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Showing papers on "Spectral density estimation published in 2018"


Journal ArticleDOI
TL;DR: This paper demonstrates that the proposed low-complexity method for line spectral estimation achieves estimation accuracy at least as good as current methods and that it does so while being orders of magnitudes faster.
Abstract: A number of recent works have proposed to solve the line spectral estimation problem by applying off-the-grid extensions of sparse estimation techniques These methods are preferable over classical line spectral estimation algorithms because they inherently estimate the model order However, they all have computation times that grow at least cubically in the problem size, thus limiting their practical applicability in cases with large dimensions To alleviate this issue, we propose a low-complexity method for line spectral estimation, which also draws on ideas from sparse estimation Our method is based on a Bayesian view of the problem The signal covariance matrix is shown to have Toeplitz structure, allowing superfast Toeplitz inversion to be used We demonstrate that our method achieves estimation accuracy at least as good as current methods and that it does so while being orders of magnitudes faster

56 citations


Journal ArticleDOI
TL;DR: A more general form of DFT interpolation based frequency estimator based on interpolation of three discrete Fourier transform spectral lines based on sinusoid signal is proposed.

47 citations


Proceedings ArticleDOI
17 Jun 2018
TL;DR: This paper develops a method for recovery of $K-sparse, sum-of-sinusoids from finitely many wrapped samples, thus avoiding clipping or saturation, and obtains a parametric sampling theorem.
Abstract: In parallel to Shannon's sampling theorem, the recent theory of unlimited sampling yields that a bandlimited function with high dynamic range can be recovered exactly from oversampled, low dynamic range samples. In this way, the unlimited sampling methodology circumvents the dynamic range problem that limits the use of conventional analog-to-digital converters (ADCs) which are prone to clipping or saturation problem. The unlimited sampling theorem is made practicable by using a unique ADC architecture-the self-reset ADC or the SR-ADC-which resets voltage before clipping, thus producing modulo or wrapped samples. While retaining full dynamic range of the input signal, surprisingly, the sampling density prescribed by the unlimited sampling theorem is independent of the maximum recordable voltage of the new ADC and depends only on the signal bandwidth. As the corresponding problem of signal recovery from such modulo samples arises in various applications with different signal models, where the original result does not directly apply, the original paper continues to trigger research follow-ups. In this paper, we investigate the case of sampling and reconstruction of a mixture of $K$ sinusoids from such modulo samples. This problem is at the heart of spectral estimation theory and application areas include active sensing, ranging, source localization, interferometry and direction-of-arrival estimation. By relying on the SR-ADCs, we develop a method for recovery of $K$ -sparse, sum-of-sinusoids from finitely many wrapped samples, thus avoiding clipping or saturation. As our signal model is completely characterized by $K$ pairs of amplitudes and frequencies, we obtain a parametric sampling theorem; we complement it with a recovery algorithm. Numerical demonstrations validate the effectivity of our approach.

45 citations


Journal ArticleDOI
TL;DR: This work quantitatively characterize the performance of both single- and multitaper Slepian estimation protocols by numerically reconstructing representative spectral densities, and demonstrates their advantage over dynamical-decoupling noise spectroscopy approaches in reducing bias from spectral leakage as well as in compensating for aliasing effects while maintaining a desired sampling resolution.
Abstract: Classical control noise is ubiquitous in qubit devices, making its accurate spectral characterization essential for designing optimized error suppression strategies at the physical level. Here, we focus on multiplicative Gaussian amplitude control noise on a driven qubit sensor and show that sensing protocols using optimally band-limited Slepian modulation offer substantial benefit in realistic scenarios. Special emphasis is given to laying out the theoretical framework necessary for extending non-parametric multitaper spectral estimation to the quantum setting by highlighting key points of contact and differences with respect to the classical formulation. In particular, we introduce and analyze two approaches (adaptive vs. single-setting) to quantum multitaper estimation, and show how they provide a practical means to both identify fine spectral features not otherwise detectable by existing protocols and to obtain reliable prior estimates for use in subsequent parametric estimation, including high-resolution Bayesian techniques. We quantitatively characterize the performance of both single- and multitaper Slepian estimation protocols by numerically reconstructing representative spectral densities, and demonstrate their advantage over dynamical-decoupling noise spectroscopy approaches in reducing bias from spectral leakage as well as in compensating for aliasing effects while maintaining a desired sampling resolution.

45 citations


Journal ArticleDOI
TL;DR: In this paper, a convex program is proposed to recover the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples, provided the frequencies are sufficiently separated, and the linear measurements obey natural conditions that are satisfied in a variety of applications.
Abstract: Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization, we do not have access directly to such equispaced samples. Rather, we only observe a severely undersampled version of these observations through linear measurements. This paper is about such generalized line spectral estimation problems. We reformulate these problems as sparse signal recovery problems over a continuously indexed dictionary, which can be solved via a convex program. We prove that the frequencies and amplitudes of the components of the mixture can be recovered perfectly from a near-minimal number of observations via this convex program. This result holds provided the frequencies are sufficiently separated, and the linear measurements obey natural conditions that are satisfied in a variety of applications.

35 citations


Journal ArticleDOI
TL;DR: In this paper, an online and real-time system is presented for detecting partial broken rotor bar (BRB) of inverter-fed squirrel cage induction motors under light load condition.

31 citations


Journal ArticleDOI
TL;DR: A new CSA processor is proposed, the CSAmin processor, which chooses the minimum between the two CSA subarray periodograms at each bearing to estimate the spatial PSD, and achieves lower variance than the product processor estimate, and keeps the PSD estimate unbiased for white Gaussian processes and asymptotically unbiased for nonwhiteGaussian processes.
Abstract: A coprime sensor array (CSA) interleaves two undersampled uniform linear arrays with coprime undersampling factors and has recently found broad applications in signal detection and estimation. CSAs commonly use the product processor by multiplying the scanned responses of two colinear subarrays to estimate the spatial power spectral density (PSD) of the received signal. This paper proposes a new CSA processor, the CSAmin processor, which chooses the minimum between the two CSA subarray periodograms at each bearing to estimate the spatial PSD. The proposed CSAmin processor resolves the CSA subarray spatial aliasing equally well as the product processor. For an extended aperture CSA, the CSAmin reduces the peak sidelobe height and total sidelobe area over the product processor for the same CSA geometry. Moreover, unlike the PSD estimate from the product processor, the PSD estimate from the CSAmin is guaranteed to be positive semidefinite. This paper derives the probability density function, the complementary cumulative distribution function (CCDF, or tail distribution), and the first two moments of the CSAmin PSD estimator in closed form for Gaussian sources in white Gaussian noise. Numerical simulations verify the derived CSAmin statistics and demonstrate that the CSAmin improves the performance over the product processor in detecting narrowband Gaussian sources in the presence of loud interferers and noise. The CSAmin spatial PSD estimate achieves lower variance than the product processor estimate, and keeps the PSD estimate unbiased for white Gaussian processes and asymptotically unbiased for nonwhite Gaussian processes.

30 citations


Journal ArticleDOI
TL;DR: In this article, the relative root mean squared errors (RMSE) of nonparametric methods for spectral estimation is compared for microwave scattering data of plasma fluctuations, and two new adaptive multi-taper weightings are presented.
Abstract: The relative root mean squared errors (RMSE) of nonparametric methods for spectral estimation is compared for microwave scattering data of plasma fluctuations. These methods reduce the variance of the periodogram estimate by averaging the spectrum over a frequency bandwidth. As the bandwidth increases, the variance decreases, but the bias error increases. The plasma spectra vary by over four orders of magnitude, and therefore, using a spectral window is necessary. We compare the smoothed tapered periodogram with the adaptive multiple taper methods and hybrid methods. We find that a hybrid method, which uses four orthogonal tapers and then applies a kernel smoother, performs best. For 300 point data segments, even an optimized smoothed tapered periodogram has a 24 \% larger relative RMSE than the hybrid method. We present two new adaptive multi-taper weightings which outperform Thomson's original adaptive weighting.

24 citations


Journal ArticleDOI
TL;DR: This letter presents a fast algorithm named iterative Vandermonde decomposition and shrinkage-thresholding (IVDST), which offers a low-complexity solution to atomic norm minimization (ANM) in off-grid compressed sensing for line spectral estimation from few measurements.
Abstract: This letter presents a fast algorithm named iterative Vandermonde decomposition and shrinkage-thresholding (IVDST), which offers a low-complexity solution to atomic norm minimization (ANM) in off-grid compressed sensing for line spectral estimation from few measurements. It implements the ANM principle via the accelerated proximal gradient (APG) technique, without invoking computationally expensive semidefinite programming (SDP). To approximate the proximal operator in each APG iteration, Vandermonde decomposition is applied to utilize the Toeplitz structure inherent in the line spectral model, and the low-rank property of the Toeplitz-structured matrix is enforced via a simple shrinkage-thresholding operation. The IVDST algorithm effectively reduces the order of computational complexity compared to SDP-based solutions. It also offers an explicit way to bridge the ANM principle with classic super-resolution line spectral estimation algorithms, such as MUSIC.

24 citations


Journal ArticleDOI
TL;DR: A fast IAA (FIAA)-based super-resolution DBS imaging method, taking advantage of the rich matrix structures of the classical narrow-band filtering, using the Hermitian feature of the echo autocorrelation matrix R to achieve its fast solution and uses the Toeplitz structure of R to realize its fast inversion.
Abstract: Doppler beam sharpening (DBS) is a critical technology for airborne radar ground mapping in forward-squint region. In conventional DBS technology, the narrow-band Doppler filter groups formed by fast Fourier transform (FFT) method suffer from low spectral resolution and high side lobe levels. The iterative adaptive approach (IAA), based on the weighted least squares (WLS), is applied to the DBS imaging applications, forming narrower Doppler filter groups than the FFT with lower side lobe levels. Regrettably, the IAA is iterative, and requires matrix multiplication and inverse operation when forming the covariance matrix, its inverse and traversing the WLS estimate for each sampling point, resulting in a notably high computational complexity for cubic time. We propose a fast IAA (FIAA)-based super-resolution DBS imaging method, taking advantage of the rich matrix structures of the classical narrow-band filtering. First, we formulate the covariance matrix via the FFT instead of the conventional matrix multiplication operation, based on the typical Fourier structure of the steering matrix. Then, by exploiting the Gohberg–Semencul representation, the inverse of the Toeplitz covariance matrix is computed by the celebrated Levinson–Durbin (LD) and Toeplitz-vector algorithm. Finally, the FFT and fast Toeplitz-vector algorithm are further used to traverse the WLS estimates based on the data-dependent trigonometric polynomials. The method uses the Hermitian feature of the echo autocorrelation matrix R to achieve its fast solution and uses the Toeplitz structure of R to realize its fast inversion. The proposed method enjoys a lower computational complexity without performance loss compared with the conventional IAA-based super-resolution DBS imaging method. The results based on simulations and measured data verify the imaging performance and the operational efficiency.

24 citations


Journal ArticleDOI
TL;DR: Ringh et al. as mentioned in this paper extended the results of their companion paper to handle approximate covariance matching, and showed that they are connected via a homeomorphism, which is well-posed and illustrate the theory by examples in spectral estimation and texture generation.
Abstract: In our companion paper [A. Ringh, J. Karlsson, and A. Lindquist, SIAM J. Control Optim., 54 (2016), pp. 1950--1982] we discussed the multidimensional rational covariance extension problem (RCEP), which has important applications in image processing and spectral estimation in radar, sonar, and medical imaging. This is an inverse problem where a power spectrum with a rational absolutely continuous part is reconstructed from a finite set of moments. However, in most applications these moments are determined from observed data and are therefore only approximate, and the RCEP may not have a solution. In this paper we extend the results of our companion paper to handle approximate covariance matching. We consider two problems, one with a soft constraint and the other one with a hard constraint, and show that they are connected via a homeomorphism. We also demonstrate that the problems are well-posed and illustrate the theory by examples in spectral estimation and texture generation.

Proceedings Article
Felipe Tobar1
03 Dec 2018
TL;DR: A joint probabilistic model for signals, observations and spectra is proposed, where SE is addressed as an inference problem and Bayes' rule is applied to find the analytic posterior distribution of the spectrum given a set of observations.
Abstract: Spectral estimation (SE) aims to identify how the energy of a signal (e.g., time series) is distributed across different frequencies. This is a challenging task when only partial and noisy observations are available, where current methods fail to find expressive representations of the data and handle uncertainty appropriately. In this context, we propose a joint probabilistic model for signals, observations and spectra, where SE is addressed as an inference problem. Assuming a Gaussian process prior over the signal, we apply Bayes' rule to find the analytic posterior distribution of the spectrum given a set of observations. Besides its expressiveness and natural ability to represent spectral uncertainty, the proposed model provides a functional-form estimate of the power spectral density which can be optimised efficiently. We include a comparison to previous methods for SE and validation on three experiments using synthetic and real-world data.

Proceedings ArticleDOI
01 Apr 2018
TL;DR: This paper model the noise as a spatially homogeneous sound field with an unknown time-varying PSD and a known time-invariant spatial coherence matrix and shows that the proposed blocking-based estimator yields the best performance when used in an MWF.
Abstract: Many multi-channel dereverberation and noise reduction techniques such as the multi-channel Wiener filter (MWF) require an estimate of the late reverberation and noise power spectral densities (PSDs). State-of-the-art multi-channel methods for estimating the late reverberation PSD typically assume that the noise PSD matrix is known. Instead of assuming that the noise PSD matrix is known, in this paper we model the noise as a spatially homogeneous sound field with an unknown time-varying PSD and a known time-invariant spatial coherence matrix. Based on this model, two joint estimators of the late reverberation and noise PSDs are proposed, i.e., a non-blocking-based estimator which simultaneously estimates the target signal, late reverberation, and noise PSDs, and a blocking-based estimator which first estimates the late reverberation and noise PSDs at the output of a blocking matrix aiming to block the target signal. Experimental results show that the proposed blocking-based estimator yields the best performance when used in an MWF, even resulting in a similar or better performance than a state-of-the-art blocking-based estimator of the late reverberation PSD which assumes that the noise PSD matrix is known.

Journal ArticleDOI
TL;DR: In this paper, the modified short-time Fourier transform is applied to the real signal reconstructed by the peak high-precision time-frequency amplitude spectrum and the high-frequency instantaneous phase spectrum at that location to obtain the stable high-principle time-fraction amplitude spectrum, initial and instantaneous phase spectra, and stable time-phase amplitude spectrum.
Abstract: The short-time Fourier transform allows calculation of the amplitude and initial phase distribution of the real signal as functions of time and frequency, whereas the wavelet transform allows calculation of the amplitude and instantaneous phase distribution of the real signal as functions of time and scale However, for a complete description of the non-stationary signal, we should obtain not only the amplitude, initial phase, and instantaneous phase distribution as functions of time and frequency simultaneously with high precision but also the amplitude distribution as a function of time and phase referred to as the time–phase amplitude spectrum In this paper, the time–phase amplitude spectrum is presented based on the high-precision time–frequency amplitude spectrum and initial and instantaneous phase spectra that are generated simultaneously by the proposed modified short-time Fourier transform To minimise the effect of noise on the high-precision time–frequency amplitude spectrum, initial and instantaneous phase spectra, and time–phase amplitude spectrum, the modified short-time Fourier transform is applied to the real signal reconstructed by the peak high-precision time–frequency amplitude spectrum and the high-precision time–frequency instantaneous phase spectrum at that location to obtain the stable high-precision time–frequency amplitude spectrum, initial and instantaneous phase spectra, and stable time–phase amplitude spectrum Compared with the short-time Fourier transform and wavelet transform, the time–frequency amplitude spectrum and initial and instantaneous phase spectra obtained by the modified short-time Fourier transform have higher precision than those obtained by the short-time Fourier transform and wavelet transform Analysis of synthetic data shows that the modified short-time Fourier transform can be used not only for the calculation of the high-precision time–frequency amplitude spectrum, initial and instantaneous phase spectra, and time–phase amplitude spectrum but also for signal reconstruction, stable high-precision time–frequency amplitude spectrum, initial and instantaneous phase spectra, and stable time–phase amplitude spectrum Analysis of real seismic data applications demonstrates that the stable time–phase amplitude spectrum reveals seismic events with high sensitivity and is well-matched for seismic data processing and interpretation

Journal ArticleDOI
TL;DR: In this paper, the authors provide a detailed analysis of the global convergence properties of an extensively studied and extremely effective fixed-point algorithm for the Kullback-Leibler approximation of spectral densities, proposed by Pavon and Ferrante in their paper.
Abstract: In this paper, we provide a detailed analysis of the global convergence properties of an extensively studied and extremely effective fixed-point algorithm for the Kullback–Leibler approximation of spectral densities, proposed by Pavon and Ferrante in their paper “On the Georgiou–Lindquist approach to constrained Kullback–Leibler approximation of spectral densities.” Our main result states that the algorithm globally converges to one of its fixed points.

Journal ArticleDOI
TL;DR: It is shown how the asymmetry of QRS complexes in various channels of an ECG signal could be modeled accurately, and an application of the proposed discrete FrH methodology on real electrocardiogram (ECG) signals in the presence of noise is demonstrated.
Abstract: We consider sampling and reconstruction of finite-rate-of-innovation (FRI) signals such as a train of pulses, where the pulses have varying degrees of asymmetry. We address the problem of asymmetry modeling starting from a given symmetric prototype. We show that among the class of unitary operators that are linear and invariant to translation and scale, the fractional Hilbert (FrH) operator is unique for parametrically modeling pulse asymmetry. The FrH operator is obtained by a trigonometric interpolation between the standard Hilbert and identity operators, where the interpolation weights are determined by the degree of asymmetry. The FrH operators are also steerable , which allows for estimation of the asymmetry factors, in addition to the delays and amplitudes, using the high-resolution spectral estimation techniques that are used for solving standard FRI problems. We also develop the discrete counterpart using discrete FrH operators and show that all the desirable properties carry over smoothly to the discrete setting as well. We derive closed-form expressions for the Cramer–Rao bounds and Hammersley–Chapman–Robbins bound, on the variances of the estimators for continuous and discrete parameters, respectively. Experimental results show that the proposed estimators have variances that meet the lower bounds. We demonstrate an application of the proposed discrete FrH methodology on real electrocardiogram (ECG) signals in the presence of noise. Specifically, we show how the asymmetry of QRS complexes in various channels of an ECG signal could be modeled accurately.

Journal ArticleDOI
TL;DR: An improved method to detect the presence of such noncoherently sampled signals as well as an iterative algorithm to obtain accurate approximations of all the frequency components with their accompanying amplitudes and phase angles is proposed.
Abstract: Time-domain near-field scanning is gaining more and more interest within EMC engineering to analyze electromagnetic near-fields of, eg, quasi-stationar devices When using a digital oscilloscope to scan the near-fields of an electronic device, the oscilloscope measures time-domain signals that comprise in most cases a large number of frequency components For many of these components, noncoherent sampling occurs, resulting in spectral leakage when calculating the frequency spectrum of the time-domain signals with the discrete Fourier transform This paper proposes an improved method to detect the presence of such noncoherently sampled signals as well as an iterative algorithm to obtain accurate approximations of all the frequency components with their accompanying amplitudes and phase angles The algorithm excels over existing algorithms in obtaining these values especially in situations where several sinusoidal components are close to each other in the spectrum This is achieved, thanks to an iterative process of removing the influence of the multiple sinusoidal components on each other This paper contains the mathematical description of the algorithm and a numerical example evaluating the accuracy of the algorithm The algorithm has a higher accuracy than the existing approaches, eg, multipoint Interpolated Discrete Fourier Transform (IpDFTs), with only a slight increase of the computational cost

Journal ArticleDOI
TL;DR: Two algorithms are proposed, which adaptively learn the number of sources and estimate their locations and the relationship between the source localization problem and the problem of computing the greatest common divisor (GCD), or more practically approximate GCD, for polynomials.
Abstract: Source localization and spectral estimation are among the most fundamental problems in statistical and array signal processing. Methods that rely on the orthogonality of the signal and noise subspaces, such as Pisarenko's method, MUSIC, and root-MUSIC, are some of the most widely used algorithms to solve these problems. As a common feature, these methods require both a priori knowledge of the number of sources and an estimate of the noise subspace. Both requirements are complicating factors to the practical implementation of the algorithms and, when not satisfied exactly, can potentially lead to severe errors. In this paper, we propose a new localization criterion based on the algebraic structure of the noise subspace that is described for the first time to the best of our knowledge. Using this criterion and the relationship between the source localization problem and the problem of computing the greatest common divisor (GCD), or more practically approximate GCD, for polynomials, we propose two algorithms, which adaptively learn the number of sources and estimate their locations. Simulation results show a significant improvement over root-MUSIC in challenging scenarios such as closely located sources, both in terms of detection of the number of sources and their localization over a broad and practical range of signal-to-noise ratios. Furthermore, no performance sacrifice in simple scenarios is observed.

Journal ArticleDOI
TL;DR: In this article, a spectral density-driven bootstrap for time series is proposed, which uses the entire sequence of estimated moving average coefficients together with appropriately generated pseudoinnovations to obtain a bootstrap pseudo-time series.
Abstract: The second‐order dependence structure of purely non‐deterministic stationary processes is described by the coefficients of the famous Wold representation. These coefficients can be obtained by factorizing the spectral density of the process. This relationship together with some spectral density estimator is used to obtain consistent estimators of these coefficients. A spectral‐density‐driven bootstrap for time series is then developed which uses the entire sequence of estimated moving average coefficients together with appropriately generated pseudoinnovations to obtain a bootstrap pseudo‐time‐series. It is shown that if the underlying process is linear and if the pseudoinnovations are generated by means of an independent and identically distributed wild bootstrap which mimics, to the extent necessary, the moment structure of the true innovations, this bootstrap proposal asymptotically works for a wide range of statistics. The relationships of the proposed bootstrap procedure to some other bootstrap procedures, including the auto‐regressive sieve bootstrap, are discussed. It is shown that the latter is a special case of the spectral‐density‐driven bootstrap, if a parametric auto‐regressive spectral density estimator is used. Simulations investigate the performance of the new bootstrap procedure in finite sample situations. Furthermore, a real life data example is presented.

Book ChapterDOI
01 Jan 2018
TL;DR: This chapter reviews recent advances in extending the notion of stationarity to random graph signals and introduces the concept of power spectral density for graph processes and proposes a number of methods for its estimation.
Abstract: Stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain. Although time-varying signals are abundant in nature, in many contemporary applications the information of interest resides in more irregular domains that can be conveniently represented using a graph. This chapter reviews recent advances in extending the notion of stationarity to random graph signals. This is a challenging task due to the irregularity of the underlying graph domain. To that end, we start by presenting coexisting stationarity definitions along with explanations of their genesis, advantages, and disadvantages. Second, we introduce the concept of power spectral density for graph processes and propose a number of methods for its estimation. These methods include nonparametric approaches such as correlograms and windowed average periodograms as well as parametric approaches. To account for distributed scenarios where the supporting graph is related to an actual network infrastructure, the last part of the chapter discusses how to estimate the power spectral density of a graph process when having access to only a subset of the nodes. To gain intuition and insights, the concepts and schemes presented throughout the chapter are illustrated with a running example based on a real-world social graph.

Proceedings ArticleDOI
01 Nov 2018
TL;DR: In this work, discrete wavelet transform (DWT) is considered for preprocessing step, Hilbert transform has been used for spectral estimation for the step of extracting features, and principal component analysis (PCA) is adopted for reducing feature vectors.
Abstract: The analysis of Electrocardiogram (ECG) signal is very cumbersome due to its non-stationary nature. ECG signal is the combination of P-wave, QRS-wave and T-wave. R-peaks detection is very important for classifying heart diseases in QRS-wave. R-peaks detection is not easy task due to the involvement of various types of noises and large length of data sets. In this work, discrete wavelet transform (DWT) is considered for preprocessing step. Hilbert transform has been used for spectral estimation for the step of extracting features. Finally, principal component analysis (PCA) is adopted for reducing feature vectors. R-peaks have been detected from reduced features on the basis of calculating the variance of principal components (PCs). The detection sensitivity (SE), positive predictivity (PP), F-measure (F-m) and mean squared error(MSE) are estimated for evaluating the performance of the proposed technique. It gave 99.88% SE, 99.88% PP, 99.88 % F-m, and 0.0766 MSE.

Proceedings ArticleDOI
15 Apr 2018
TL;DR: This paper evaluates one new and some of the existing and commonly used noise PSD estimation algorithms in terms of the spectral estimation accuracy and the enhancement performance for different commonly encountered background noises, which are stationary and non-stationary in nature.
Abstract: The estimation of the noise power spectral density (PSD) forms a critical component of several existing single channel speech enhancement systems In this paper, we evaluate one new and some of the existing and commonly used noise PSD estimation algorithms in terms of the spectral estimation accuracy and the enhancement performance for different commonly encountered background noises, which are stationary and non-stationary in nature The evaluated algorithms include the Minimum Statistics, MMSE, IMCRA methods and a new model-based method

Posted Content
TL;DR: This work uses a reference spectrum as provided by a hyperspectral image camera, and proposes efficient deep learning solutions for sensitivity function estimation and spectral reconstruction from a single RGB image.
Abstract: In contrast to the current literature, we address the problem of estimating the spectrum from a single common trichromatic RGB image obtained under unconstrained settings (e.g. unknown camera parameters, unknown scene radiance, unknown scene contents). For this we use a reference spectrum as provided by a hyperspectral image camera, and propose efficient deep learning solutions for sensitivity function estimation and spectral reconstruction from a single RGB image. We further expand the concept of spectral reconstruction such that to work for RGB images taken in the wild and propose a solution based on a convolutional network conditioned on the estimated sensitivity function. Besides the proposed solutions, we study also generic and sensitivity specialized models and discuss their limitations. We achieve state-of-the-art competitive results on the standard example-based spectral reconstruction benchmarks: ICVL, CAVE, NUS and NTIRE. Moreover, our experiments show that, for the first time, accurate spectral estimation from a single RGB image in the wild is within our reach.

Proceedings ArticleDOI
14 Apr 2018
TL;DR: The possibility of extending the detection range of FMCW LIDAR beyond the coherence range of its laser by improving the spectral estimation algorithm by exploiting the Lorentzian prior of the received signal in the spectral domain is demonstrated.
Abstract: Frequency-modulated continuous-wave (FMCW) LIDAR is a promising technology for next-generation integrated 3D imaging systems. However, it has been considered difficult to apply FMCW LIDAR for long-distance (> 100m) targets, such as those in automotive and airborne applications. Maintaining coherence between the reflected beam from the target and locally forwarded beam becomes a significant challenge for tunable laser design. This paper demonstrates the possibility of extending the detection range of FMCW LIDAR beyond the coherence range of its laser by improving the spectral estimation algorithm. By exploiting the Lorentzian prior of the received signal in the spectral domain, > 10x improvement in ranging accuracy is achieved compared to traditional algorithms that do not consider phase noise in the signal model. In light of this finding, the end-to-end modeling framework is presented to examine true system-level trade-offs of FMCW LIDAR and the feasibility of long -distance measurement.

Proceedings ArticleDOI
29 Nov 2018
TL;DR: Non-parametric spectral estimation techniques are shown to be able to detect an alteration in an audio recording, where a short utterance recorded in Europe is replaced by the same content recorded in the US.
Abstract: The Electric Network Frequency (ENF) criterion provides useful forensic evidence for multimedia authentication. In this paper, a systematic study of non-parametric and parametric spectral estimation methods is conducted for ENF extraction. Fast implementations of the Capon method and the Iterative Adaptive Approach, which exploit the Gohberg-Semencul factorization of the inverse covariance matrix, are included as well. When long segments are used, a very high matching accuracy is achieved. That is, the maximum correlation-coefficient between the extracted ENF and the ground truth may exceed 99%. Similarly, the standard deviation of error maybe as small as 1.069 · 10-3. Non-parametric spectral estimation techniques are shown to be able to detect an alteration in an audio recording, where a short utterance recorded in Europe is replaced by the same content recorded in the US.

Journal ArticleDOI
TL;DR: This parametric spectral estimation achieved a 5-fold improvement in the frequency resolution compared with Fourier-based methods, and revealed previously unresolved frequency information that led to over 80% correct signal classification for linear and non-linear echo signals.
Abstract: Ultrasound contrast imaging (UCI) aims to detect flow changes in the vascular bed that can help differentiate normal from diseased tissues thus providing an early screening tool for diagnosis or treatment monitoring. Ultrasound contrast agents (UCAs), used in UCI, are microbubbles that scatter ultrasound non-linearly. To date the signal processing research has successfully subtracted signals from the linear response of tissue (linear signals), but, in general, has not provided a sensitive detection that is specific to the UCA signal. This paper develops a method for the temporal and spectral estimation of linear and non-linear ultrasound echo signals. This technique is based on non-parametric methods for coarse estimation, followed by a parametric method within a Bayesian framework for estimation refinement. The results show that the pulse location can be estimated to within ±3 sample points accuracy for signals consisting of ≈ 80 sample points depending on the signal type, while the frequency content can be estimated to within 0.050 MHz deviations for frequencies in the 1 to 4 MHz range. This parametric spectral estimation achieved a 5-fold improvement in the frequency resolution compared with Fourier-based methods, and revealed previously unresolved frequency information that led to over 80% correct signal classification for linear and non-linear echo signals.

Journal ArticleDOI
TL;DR: The results show that the ISAF improves the CFT method in estimating ocean wave spectra, and a filter referred to as the inverse sampling averaging filter (ISAF) is proposed to be integrated with the C FT method in order to mitigate the effect of the sampling process.
Abstract: In this paper, the effect of the ocean surface sampling process on the ocean wave spectral estimation using the Cartesian Fourier transform (CFT) method on $X$ -band marine radar data is investigated. Our analysis shows that the ocean surface sampling process involves a spatial averaging process that might be described as a 2-D low pass filter. Furthermore, a filter referred to as the inverse sampling averaging filter (ISAF) is proposed to be integrated with the CFT method in order to mitigate the effect of the sampling process. For validation, the CFT-with-ISAF method as well as the CFT-without-ISAF method were used to estimate ocean wave spectra and sea state parameters from $X$ -band marine radar field data. The estimates from both methods were compared to ground truth estimates generated using TRIAXYS wave buoy data. The results show that the ISAF improves the CFT method in estimating ocean wave spectra. The recorded accuracy improvements in estimating the non-directional wave spectrum, the peak wave period, the mean wave period, the zero-crossing wave period, and the peak wave direction were 11%, 12%, 21%, 17%, and 34%, respectively. The performances of significant wave height estimation using the ISAF method and the standard CFT method were validated against ground truth estimates and found to be comparable.

Posted Content
TL;DR: This paper studied from one-bit quantized samples where variational line spectral estimation (VALSE) combined expectation propagation (EP) VALSE-EP method is proposed and can be easily extended to solve the LSE with the multiple measurement vectors (MMVs).
Abstract: In this paper, the line spectral estimation (LSE) problem is studied from one-bit quantized samples where variational line spectral estimation (VALSE) combined expectation propagation (EP) VALSE-EP method is proposed. Since the original measurements are heavily quantized, performing the off-grid frequency estimation is very challenging. Referring to the expectation propagation (EP) principle, this quantized model is decomposed as two modules, one is the componentwise minimum mean square error (MMSE) module, the other is the standard linear model where the variational line spectrum estimation (VALSE) algorithm can be performed. The VALSE-EP algorithm iterates between the two modules in a turbo manner. In addition, this algorithm can be easily extended to solve the LSE with the multiple measurement vectors (MMVs). Finally, numerical results demonstrate the effectiveness of the proposed VALSE-EP method.

Posted Content
TL;DR: An efficient grid-less Bayesian algorithm named VALSE-EP is proposed, which is a combination of the high resolution and low complexity gridless variational line spectral estimation (VALSE) and expectation propagation (EP).
Abstract: Efficient estimation of line spectral from quantized samples is of significant importance in information theory and signal processing, e.g., channel estimation in energy efficient massive MIMO systems and direction of arrival estimation. The goal of this paper is to recover the line spectral as well as its corresponding parameters including the model order, frequencies and amplitudes from heavily quantized samples. To this end, we propose an efficient grid-less Bayesian algorithm named VALSE-EP, which is a combination of the variational line spectral estimation (VALSE) and expectation propagation (EP). The basic idea of VALSE-EP is to iteratively approximate the challenging quantized model of line spectral estimation as a sequence of simple pseudo unquantized models so that the VALSE can be applied. Note that the noise in the pseudo linear model is heteroscedastic, i.e., different components having different variances, and a variant of the VALSE is re-derived to obtain the final VALSE-EP. Moreover, to obtain a benchmark performance of the proposed algorithm, the Cramer Rao bound (CRB) is derived. Finally, numerical experiments on both synthetic and real data are performed, demonstrating the near CRB performance of the proposed VALSE-EP for line spectral estimation from quantized samples.

Journal ArticleDOI
TL;DR: In vivo results demonstrated that the Capon estimator can provide spectral estimates with sufficient quality for quantitative analysis using packet-based CFI acquisitions.
Abstract: Interleaved acquisitions used in conventional triplex mode result in a tradeoff between the frame rate and the quality of velocity estimates. On the other hand, workflow becomes inefficient when the user has to switch between different modes, and measurement variability is increased. This paper investigates the use of power spectral Capon estimator in quantitative Doppler analysis using data acquired with conventional color flow imaging (CFI) schemes. To preserve the number of samples used for velocity estimation, only spatial averaging was utilized, and clutter rejection was performed after spectral estimation. The resulting velocity spectra were evaluated in terms of spectral width using a recently proposed spectral envelope estimator. The spectral envelopes were also used for Doppler index calculations using in vivo and string phantom acquisitions. In vivo results demonstrated that the Capon estimator can provide spectral estimates with sufficient quality for quantitative analysis using packet-based CFI acquisitions. The calculated Doppler indices were similar to the values calculated using spectrograms estimated on a commercial ultrasound scanner.