Ted Kronvall

Joint DOA and Multi-Pitch Estimation Using Block Sparsity

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 indicate the preferable performance of the proposed estimator as compared to current state-of-the-art methods.

Sparse chroma estimation for harmonic audio

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.

Sparse localization of harmonic audio sources

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 methods 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 methods feasibility when used with real recordings.

Sparse modeling of chroma features

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 Cramer-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. HighlightsTwo chroma estimators are proposed, exploiting the harmonic structure of music.A sparse modeling framework is used, not requiring explicit model order knowledge.One estimator assumes stationarity, promoting chroma with spectrally smooth partials.One estimator allows for amplitude modulation by using a B-spline representation.A Cramer-Rao lower bound is derived for the chroma-specific signal model.

Multi-pitch estimation via fast group sparse learning

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 dictionarys 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.

Non-parametric data-dependent estimation of spectroscopic echo-train signals

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.

Group-sparse regression using the covariance fitting criterion

A generalization of the covariance fitting criteria, for grouped variables, is presented.An hyperparameter-free analogue to the SPICE method is proposed for grouped variables, termed group-SPICE.The connection between group-SPICE and the group-LASSO (for both dense and sparse groups) is established.An efficient iterative implementation is presented for both homoscedastic and heteroscedastic noise.Group-SPICE is verified for synthetic data, as well as applied to the multi-pitch estimation problem. 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.

Sparse chroma estimation for harmonic non-stationary audio

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.

An adaptive penalty approach to multi-pitch estimation

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 suboctave, 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.

Hyperparameter selection for group-sparse regression: A probabilistic approach

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. (Less)