Stefan Ingi Adalbjörnsson

Multi-pitch estimation exploiting block sparsity

We study the problem of estimating the fundamental frequencies of a signal containing multiple harmonically related sinusoidal components using a novel block sparse signal representation. An efficient algorithm for solving the resulting optimization problem is devised exploiting a novel variable step-size alternating direction method of multipliers (ADMM). The resulting algorithm has guaranteed convergence and shows notable robustness to the f0 vs f 0 / 2 ambiguity problem. The superiority of the proposed method, as compared to earlier presented estimation techniques, is demonstrated using both simulated and measured audio signals, clearly indicating the preferable performance of the proposed technique. HighlightsWe consider the modeling of multi-pitch signal using a novel block sparse signal model.A total variation penalty hinders the ubiquitous f0/2 vs f0 problem.Efficient implementations of the resulting criteria are derived using the alternating direction method of multipliers framework.Model orders are set automatically using a combination of sparse heuristics and a Bayesian information criterion.

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.

High resolution sparse estimation of exponentially decaying N-dimensional signals

In this work, we consider the problem of high-resolution estimation of the parameters detailing a two-dimensional (2-D) signal consisting of an unknown number of exponentially decaying sinusoidal components. Interpreting the estimation problem as a block (or group) sparse representation problem allows the decoupling of the 2-D data structure into a sum of outer-products of 1-D damped sinusoidal signals with unknown damping and frequency. The resulting non-zero blocks will represent each of the 1-D damped sinusoids, which may then be used as non-parametric estimates of the corresponding 1-D signals; this implies that the sought 2-D modes may be estimated using a sequence of 1-D optimization problems. The resulting sparse representation problem is solved using an iterative ADMM-based algorithm, after which the damping and frequency parameter can be estimated by a sequence of simple 1-D optimization problems.

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.

Estimating multiple pitches using block sparsity

We study the problem of estimating the fundamental frequencies of a signal containing multiple harmonically related sinusoidal signals using a novel block sparsity representation of the signal model. An efficient algorithm for solving the resulting optimization is devised exploiting an alternating directions method of multipliers (ADMM) formulation of the problem. The superiority of the proposed method, as compared to earlier methods, is demonstrated using both simulated and measured audio signals.

Efficient block and time-recursive estimation of sparse Volterra systems

We investigate the application of non-convex penalized least squares for parameter estimation in the Volterra model. Sparsity is promoted by introducing a weighted ℓq penalty on the parameters and efficient batch and time recursive algorithms are devised based on the cyclic coordinate descent approach. Numerical examples illustrate the improved performance of the proposed algorithms as compared the weighted ℓ1 norm.

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.

High resolution sparse estimation of exponentially decaying signals

We consider the problem of sparse modeling of a signal consisting of an unknown number of exponentially decaying sinusoids. Since such signals are not sparse in an oversampled Fourier matrix, earlier approaches typically exploit large dictionary matrices that include not only a finely spaced frequency grid but also a grid over the considered damping factors. The resulting dictionary is often very large, resulting in a computationally cumbersome optimization problem. Here, we instead introduce a novel dictionary learning approach that iteratively refines the estimate of the candidate damping factor for each sinusoid, thus allowing for both a quite small dictionary and for arbitrary damping factors, not being restricted to a grid. The performance of the proposed method is illustrated using simulated data, clearly showing the improved performance as compared to previous techniques.