Filip Elvander

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.

Online Estimation of Multiple Harmonic Signals

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.

Using optimal transport for estimating inharmonic pitch signals

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.

Designing optimal sampling schemes

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.

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.

Multi-dimensional grid-less estimation of saturated signals

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.

Robust non-negative least squares using sparsity

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.

Time-recursive multi-pitch estimation using group sparse recursive least squares

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 speed.