Spectral Estimation Method Research Articles

SPICE-Based SAR Tomography over Forest Areas Using a Small Number of P-Band Airborne F-SAR Images Characterized by Non-Uniformly Distributed Baselines

Synthetic aperture radar tomography (TomoSAR) has been proven to be a useful way to reconstruct vertical structure over forest areas with P-band images, on account of its three-dimensional imaging ability. In the case of a small number of non-uniformly distributed acquisitions, compressive sensing (CS) is generally adopted in TomoSAR. However, the performance of CS depends on the selected hyperparameter, which is closely related to the noise of a pixel. In this paper, to overcome this limitation, we propose a sparse iterative covariance-based estimation (SPICE) approach based on the wavelet and orthogonal sparse basis (W&O-SPICE) for application over forest areas. SPICE is a sparse spectral estimation method that achieves a high vertical resolution, and takes account of the noise adaptively for each resolution cell. Thus, it does not require the user to select a hyperparameter. Furthermore, the used sparse basis not only ensures the sparsity of the forest canopy scattering contribution, but it can also keep the original sparse information of the ground contribution. The proposed method was tested in simulated experiments and the results demonstrated that W&O-SPICE can successfully reconstruct the vertical structure of a forest. Moreover, three P-band fully polarimetric airborne SAR images with non-uniformly distributed baselines were applied to reconstruct the vertical structure of a tropical forest in Mabounie, Gabon. The underlying topography and forest height were estimated, and the root-mean-square errors (RMSEs) were 6.40 m and 4.50 m with respect to the LiDAR digital terrain model (DTM) and canopy height model (CHM), respectively. In addition, W&O-SPICE showed a better performance than W&O-CS, beamforming, Capon, and the iterative adaptive approach (IAA).

Grid-less variational Bayesian line spectral estimation with multiple measurement vectors

Line spectral estimation (LSE) with multiple measurement vector (MMV) is studied utilizing the Bayesian variational inference. Motivated by the recent grid-less variational line spectral estimation (VALSE) method, we develop the MMV VALSE (MVALSE). The MVALSE shares the advantages of the VALSE method, such as automatically estimating the model order, noise variance, weight variance, and providing the uncertainty of the frequency estimates. The MVALSE can be viewed as applying the VALSE with single measurement vector to each snapshot, and combining the intermediate data appropriately. Furthermore, the MVALSE is developed to perform sequential estimation. Numerical results demonstrate the effectiveness of the MVALSE method, compared to the state-of-the-art MMV methods.

Study on the change characteristics of regional geoelectric fields

In this study, we illustrate the temporal variations of the geoelectric field and geomagnetic field by data from eight geoelectric field stations and four geomagnetic field stations in Mainland China in 2011. The maximum entropy spectral estimation method (MEM) was used to process the data in our study. The results show that: (i) it is obvious seasonal changes at inland geoelectric field stations and monthly changes at coastal geoelectric field stations; (ii) obvious seasonal changes can be observed at geomagnetic field stations and its seasonal changing curve of component H is most similar to that of the geoelectric field; and (iii) monthly changes of geoelectric field are caused by the combined action of solar and lunar tidal forces, and the seasonal changes of geoelectric field are caused by electromagnetic induction of the seasonal changes of ionospheric current induction intensity inside the Earth.

Visual representation of DNA sequences for exon detection using non-parametric spectral estimation techniques

This paper presents a new approach for modeling of DNA sequences for the purpose of exon detection. The proposed model adopts the sum-of-sinusoids concept for the representation of DNA sequences. The objective of the modeling process is to represent the DNA sequence with few coefficients. The modeling process can be performed on the DNA signal as a whole or on a segment-by-segment basis. The created models can be used instead of the original sequences in a further spectral estimation process for exon detection. The accuracy of modeling is evaluated evaluated by using the Root Mean Square Error (RMSE) and the R-square metrics. In addition, non-parametric spectral estimation methods are used for estimating the spectral of both original and modeled DNA sequences. The results of exon detection based on original and modeled DNA sequences coincide to a great extent, which ensures the success of the proposed sum-of-sinusoids method for modeling of DNA sequences.

Spectra estimation from raw camera responses based on adaptive local-weighted linear regression

An improved spectral reflectance estimation method is developed to transform raw camera RGB responses to spectral reflectance. The novelty of our method is to apply a local weighted linear regression model for spectral reflectance estimation and construct the weighting matrix using a Gaussian function in CIELAB uniform color space. The proposed method was tested using both a standard color chart and a set of textile samples, with a digital RGB camera and by ten times ten-fold cross-validation. The results demonstrate that our method gives the best accuracy in estimating both the spectral reflectance and the colorimetric values in comparison with existing methods.

Nonparametric and parametric methods of spectral analysis

Spectral Analysis is one of the most important methods in signal processing. In practical application, it is critical to discuss the power spectral density estimation of finite data sampled from some stationary time series. A spectral estimator is expected to have good statistical properties such as consistency, high resolution and small variance. For one spectral estimation method, there exists a trade-off between high resolution and small variance. The paper provides a comparison of several popular spectral methods from both theoretical properties and practical applications. We first address several basic nonparametric methods, whose statistical characters are analysed. Then we explain the connections and differences between temporal windowing and lag windowing. Thereafter, the confidence intervals of both windows are given and used to evaluate the estimated results. Besides, several different parametric estimation methods of autoregressive time series are compared, and whose properties and effects are also introduced. Building on our understanding of these studies, we then apply parametric and nonparametric spectral estimation methods on the data of ocean surface wave height.

Generalised Linear Cepstral Models for the Spectrum of a Time Series

The paper introduces the class of generalised linear models with Box-Cox link for the spectrum of a time series. The Box-Cox transformation of the spectral density is represented as a finite Fourier polynomial, with coefficients, that we term generalised cepstral coefficients, providing a complete characterisation of the properties of the random process. The link function depends on a power transformation parameter and encompasses the exponential model (logarithmic link), the autoregressive model (inverse link), and the moving average model (identity link). One of the merits of this model class is the possibility of nesting alternative spectral estimation methods under the same likelihood-based framework, so that the selection of a particular parametric spectrum amounts to estimating the transformation parameter. We also show that the generalised cepstral coefficients are a one to one function of the inverse partial autocorrelations of the process, which can be used to evaluate the mutual information between the past and the future of the process.

Electroencephalogram dynamics during general anesthesia predict the later incidence and duration of burst-suppression during cardiopulmonary bypass

ObjectiveElectroencephalogram burst-suppression during general anesthesia is associated with post-operative delirium (POD). Whether burst-suppression causes POD or merely reflects susceptibility to POD is unclear. We hypothesized decreased intraoperative alpha (8–12 Hz) and beta (13–33 Hz) power prior to the occurrence of burst-suppression in susceptible patients. MethodsWe analyzed intraoperative electroencephalogram data of cardiac surgical patients undergoing cardiopulmonary bypass (CPB). We detected the incidence and duration of CPB burst-suppression with an automated burst-suppression detection algorithm. We analyzed EEG data with multitaper spectral estimation methods. We assessed associations between patient characteristics and burst-suppression using Binomial and Zero-inflated Poisson Regression Models. ResultsWe found significantly decreased alpha and beta power (7.8–22.95 Hz) in the CPB burst-suppression cohort. The odds ratio for the association between point estimates for alpha and beta power (7.8–22.95 Hz) and the incidence of burst-suppression was 0.88 (95% CI: 0.79–0.98). The incidence rate ratio for the association between point estimates for power between the alpha and beta range and the duration of burst-suppression was 0.89 (95% CI: 0.84–0.93). ConclusionDecreased intra-operative power within the alpha and beta range was associated with susceptibility to burst-suppression during CPB. SignificanceThis dynamic may be used to develop principled neurophysiological-based approaches to aid the preemptive identification and targeted care of POD vulnerable patients.

SAR tomography for point-like and volumetric scatterers using a regularised iterative adaptive approach

ABSTRACTSynthetic aperture radar (SAR) tomography has been shown to be an effective and important tool for the monitoring of infrastructures and the investigation of forest vertical structure. However, the existing tomographic imaging algorithms, including spectral estimation and compressive sensing, can only be applied to SAR dataset over urban areas or over vegetated areas, while providing superresolution capability and working on single-look interferometric data. In this study, we propose a tomographic processing algorithm for SAR tomography based on Tikhonov regularisation and iterative adaptive approach (IAA), referred to as RIAA. As a nonparametric spatial spectral estimation method, RIAA allows the application to scenarios with point-like scatterers as well as with volumetric scatterers. The proposed method also provides superresolution capability and works on single-look SAR images. The performance of the proposed algorithm is verified by simulated data, TerraSAR-X strip-map and BioSAR 2007 P-band datasets over the urban and forested areas, respectively.

An Investigation Into the Impact of Band Error Variance Estimation on Intrinsic Dimension Estimation in Hyperspectral Images

There have been a significant number of recent papers about hyperspectral imaging, which propose various methods for estimating the number of materials/endmembers in hyperspectral images. This is sometimes called the “intrinsic” dimension (ID) of the image. Estimation of the error variance in each spectral band is a critical first step in ID estimation. The estimated error variances can then be used to preprocess (e.g., whiten) the data, prior to ID estimation. A range of variance estimation methods have been advocated in the literature. We investigate the impact of five variance estimation methods (three using spatial information and two using spectral information) on five ID estimation methods, with the aid of four different, but semirealistic, sets of simulated hyperspectral images. Our findings are as follows: first, for all four sets, the two spectral variance estimation methods significantly outperform the three spatial methods; second, when used with the spectral variance estimation methods, two of the ID estimation methods (called random matrix theory and NWHFC) consistently outperform the other three ID estimation methods; third, the better spectral variance estimation method sometimes gives negative variance estimates; fourth, we introduce a simple correction that guarantees positivity; and fifth, we give a fast algorithm for its computation.

High-resolution space-time spectral estimation method for array signal based on deconvolution

Conventional beamforming and classical spectral estimation methods are widely used in array signal processing to estimate the angular and frequency spectrum, respectively. But the spectra provided by these algorithms appear as low resolutions and high side lobes because of the limited array aperture and the number of snapshots. Then a multi-dimensional window function is defined, which is composed of the snapshot number and array aperture. Based on the theories of space-time joint spectral estimation, the multi-dimensional power spectrum about the azimuthal angle and frequency of array signal can be deduced as the convolution of the multi-dimensional power spectrum of the true signal and the power spectrum of the multi-dimensional window function. Therefore, the deconvolution algorithm can be introduced to remove the influence from the window function to recover the power spectrum of the true signal which is considered to be received from the infinite time and space. It is illustrated from simulations and experimental data processing that the deconvolution method can greatly improve the angular and frequency resolutions of the multi-dimensional spectrum, suppress the side lobes and provide extra signal-to-noise ratio, which can be applied for multi-target identification and weak signal detection.

Reconstructing signal from quantized signal based on singular spectral analysis

Singular spectral analysis (SSA) is a nonparametric spectral estimation method for performing the time series analysis. It represents a signal as the sum of its components. In this manuscript, a nearly cyclostationary signal is considered. The signal is quantized and the SSA is employed to reconstruct the original signal based on the quantized signal. First, the reconstructed signal is modeled as the weighted sum of the SSA components. In order to estimate the weights, each quantization level is considered as a class. Different signal values are associated with different probabilities of the corresponding classes via the sigmoid functions defined based on the distances between the signal values and the corresponding quantized levels. Therefore, our proposed method provides the optimal estimate of a given signal in the minimum cross entropy sense. Computer numerical simulation results show that our proposed method can reduce the quantization error and reconstruct the original signal more accurately compared to some existing algorithms.

A Maximum Likelihood Based Nonparametric Iterative Adaptive Method of Synthetic Aperture Radar Tomography and Its Application for Estimating Underlying Topography and Forest Height.

Synthetic aperture radar tomography (TomoSAR) is an important way of obtaining underlying topography and forest height for long-wavelength datasets such as L-band and P-band radar. It is usual to apply nonparametric spectral estimation methods with a large number of snapshots over forest areas. The nonparametric iterative adaptive approach for amplitude and phase estimation (IAA-APES) can obtain a high resolution; however, it only tends to work well with a small number of snapshots. To overcome this problem, this paper proposes the nonparametric iterative adaptive approach based on maximum likelihood estimation (IAA-ML) for the application over forest areas. IAA-ML can be directly used in forest areas, without any prior information or preprocessing. Moreover, it can work well in the case of a large number of snapshots. In addition, it mainly focuses on the backscattered power around the phase centers, helping to detect their locations. The proposed IAA-ML estimator was tested in simulated experiments and the results confirmed that IAA-ML obtains a higher resolution than IAA-APES. Moreover, six P-band fully polarimetric airborne SAR images were applied to acquire the structural parameters of a forest area. It was found that the results of the HH polarization are suitable for analyzing the ground contribution and the results of the HV polarization are beneficial when studying the canopy contribution. Based on this, the underlying topography and forest height of a test site in Paracou, French Guiana, were estimated. With respect to the Light Detection and Ranging (LiDAR) measurements, the standard deviation of the estimations of the IAA-ML TomoSAR method was 2.11 m for the underlying topography and 2.80 m for the forest height. Furthermore, compared to IAA-APES, IAA-ML obtained a higher resolution and a higher estimation accuracy. In addition, the estimation accuracy of IAA-ML was also slightly higher than that of the SKP-beamforming technique in this case study.

Spectral Estimation Methods for Evaluating iPPG Pulse Rate Variability.

Non-contact measurement of physiological parameters, like pulse rate variability (PRV), has numerous applications in medicine and affective computing. PRV is an informative measure of autonomic nervous system activity. Spectral estimation from unevenly sampled, non-stationary data is integral to pulse rate variability frequency-domain analysis. We present the first comparison of results of PRV computation using the Lomb-Scargle method and Bayesian Spectral Estimation. The Lomb-Scargle method performs well, even in the presence of missing beats. However, the Bayesian Spectral Estimation method has advantages when tracking changes in amplitude and frequency. We illustrate these characteristics with results from synthetic data and real non-contact imaging photoplethysmography measurements.

The Test on the Short Period Mode of the Simulator With Time-Frequency Combination

Based on flight simulation data and measured data, the article extracted short cycle time of correlating parameters curve from a certain type of flight simulators. And in the time domain, using the average standardized distance test method and gray correlation analysis method for this type of simulator simulation data. In the frequency domain, the classical spectral estimation method is used for quantitative detection, and the consistency test of flight simulation data and flight parameters is realized. Then the evidence theory is improved and thus the synthesized type simulator short cycle when the correlating parameters and frequency domain the consistency of the test results, verify the longitudinal short-period mode type simulator fidelity is better.

A signal processing framework for operational modal analysis in time and frequency domain

Abstract In operational modal analysis (OMA), correlation functions, sometimes referred to as covariance functions, are commonly used for modal parameter extraction. Other techniques for parameter estimation use spectral density estimates. There are several known techniques for computing spectral density and correlation functions. The most common technique for spectral density estimates, is Welch’s method. A more infrequently used technique, however, is based on computing the discrete Fourier transform (DFT) of the entire signals, and multiplying these DFTs into auto and cross-periodograms. To produce a correlation function, the inverse Fourier transform of the periodogram is used. To produce spectral density estimates, the periodogram may be smoothed. In the present paper this method of computing the spectral and correlation functions is investigated, and compared to other methods of spectral and correlation estimation. It is shown that the method has several advantages not only for estimation of spectra and correlation functions, but also because filtering, integration and differentiation, removal of harmonics, and compensation for non-ideal sensor characteristics are functions that can readily be encompassed in this technique, with high performance, at a minimum of computational cost. Furthermore, two methods to remove harmonics in spectral densities as well as in correlation functions, are developed in the paper. The first method, frequency domain editing (FDE), removes one or more stable harmonics, where variations of the frequency are small. The other method, order domain deletion (ODD), works in cases where the frequency of the harmonic, or harmonics, varies, and where the instantaneous frequency as a function of time is known, for example by processing a tacho signal. Based on the several advantages with using long DFTs as the estimation method for spectra and correlation functions, it is recommended as the standard framework for signal processing in OMA applications.

Reduced Dimension Based Two-Dimensional DOA Estimation with Full DOFs for Generalized Co-Prime Planar Arrays.

In this paper, we investigate the problem of two-dimensional (2D) direction-of-arrival (DOA) estimation for generalized co-prime planar arrays. The classic multiple signal classification (MUSIC)-based methods can provide a superior estimation performance, but suffer from a tremendous computational burden caused by the 2D spectral search. To this end, we reduce the 2D problem into a one-dimensional (1D) one and propose a reduced dimension partial spectral search estimation method, which can compress the search region into a small 1D sector. Moreover, the proposed method can utilize the full information of the entire array without degrees-of-freedom loss. Furthermore, an iterative approach is also proposed to reduce complexity and improve performance. Simulation results show that the proposed methods can provide improved performance with substantially reduced complexity, as compared to other state-of-the-art methods.

Multimodal fusion of EEG and fMRI for epilepsy detection

Technology of brain–computer interface (BCI) provides a new way of communication and control without language or physical action. Brain signal tracking and positioning is the basis of BCI research, while brain modeling affects the treatment analysis of (EEG) and functional magnetic resonance imaging (fMRI) directly. This paper proposes human ellipsoid brain modeling method. Then, we use non-parametric spectral estimation method of time–frequency analysis to deal with simulation and real EEG of epilepsy patients, which utilizes both the high spatial and the high time resolution to improve the doctor’s diagnostic efficiency.

Superfast Line Spectral Estimation

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 which 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.

Non‐Parametric Spectral Density Estimation Under Long‐Range Dependence

One major aim of time series analysis, particularly in the physical and geo‐sciences, is the estimation of the spectral density function. With weakly dependent time processes, non‐parametric, kernel‐based methods are available for spectral density estimation, which involves smoothing the periodogram by a kernel function. However, a similar non‐parametric approach is presently unavailable for strongly, or long‐range, dependent processes. In particular, as the spectral density function under long‐range dependence commonly has a pole at the origin, kernel‐based methods developed for weakly dependent processes (i.e., with bounded spectral densities) do not apply readily for long‐range dependence without suitable modification. To address this, we propose a non‐parametric kernel‐based method for spectral density estimation, which is valid under both weak and strong dependence. Based on the initial or pilot estimator of the long‐memory parameter, the method involves a frequency domain transformation to dampen the dependence in periodogram ordinates and mimic kernel‐based estimation under weak dependence. Under mild assumptions, the proposed non‐parametric spectral density estimator is shown to be uniformly consistent, and general expressions are provided for rates of estimation error and optimal kernel bandwidths. The method is investigated through simulation and illustrated through data examples, which also consider bandwidth selection.