPCO 2017. - 9780992862671 ; , s. 2101-2105
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Konferensbidrag (refereegranskat)abstract
- In this paper, we present a time-recursive implementation of a recent hyperparameter-free group-sparse estimation technique. This is achieved by reformulating the original method, termed group-SPICE, as a square-root group-LASSO with a suitable regularization level, for which a time-recursive implementation is derived. Using a proximal gradient step for lowering the computational cost, the proposed method may effectively cope with data sequences consisting of both stationary and non-stationary signals, such as transients, and/or amplitude modulated signals. Numerical examples illustrates the efficacy of the proposed method for both coherent Gaussian dictionaries and for the multi-pitch estimation problem.
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| 17. |
- Kronvall, Ted, et al.
(författare)
-
Online Group-Sparse Regression Using the Covariance Fitting Criterion
- 2017
-
Ingår i: Proceedings of the 25th European Signal Processing Conference (EUSIPCO). - 2076-1465. - 9780992862688 ; CFP1740S-USB
-
Konferensbidrag (refereegranskat)abstract
- In this paper, we present a time-recursive implementation of a recent hyperparameter-free group-sparse estimation technique. This is achieved byr eformulating the original method, termed group-SPICE, as a square-root group-LASSO with a suitable regularization level, for which a time-recursive implementation is derived. Using a proximal gradient step for lowering the computational cost, the proposed method may effectively cope with data sequences consisting of both stationary and non-stationary signals, such as transients, and/or amplitude modulated signals. Numerical examples illustrates the efficacy of the proposed method for both coherent Gaussian dictionaries and for the multi-pitch estimation problem.
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| 18. |
- Kronvall, Ted, et al.
(författare)
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Sparse Chroma Estimation for Harmonic Audio
- 2015
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Ingår i: 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). - 2379-190X. - 9781467369978 ; , s. 579-583
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Konferensbidrag (refereegranskat)abstract
- This work treats the estimation of the chromagram for harmonic audio signals using a block sparse reconstruction framework. Chroma has been used for decades as a key tool in audio analysis, and is typically formed using a Fourier-based framework that maps the fundamental frequency of a musical tone to its corresponding chroma. Such an approach often leads to problems with tone ambiguity, which we avoid by taking into account the harmonic structure and perceptional attributes in music. The performance of the proposed method is evaluated using real audio files, clearly showing preferable performance as compared to other commonly used methods.
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| 19. |
- Kronvall, Ted, et al.
(författare)
-
Sparse Modeling of Chroma Features
- 2017
-
Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684. ; 130, s. 105-117
-
Tidskriftsartikel (refereegranskat)abstract
- This work treats the estimation of chroma features for harmonic audio signals using a sparse reconstruction framework. Chroma has been used for decades as a key tool in audio analysis, and is typically formed using a periodogram-based approach that maps the fundamental frequency of a musical tone to its corresponding chroma. Such an approach often leads to problems with tone ambiguity. We address this ambiguity via sparse modeling, allowing us to appropriately penalize ambiguous estimates while taking the harmonic structure of tonal audio into account. Furthermore, we also allow for signals to have time-varying envelopes. Using a spline-based amplitude modulation of the chroma dictionary, the presented estimator is able to model longer frames than what is conventional for audio, as well as to model highly time-localized signals, and signals containing sudden bursts, such as trumpet or trombone signals. Thus, we may retain more signal information as compared to alternative methods. The performances of the proposed methods are evaluated by analyzing the average estimation errors for synthetic signals, as compared to the Cramér–Rao lower bound, and by visual inspection for estimates of real instrument signals. The results show strong visual clarity, as compared to other commonly used methods.
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| 20. |
- Kronvall, Ted
(författare)
-
Sparse Modeling of Grouped Line Spectra
- 2015
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This licentiate thesis focuses on clustered parametric models for estimation of line spectra, when the spectral content of a signal source is assumed to exhibit some form of grouping. Different from previous parametric approaches, which generally require explicit knowledge of the model orders, this thesis exploits sparse modeling, where the orders are implicitly chosen. For line spectra, the non-linear parametric model is approximated by a linear system, containing an overcomplete basis of candidate frequencies, called a dictionary, and a large set of linear response variables that selects and weights the components in the dictionary. Frequency estimates are obtained by solving a convex optimization program, where the sum of squared residuals is minimized. To discourage overfitting and to infer certain structure in the solution, different convex penalty functions are introduced into the optimization. The cost trade-off between fit and penalty is set by some user parameters, as to approximate the true number of spectral lines in the signal, which implies that the response variable will be sparse, i.e., have few non-zero elements. Thus, instead of explicit model orders, the orders are implicitly set by this trade-off. For grouped variables, the dictionary is customized, and appropriate convex penalties selected, so that the solution becomes group sparse, i.e., has few groups with non-zero variables. In an array of sensors, the specific time-delays and attenuations will depend on the source and sensor positions. By modeling this, one may estimate the location of a source. In this thesis, a novel joint location and grouped frequency estimator is proposed, which exploits sparse modeling for both spectral and spatial estimates, showing robustness against sources with overlapping frequency content. For audio signals, this thesis uses two different features for clustering. Pitch is a perceptual property of sound that may be described by the harmonic model, i.e., by a group of spectral lines at integer multiples of a fundamental frequency, which we estimate by exploiting a novel adaptive total variation penalty. The other feature, chroma, is a concept in musical theory, collecting pitches at powers of 2 from each other into groups. Using a chroma dictionary, together with appropriate group sparse penalties, we propose an automatic transcription of the chroma content of a signal.
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| 21. |
- Kronvall, Ted, et al.
(författare)
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Sparse Multi-Pitch and Panning Estimation of Stereophonic Signals
- 2016
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Ingår i: Proceedings of the 11th IMA International Conference on Mathematics in Signal Processing.
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Konferensbidrag (refereegranskat)abstract
- In this paper, we propose a novel multi-pitch estimator for stereophonic mixtures, allowing for pitch estimation on multi-channel audio even if the amplitude and delay panning parameters are unknown. The presented method does not require prior knowledge of the number of sources present in the mixture, nor on the number of harmonics in each source. The estimator is formulated using a sparse signal framework, and an efficient implementation using the ADMM is introduced. Numerical simulations indicate the preferable performance of the proposed method as compared to several commonly used multi-channel single pitch estimators, and a commonly used multi-pitch estimator.
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