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In this paper, we examine the problem of target detection for the multistatic passive radar. Passive radar systems leverage the existing wireless sources, such as radio/TV stations and cellular signals that are referred to as illuminators of opportunity (IOs), to illuminate the environment and provide surveillance functions. Usually, these IO source signals are sparse or locally sparse in the frequency domain. We develop a passive multistatic detector by exploiting the sparsity or local sparsity of the IO signals. To improve the computational efficiency, two fast implementations of the proposed detector are also introduced. Simulation results show that the proposed approaches outperform the conventional passive detection methods that model the IO signals as unknown without any specific structures.

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.

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.

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.

In this work, we consider the problem of high-resolution estimation of the parameters detailing an N-dimensional (N-D) signal consisting of an unknown number of exponentially decaying sinusoidal components. 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. Even in the 2-D case, the resulting dictionary is typically very large, resulting in a computationally cumbersome optimization problem. Here, we introduce a sparse modeling framework for N-dimensional exponentially damped sinusoids using the Kronecker structure inherent in the model. Furthermore, we introduce a novel dictionary learning approach that iteratively refines the estimate of the candidate frequency and damping coefficients for each component, thus allowing for smaller dictionaries, and for frequency and damping parameters that are not 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. HighlightsA novel gridless sparsity-based parameter estimation method for damped, possibly nonuniformly sampled, multidimensional sinusoids.Statistically efficient performance is illustrated in the numerical section.Efficient implementation using the ADMM framework, as well as exploiting the Kronecker structure of resulting dictionaries.

In this work, 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 Cram´er-Rao lower bound.

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.

In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the sum of the Cramer–Rao lower bounds for the parameters of interest, given a desired number of sampling points. The proposed framework allows for selecting an arbitrary subset of the parameters detailing the model, as well as weighing the importance of the different parameters. Also presented is a scheme for incorporating any imprecise a priori knowledge of the locations of the parameters, as well as defining estimation performance bounds for the parameters of interest. Numerical examples illustrate the efficiency of the proposed scheme.

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.