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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.

In this paper, we propose a gridless method for estimating an unknown number of fundamental frequencies. Starting with a conventional dictionary matrix, containing sets of candidate fundamental frequencies and their corresponding harmonics, a nonconvex log-sum cost function is formed such that it imposes the harmonic structure and treats every fundamental frequency in the dictionary as a parameter. The cost function is iteratively decreased by minimizing a surrogate function, and, in each iteration, the fundamental frequencies are refined, whereas redundant parameters are omitted from the dictionary. The proposed method is tested on both real and simulated data, showing its preferred performance as compared to other state-of-the-art multipitch estimators.

In this paper, we propose a blind channel deconvolution method based on the Least Absolute Shrinkage and Selection Operator (LASSO). Using a Toeplitz structured formulation of the received signal, we form an iterative blind deconvolution scheme, alternatively estimating the underwater impulse response, and alternatively the transmitted waveform. The resulting optimizations are convex, and we formulate a computationally efficient solver using the Alternating Direction Method of Multipliers (ADMM). We illustrate the performance of the resulting estimator using both simulated and measured underwater signals.

The decomposition of nonlinear chirp modes is a challenging task, typically requiring prior knowledge of the number of modes a signal contains. In this work, we present a greedy nonlinear chirp mode estimation (NCME) technique that forms the used decomposition basis from the signal itself, using an arctangent demodulation technique. The resulting decomposition is formed by considering the residual energy and smoothness of the instantaneous amplitude. We also derive a computationally efficient implementation of the resulting estimator, using the alternating direction method of multipliers (ADMM). Numerical simulations and experimental data analysis illustrate the effectiveness and advantages of the proposed method.

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.

In this paper, we propose a blind channel deconvolution method based on a sparse reconstruction framework exploiting a wideband dictionary under the (relatively weak) assumption that the transmitted signal may be assumed to be well modelled as a sum of sinusoids. Using a Toeplitz structured formulation of the received signal, we form an iterative blind deconvolution scheme, alternatively estimating the underwater impulse response and the transmitted waveform. The resulting optimization problems are convex, and we formulate a computationally efficient solver using the Alternating Direction Method of Multipliers (ADMM). We illustrate the performance of the resulting estimator using both simulated and measured underwater signals.

This work proposes a 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.

In this work, we extend the popular sparse iterative covariance-based estimator (SPICE) by generalizing the formulation to allow for different norm constraint on the signal and noise parameters in the covariance model. For any choice of norms, the resulting generalized SPICE method enjoys the same benefits as the regular SPICE method, including being hyperparameter free, although the choice of norm is shown to govern the sparsity in the resulting solution. Furthermore, we show that there is a connection between the generalized SPICE and a penalized regression problem, both for the case were one allows the noise parameters to differ for each sample, and when treating each noise parameter as being equal. We examine the performance of the method for different choices of norms, and compare the results to the original SPICE method, showing the benefits of using the generalized version. We also provide a way of solving the generalized SPICE using a gridless method, which solves a semi-definite programming problem.

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.

In this work, we propose a computationally efficient algorithm for estimating multi-dimensional spectral lines. The method treats the data tensor's dimensions separately, yielding the corresponding frequency estimates for each dimension. Then, in a second step, the estimates are ordered over dimensions, thus forming the resulting multidimensional parameter estimates. For high dimensional data, the proposed method offers statistically efficient estimates for moderate to high signal to noise ratios, at a computational cost substantially lower than typical non-parametric Fourier-transform based periodogram solutions, as well as to state-of-the-art parametric estimators.

In this work, we extend the sparse iterative covariance-based estimator (SPICE), by generalizing the formulation to allow for different norm constraints on the signal and noise parameters in the covariance model. For a given norm, the resulting extended SPICE method enjoys the same benefits as the regular SPICE method, including being hyper-parameter free, although the choice of norms are shown to govern the sparsity in the resulting solution. Furthermore, we show that solving the extended SPICE method is equivalent to solving a penalized regression problem, which provides an alternative interpretation of the proposed method and a deeper insight on the differences in sparsity between the extended and the original SPICE formulation. We examine the performance of the method for different choices of norms, and compare the results to the original SPICE method, showing the benefits of using the extended formulation. We also provide two ways of solving the extended SPICE method; one grid-based method, for which an efficient implementation is given, and a gridless method for the sinusoidal case, which results in a semi-definite programming problem.

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.

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.

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.

Estimating the parameters of damped modes is generally computationally cumbersome, especially in cases when the model order of the signal is not known a priori. In this work, we propose a computationally efficient grid-less sparse reconstruction technique based on the recent SURE estimator developed for sinusoidal signals, extending it as to also allow for damped modes. In contrast to other estimators the proposed method allows for a non-uniform sampling scheme, thus presenting superior performance in applications where uniform sampling is suboptimal, hence broadening the application range. The performance of the proposed method is illustrated using both simulated and real spectroscopic data, clearly showing the improved performance as compared to previous techniques.