Johan Swärd

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 Semi-Parametric Estimation of Harmonic Chirp Signals

In this paper, we present a method for estimating the parameters detailing an unknown number of linear, possibly harmonically related, chirp signals, using an iterative sparse reconstruction framework. The proposed method is initiated by a re-weighted group-sparsity approach, followed by an iterative relaxation-based refining step, to allow for high-resolution estimates. Numerical simulations illustrate the achievable performance, offering a notable improvement as compared to other recent approaches. The resulting estimates are found to be statistically efficient, achieving the corresponding Cramér-Rao lower bound.

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.

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.

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.

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.

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.

Sparse semi-parametric chirp estimation

In this work, we present a method for estimating the parameters detailing an unknown number of linear chirp signals, using an iterative sparse reconstruction framework. The proposed method is initiated by a re-weighted Lasso approach, and then use an iterative relaxation-based refining step to allow for high resolution estimates. The resulting estimates are found to be statistically efficient, achieving the Cramér-Rao lower bound. Numerical simulations illustrate the achievable performance, offering a notable improvement as compared to other recent approaches.

Subspace-based estimation of symbolic periodicities

In this work, we propose a novel subspace-based estimator of periodicities in symbolic sequences. The estimator exploits the harmonic structure naturally occurring in symbolic sequences and iteratively forms the estimate of the periodicities using a MUSIC-like formulation. The estimator allows for alphabets of different sizes, but is here illustrated using both simulated and real DNA measurements, showing a notable performance gain as compared to other common estimators.

Generalized sparse covariance-based estimation

In this work, we generalize the recent sparse iterative covariance-based estimator (SPICE) by extending the problem formulation to allow for different norm constraints on the signal and noise parameters in the covariance model. The resulting extended SPICE algorithm offers the same benefits as the regular SPICE algorithm, including being hyper-parameter free, but the choice of norms allows further control of the sparsity in the resulting solution. We also show that the proposed extension is equivalent to solving a penalized regression problem, providing further insight into the differences between the extended and original SPICE formulations. The performance of the method is evaluated for different choices of norms, indicating the preferable performance of the extended formulation as compared to the original SPICE algorithm. Finally, we introduce two implementations of the proposed algorithm, one gridless formulating for the sinusoidal case, resulting in a semi-definite programming problem, and one grid-based, for which an efficient implementation is given.