Showing papers on "Spectral density estimation published in 2020"

DeepMMSE: A Deep Learning Approach to MMSE-Based Noise Power Spectral Density Estimation

Abstract: An accurate noise power spectral density (PSD) tracker is an indispensable component of a single-channel speech enhancement system. Bayesian-motivated minimum mean-square error (MMSE)-based noise PSD estimators have been the most prominent in recent time. However, they lack the ability to track highly non-stationary noise sources due to current methods of a priori signal-to-noise (SNR) estimation. This is caused by the underlying assumption that the noise signal changes at a slower rate than the speech signal. As a result, MMSE-based noise PSD trackers exhibit a large tracking delay and produce noise PSD estimates that require bias compensation. Motivated by this, we propose an MMSE-based noise PSD tracker that employs a temporal convolutional network (TCN) a priori SNR estimator. The proposed noise PSD tracker, called DeepMMSE makes no assumptions about the characteristics of the noise or the speech, exhibits no tracking delay, and produces an accurate estimate that requires no bias correction. Our extensive experimental investigation shows that the proposed DeepMMSE method outperforms state-of-the-art noise PSD trackers and demonstrates the ability to track abrupt changes in the noise level. Furthermore, when employed in a speech enhancement framework, the proposed DeepMMSE method is able to outperform state-of-the-art noise PSD trackers, as well as multiple deep learning approaches to speech enhancement. Availability: DeepMMSE is available at: https://github.com/anicolson/DeepXi .

Deep-inverse correlography: towards real-time high-resolution non-line-of-sight imaging

Abstract: Low signal-to-noise ratio (SNR) measurements, primarily due to the quartic attenuation of intensity with distance, are arguably the fundamental barrier to real-time, high-resolution, non-line-of-sight (NLoS) imaging at long standoffs. To better model, characterize, and exploit these low SNR measurements, we use spectral estimation theory to derive a noise model for NLoS correlography. We use this model to develop a speckle correlation-based technique for recovering occluded objects from indirect reflections. Then, using only synthetic data sampled from the proposed noise model, and without knowledge of the experimental scenes nor their geometry, we train a deep convolutional neural network to solve the noisy phase retrieval problem associated with correlography. We validate that the resulting deep-inverse correlography approach is exceptionally robust to noise, far exceeding the capabilities of existing NLoS systems both in terms of spatial resolution achieved and in terms of total capture time. We use the proposed technique to demonstrate NLoS imaging with 300 µm resolution at a 1 m standoff, using just two 1/8th ${s}$s exposure-length images from a standard complementary metal oxide semiconductor detector.

A perceptually motivated approach for low-complexity, real-time enhancement of fullband speech

Abstract: Over the past few years, speech enhancement methods based on deep learning have greatly surpassed traditional methods based on spectral subtraction and spectral estimation. Many of these new techniques operate directly in the the short-time Fourier transform (STFT) domain, resulting in a high computational complexity. In this work, we propose PercepNet, an efficient approach that relies on human perception of speech by focusing on the spectral envelope and on the periodicity of the speech. We demonstrate high-quality, real-time enhancement of fullband (48 kHz) speech with less than 5% of a CPU core.

A Perceptually-Motivated Approach for Low-Complexity, Real-Time Enhancement of Fullband Speech

Abstract: Over the past few years, speech enhancement methods based on deep learning have greatly surpassed traditional methods based on spectral subtraction and spectral estimation. Many of these new techniques operate directly in the the short-time Fourier transform (STFT) domain, resulting in a high computational complexity. In this work, we propose PercepNet, an efficient approach that relies on human perception of speech by focusing on the spectral envelope and on the periodicity of the speech. We demonstrate high-quality, real-time enhancement of fullband (48 kHz) speech with less than 5% of a CPU core.

Remote Measurement of Human Vital Signs Based on Joint-Range Adaptive EEMD

Abstract: Remote techniques for measuring human vital signs have attracted great interests due to the benefits shown in medical monitoring and military applications. Compared with continuous-wave Doppler radar, frequency-modulated continuous-wave (FMCW) radar which can discriminate vital signs from different distances, shows potential for reducing the interferences from other targets and the environment. However, in the state-of-the-art algorithms, only one chirp per frame is utilized for FMCW-based vital sign monitoring. Moreover, the vital signal is extracted from only one range bin of the fast Fourier transform. Which does not make full utilization of the long system idle time, and loses the power distributed on other range bins. By exploiting the relationship between respiration and heartbeat vibrations, an adaptive identification embedded ensemble empirical mode decomposition (EEMD) method for joint-range spectral estimation is proposed to measure the heart rate. First, A multi-chirp processing is presented for a 2-dimensional phase accumulation. Then the phase signals from a sequence of range bins are decomposed with a fast adaptive identification process. Finally, with the identified heartbeat components, we solve a multiple measurement vectors problem to estimate the heart rate. Experimental results showed that, at the detection range from 1 m~ 2.5 m, the proposed method can robustly distinguish the heartbeat from respiration and its harmonics and accurately estimate the heart rate with a root mean square error less than 6 bpm.

On the Well-Posedness of a Parametric Spectral Estimation Problem and Its Numerical Solution

Abstract: This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a solution can be based on prior functions. We show that the problem is well-posed when formulated in a parametric fashion, and that the solution parameter depends continuously on the prior function. In this way, we are able to obtain a smooth parametrization of admissible spectral densities. Based on this result, the problem is reparametrized via a bijective change of variables out of a numerical consideration, and then a continuation method is used to compute the unique solution parameter. Numerical aspects, such as convergence of the proposed algorithm and certain computational procedures are addressed. A simple example is provided to show the effectiveness of the algorithm.

Simultaneous Spectral Estimation of Dephasing and Amplitude Noise on a Qubit Sensor via Optimally Band-Limited Control

Abstract: The fragility of quantum systems makes them ideally suited for sensing applications at the nanoscale. However, interpreting the output signal of a qubit-based sensor is generally complicated by background clutter due to out-of-band spectral leakage, as well as ambiguity in signal origin when the sensor is operated with noisy hardware. We present a sensing protocol based on optimally band-limited ``Slepian functions'' that can overcome these challenges, by providing narrowband sensing of ambient dephasing noise, coupling additively to the sensor along the $z$ axis, while permitting isolation of the target noise spectrum from other contributions coupling along a different axis. This is achieved by introducing a finite-difference control modulation, which linearizes the sensor's response and affords tunable band-limited ``windowing'' in frequency. Building on these techniques, we experimentally demonstrate two spectral estimation capabilities using a trapped-ion qubit sensor. We first perform efficient experimental reconstruction of a ``mixed'' dephasing spectrum, composed of a broadband $1/f$-type spectrum with discrete spurs. We then demonstrate the simultaneous reconstruction of overlapping dephasing and control noise spectra from a single set of measurements, in a setting where the two noise sources contribute equally to the sensor's response. Our approach provides a direct means to augment quantum-sensor performance in the presence of both complex broadband noise environments and imperfect control signals, by optimally complying with realistic time-bandwidth constraints.

Gravitational-wave astronomy with an uncertain noise power spectral density

Abstract: In order to extract information about the properties of compact binaries, we must estimate the noise power spectral density of gravitational-wave data, which depends on the properties of the gravitational-wave detector. In practice, it is not possible to know this perfectly, only to estimate it from the data. Multiple estimation methods are commonly used and each has a corresponding statistical uncertainty. However, this uncertainty is widely ignored when measuring the physical parameters describing compact binary coalescences, and the appropriate likelihoods which account for the uncertainty are not well known. In order to perform increasingly precise astrophysical inference and model selection, it will be essential to account for this uncertainty. In this work, we derive the correct likelihood for one of the most widely used estimation methods in gravitational-wave transient analysis, the median average. We demonstrate that simulated Gaussian noise follows the predicted distributions. We then examine real gravitational-wave data at and around the time of GW151012, a relatively low-significance binary black hole merger event. We show that the data are well described by stationary-Gaussian noise and explore the impact of different noise power spectral density estimation methods on the astrophysical inferences we draw about GW151012.

Three-Dimensional Terahertz Continuous Wave Imaging Radar for Nondestructive Testing

Abstract: In recent years, our research group has been devoting substantial efforts to the research and development of active all-solid-state electronic terahertz (THz) continuous wave imaging systems for nondestructive testing, which is currently benefitting from the increasing amount of transmitting power, high performance/cost ratio and adaptability to engineering. In this paper, an in-house developed broadband linear frequency modulated continuous wave (LFMCW) three-dimensional (3D) THz imaging system is described, and two sets of experimental platforms are set up to assist the planning and completion of the research, including a narrow-band LFMCW 3D imaging radar and a wide-band stepped-frequency modulated continuous wave 3D imaging radar. For 3D imaging systems, to cope with demanding scenarios and to achieve excellent imaging performance, various reconstruction algorithms are explored. The first is a spectral refinement and correction approach based on fast Fourier transform and modern spectral estimation for accurate thickness measurement. The second is the synthetic aperture radar imaging algorithm for surface detection or internal detection of objects with lower refractive index. The third is a 3D reconstruction algorithm based on half space Green's function and the exploding source model for the interior detection of materials with higher refractive index. The fourth is the frequency interference algorithm combining phase unwrapping to measure uneven and nonplanar surfaces. Exploiting these systems, along with the associated experimental platforms and reconstruction algorithms, we successfully implemented non-destructive testing for objects with various defects and of different materials, such as polymer boards with voids, and foam with inclusions.

A Time-Based Sampling Framework for Finite-Rate-of-Innovation Signals

Abstract: Time-based sampling of continuous-time signals is an alternative to Shannon’s sampling paradigm in which the signal is encoded using a sequence of nonuniform time instants. The standard methods for reconstructing signals in bandlimited and shift-invariant spaces from their nonuniform measurements employ alternating projections algorithms. In this paper, we consider the problem of sampling and perfect reconstruction of periodic finite-rate-of-innovation (FRI) signals using crossing-time-encoding machine (C-TEM) and integrate-and-fire TEM (IF-TEM). We formulate the reconstruction problem in the frequency domain and develop techniques to compute the Fourier coefficients, which contain the unknown parameters of the signal in the form of a sum of weighted complex exponentials. The parameters are then estimated using high-resolution spectral estimation techniques. Unlike state-of-the-art methods, the proposed method is generalized to incorporate reconstruction of periodic FRI signals consisting of weighted and shifted versions of an arbitrary pulse with arbitrarily close delays, and is compatible with a large class of sampling kernels. We provide sufficient conditions for sampling and perfect reconstruction using C-TEM and IF-TEM. We present simulation results to support our claims. We also discuss an extension to the sampling of aperiodic FRI signals.

Average-case Acceleration Through Spectral Density Estimation

Abstract: We develop a framework for the average-case analysis of random quadratic problems and derive algorithms that are optimal under this analysis. This yields a new class of methods that achieve acceleration given a model of the Hessian's eigenvalue distribution. We develop explicit algorithms for the uniform, Marchenko-Pastur, and exponential distributions. These methods are momentum-based algorithms, whose hyper-parameters can be estimated without knowledge of the Hessian's smallest singular value, in contrast with classical accelerated methods like Nesterov acceleration and Polyak momentum. Through empirical benchmarks on quadratic and logistic regression problems, we identify regimes in which the the proposed methods improve over classical (worst-case) accelerated methods.

Time-Frequency Analysis Based on Minimum-Norm Spectral Estimation to Detect Induction Motor Faults

Abstract: In this work, a new time-frequency tool based on minimum-norm spectral estimation is introduced for multiple fault detection in induction motors. Several diagnostic techniques are available to identify certain faults in induction machines; however, they generally give acceptable results only for machines operating under stationary conditions. Induction motors rarely operate under stationary conditions as they are constantly affected by load oscillations, speed waves, unbalanced voltages, and other external conditions. To overcome this issue, different time-frequency analysis techniques have been proposed for fault detection in induction motors under non-stationary regimes. However, most of them have low-resolution, low-accuracy or both. The proposed method employs the minimum-norm spectral estimation to provide high frequency resolution and accuracy in the time-frequency domain. This technique exploits the advantages of non-stationary conditions, where mechanical and electrical stresses in the machine are higher than in stationary conditions, improving the detectability of fault components. Numerical simulation and experimental results are provided to validate the effectiveness of the method in starting current analysis of induction motors.

Reconstruction of Fri Signals Using Deep Neural Network Approaches

Abstract: Finite Rate of Innovation (FRI) theory considers sampling and reconstruction of classes of non-bandlimited continuous signals that have a small number of free parameters, such as a stream of Diracs. The task of reconstructing FRI signals from discrete samples is often transformed into a spectral estimation problem and solved using Prony’s method and matrix pencil method which involve estimating signal subspaces. They achieve an optimal performance given by the Cramer-Rao bound yet break down at a certain peak signal-to-´ noise ratio (PSNR). This is probably due to the so-called subspace swap event. In this paper, we aim to alleviate the subspace swap problem and investigate alternative approaches including directly estimating FRI parameters using deep neural networks and utilising deep neural networks as denoisers to reduce the noise in the samples. Simulations show significant improvements on the breakdown PSNR over existing FRI methods, which still outperform learning-based approaches in medium to high PSNR regimes.

Separable Estimation of Ambient Noise Spectrum in Synchrophasor Measurements in the Presence of Forced Oscillations

Abstract: The ambient noise in synchrophasor measurements carries core dynamic signatures of a power system and its spectrum can strongly reflect the dynamic properties and operating conditions of the system and its loads. Typically, the ambient noise spectrum is estimated from a window of measurements captured during steady state operating conditions of the system. The presence of any Forced Oscillation (FO) in the measurement window severely biases the estimated ambient noise spectrum. In this article, an algorithm is proposed for separable estimation of the ambient noise spectrum in the presence of periodic FOs in synchrophasor measurements. The algorithm utilizes the Thomson's multitaper spectral estimation and harmonic analysis techniques and is capable of effectively reducing the bias in estimating the ambient noise spectrum due to the presence of FOs in the measurements. The performance of the estimator is analyzed theoretically and the theoretical results are verified experimentally using simulation studies. Application of the algorithm to field measured data illustrates that the algorithm is capable of effectively reducing the bias introduced by FOs in estimating the ambient noise spectrum from the synchrophasor measurements containing both ambient noise and FOs.

A Theory of Computational Resolution Limit for Line Spectral Estimation

Abstract: Line spectral estimation is a classical signal processing problem that aims to estimate the line spectra from their signal which is contaminated by deterministic or random noise. Despite a large body of research on this subject, the theoretical understanding of this problem is still elusive. In this paper, we introduce and quantitatively characterize the two resolution limits for the line spectral estimation problem under deterministic noise: one is the minimum separation distance between the line spectra that is required for exact detection of their number, and the other is the minimum separation distance between the line spectra that is required for a stable recovery of their supports. The quantitative results imply a phase transition phenomenon in each of the two recovery problems, and also the subtle difference between the two. We further propose a sweeping singular-value-thresholding algorithm for the number detection problem and conduct numerical experiments. The numerical results confirm the phase transition phenomenon in the number detection problem.

ADMM–Net: A Deep Learning Approach for Parameter Estimation of Chirp Signals Under Sub-Nyquist Sampling

Abstract: Parameter estimation of chirp signals plays an important role in the field of radar countermeasures. Compressed sensing (CS) based sub-Nyquist sampling and parameter estimation methods alleviates the pressure on hardware systems to acquire and process chirp signals with large time-bandwidths. In this paper, a framework based on the fractional Fourier transform (FrFT) and alternating direction method of multipliers network (ADMM-Net) is proposed to realize chirp signal parameter estimation under sub-Nyquist sampling. The whole framework is composed of multiple parallel ADMM-Nets, where each ADMM-Net is defined over a data flow graph, which is derived from the iterative procedures of the ADMM algorithm for optimizing a CS-based $p$ -order FrFT spectral estimation model. The chirp rate and central frequency of chirp signals are obtained through a two-dimensional search on the spectrum image output by the network group. Experiments demonstrate that the proposed ADMM-Net-based method can achieve higher estimation accuracy and computational efficiency at lower signal-to-noise ratios and sampling ratios than traditional CS methods. We also demonstrate that the proposed ADMM-Net-based framework has strong generalization ability for multi-component chirp signals. Furthermore, we further generalize ADMM-Net to GADMM-Net, in which the activation function is data-driven instead of model-driven. Experiments demonstrate that GADMM-Net significantly improves on the basic ADMM-Net and achieves higher spectral resolution with faster computation speed.

M$^2$-Spectral Estimation: A Flexible Approach Ensuring Rational Solutions.

Abstract: This paper concerns a spectral estimation problem for multivariate (i.e., vector-valued) signals defined on a multidimensional domain, abbreviated as M$^2$. The problem is posed as solving a finite number of trigonometric moment equations for a nonnegative matricial measure, which is well known as the \emph{covariance extension problem} in the literature of systems and control. This inverse problem and its various generalizations have been extensively studied in the past three decades, and they find applications in diverse fields such as modeling and system identification, signal and image processing, robust control, circuit theory, etc. In this paper, we address the challenging M$^2$ version of the problem, and elaborate on a solution technique via convex optimization with the $\tau$-divergence family. In particular, we show that by properly choosing the parameter of the divergence index, the optimal spectrum is a rational function, that is, the solution is a spectral density which can be represented by a finite dimensional system, as desired in many practical applications.

Gravitational-wave astronomy with an uncertain noise power spectral density

Abstract: In order to extract information about the properties of compact binaries, we must estimate the noise power spectral density of gravitational-wave data, which depends on the properties of the gravitational-wave detector. In practice, it is not possible to know this perfectly, only to estimate it from the data. Multiple estimation methods are commonly used and each has a corresponding statistical uncertainty. However, this uncertainty is widely ignored when measuring the physical parameters describing compact binary coalescences, and the appropriate likelihoods which account for the uncertainty are not well known. In order to perform increasingly precise astrophysical inference and model selection, it will be essential to account for this uncertainty. In this work, we derive the correct likelihood for one of the most widely used estimation methods in gravitational-wave transient analysis, the median average. We demonstrate that simulated Gaussian noise follows the predicted distributions. We then examine real gravitational-wave data at and around the time of GW151012, a relatively low-significance binary black hole merger event. We show that the data are well described by stationary-Gaussian noise and explore the impact of different noise power spectral density estimation methods on the astrophysical inferences we draw about GW151012.

High-Resolution Power Spectral Estimation Method Using Deconvolution

Abstract: Spectral analysis is a significant technique applied in many fields to infer the signal spectral contents. However, the frequency resolution of a signal spectrum estimation result is limited by its finite data length, especially when using a Fourier-based method. Extra processing gain [i.e., signal-to-noise ratio (SNR) improvement] is always required for weak target detection. In this paper, a high-resolution spectrum estimation method using a deconvolution algorithm is proposed. According to classical spectral analysis, a power spectrum derived from a finite data length is related to the convolution of the true power spectrum from an infinite length data set with the power spectrum from a window function. Therefore, using a deconvolution algorithm on the power spectrum estimated by classical spectral analysis can remove the influence from the window function, such as spectral leakage. The deconvolved power spectrum can robustly obtain a sufficiently high-frequency resolution and low sidelobes with relatively few calculations. The proposed method can also provide a deconvolution gain, which plays an important role in weak signal detection as it is capable of enhancing the signal and reducing background noise. Its performance is analyzed in simulations as well as with measured experimental data.

On Quantized Analog Compressive Sensing Methods for Efficient Resonator Frequency Estimation

Abstract: In many applications such as gravimetric sensing, there is a need to rapidly estimate the center resonant frequency of the sensor system. This paper proposes and compares different quantized analog compressive sensing approaches for rapid frequency estimation. In particular, we discuss (a) Atomic norm Soft Thresholding - Semidefinite Programming (AST-SDP), (b) Atomic norm Soft Thresholding - Alternating Direction Method of Multipliers (AST-ADMM) and (c) Superfast Line Spectral Estimation (LSE) algorithms. As a result of this comparison we report that Superfast LSE achieves a good trade-off between computational speed, quantization, and error in frequency estimation among the three approaches. We further compare the compressive sensing approaches to several classical methods such as the Prony’s algorithm and the Pisarenko’s algorithm and show that compressive sensing based approaches remain robust to higher quantization errors. Finally, experimental results are shown for a quartz crystal and a MEMS based gravimetric sensor. Frequency measurement results with the quartz crystal show that a resolution of 0.1 ppm RMSE is achieved with the compressed sensing approach.

A new kernel-based approach for spectral estimation

Abstract: The paper addresses the problem to estimate the power spectral density of an ARMA zero mean Gaussian process. We propose a kernel based maximum entropy spectral estimator. The latter searches the optimal spectrum over a class of high order autoregressive models while the penalty term induced by the kernel matrix promotes regularity and exponential decay to zero of the impulse response of the corresponding one-step ahead predictor. Moreover, the proposed method also provides a minimum phase spectral factor of the process. Numerical experiments showed the effectiveness of the proposed method.