Nonparametric Spectral Estimation Methods Research Articles

Climate change impacts on river discharge to the Sea of Marmara

The Sea of Marmara, located in Northwestern Türkiye, is under multiple stressors, including climate change and industrial, agricultural, and domestic pollution, that cause deoxygenation in coastal waters, with multiregional consequences affecting the surface and deep-water masses transported to the Mediterranean and Black Seas, respectively, via its straits. With climate-change driven changes in the intensity of extreme precipitation events, the marine environment becomes more vulnerable to increasing terrestrial pollutants. Evaluating the spatial and temporal variation of river runoff is crucial to understanding the interaction between the geophysical and hydrogeochemical processes that affects the nutrient balance of the sea. This study aims to (i) explore the historical (for the period 1960-2021) and spatial changes of monthly-averaged coastal discharges along the coastline of the Sea of Marmara for the first time, based on observations from the national hydrological service; (ii) analyze the change in long-term and seasonal trends of runoff and net-precipitation rate and derive a regional relation between the two parameters. Single Spectrum Analysis (SSA) is used to obtain the trends. Gaps in the time series are filled in using a non-parametric spectral estimation method. Discharges from the northern, eastern, and southern basins are, respectively, 3%, 17%, and 80% of the total discharge, which has varied between 1.5 and 15 km3 per year in the last decade, with short-lived extremes occurring in early spring. Total runoff rate shows a declining long-term trend that is accelerating with increasing evaporation. The intensity of the terrestrial precipitation extremes shows a temporal increase; there is a quadratic relation between the long-term trends of net precipitation and total runoff. Quantification of nutrient load distribution along the coastline associated with the spatial-temporal changes in coastal fluxes is urgent because the cumulative stressors (warming, nutrient overenrichment, pollutants) pose a threat of triggering extreme events and eutrophication in the Sea of Marmara with multiregional impact.

BUILDING RECONSTRUCTION BASED ON A SMALL NUMBER OF TRACKS USING NONPARAMETRIC SAR TOMOGRAPHIC METHODS

Abstract. Nowadays, the synthetic aperture radar (SAR) tomography (TomoSAR) technique plays a notable role in the 3D reconstruction of urban buildings through several SAR acquisitions with slightly different positions. Nonparametric-based TomoSAR spectral estimation algorithms usually work well when a large number of SAR observations. In this study, with a limited number of SAR images, we have assessed the efficiency of the nonparametric spectral estimation methods, including maximum entropy (ME), singular value decomposition (SVD), linear prediction (LP), Capon, minimum norm (MN), and beamforming (BF) in the reconstruction of the third dimension of urban buildings. The experiments are conducted on both simulated and TerraSAR-X stripmap images to indicate the effectiveness of the LP proposed estimation algorithm. The analysis of the results proves that by minimizing the average output signal power over the antenna array elements, the LP spectral estimation achieves the discrimination of distinct scatterers inside an image pixel. In addition, this low computational estimator improves the sidelobe suppression and the height estimates of the scatterers in the complex multiple-scattering urban environment. Compared to SVD, maximum entropy, Capon, minimum norm, and beamforming, the height of the Eskan tower in Tehran, Iran, obtained with the LP technique, is considerably near to field-based measurement.

Building profile reconstruction based on double subspace TomoSAR

ABSTRACT Synthetic aperture radar (SAR) tomography (TomoSAR) is an attractive technology for the three-dimensional (3D) reconstruction of buildings through multiple coherent SAR images. This technique can overcome the limitations of interferometry in multi-scatterer resolution and play a significant role in the analysis of urban areas. The robustness of the many advanced nonparametric spectral estimation approaches is founded on a high number of observations. In this work, we evaluate the abilities of five nonparametric spectral estimation methods, including double subspace (DS), maximum entropy (ME), minimum norm (MN), Capon, and beamforming (BF), to separate scattering contributions with a small number of SAR images in the tomographic reconstruction of urban environments. DS is a high-resolution estimator based on the existence of non-uniform noise, which assesses the noise subspace via eigendecomposition of some appropriately designed matrix without comprehending the noise covariance matrix. The study results indicate that DS can distinguish the scatterers in one azimuth-range resolution and satisfactorily dissuade the appearance of unpleasant side lobes. To investigate the effectiveness of DS and compare that with other expressed methods, both simulated and real SAR datasets were acquired from TerraSAR-X strip-map images of the city of Tehran, Iran. The experimental results on real SAR images demonstrate that the DS can remarkably enhance building reconstruction in the urban environment. The estimated height of the scatters utilizing the DS technique is similar to the data obtained from ground observations.

Building Height Reconstruction Based on Propagator and Generalized Maximum Entropy-TomoSAR

In recent years, the synthetic aperture radar tomography (TomoSAR) technique is becoming an increasingly hot research topic in the three-dimensional (3D) reconstruction of the structure of urban buildings. The robustness of the many advanced non-parametric spectral estimation methods in use is based on a high number of observations. This letter aims to evaluate the ability of the five non-parametric estimator techniques, including propagator, generalized maximum entropy (GME), minimum norm (MN), singular value decomposition (SVD), and capon in the separation of scattering contributions with a small number of SAR images. The performance comparison of the employed algorithms is carried out on the simulated and real datasets. The study results show that the novel high-resolution propagator and generalized maximum entropy estimators, respectively, based on the partitioning and extrapolation of the covariance matrix, can discriminate the number of scatterers in one azimuth-range resolution and satisfactorily prevent the appearance of undesirable sidelobes. The experimental results on real SAR images acquired by the TerraSAR-X satellite show the proposed propagator spectral estimation can significantly improve the 3D building reconstruction in the urban environment. Also, the estimated height of the scatters using the propagator technique is similar to the data obtained from ground observations.

Fast and accurate spectral-estimation axial super-resolution optical coherence tomography.

Spectral-estimation OCT (SE-OCT) is a computational method to enhance the axial resolution beyond the traditional bandwidth limit. However, it has not yet been used widely due to its high computational load, dependency on user-optimized parameters, and inaccuracy in intensity reconstruction. In this study, we implement SE-OCT using a fast implementation of the iterative adaptive approach (IAA). This non-parametric spectral estimation method is optimized for use on OCT data. Both in simulations and experiments we show an axial resolution improvement with a factor between 2 and 10 compared to standard discrete Fourier transform. Contrary to parametric methods, IAA gives consistent peak intensity and speckle statistics. Using a recursive and fast reconstruction scheme the computation time is brought to the sub-second level for a 2D scan. Our work shows that SE-OCT can be used for volumetric OCT imaging in a reasonable computation time, thus paving the way for wide-scale implementation of super-resolution OCT.

Evaluation of Nonparametric SAR Tomography Methods for Urban Building Reconstruction

Recently, the synthetic aperture radar tomography (TomoSAR) technique has attracted significant attention owing to its 3-D reconstruction capability of complex urban environments. The availability of a high number of images is usually a requirement for nonparametric spectral estimation methods. This letter evaluates the potential of four nonparametric spectral estimation algorithms, that is: 1) linear prediction (LP); 2) minimum norm (MN); 3) singular value decomposition (SVD); and 4) Capon for improved tomographic reconstruction of the third dimension of built-up areas with a small number of observations. The performance analysis is carried out for both simulated and real SAR datasets. The returns from the employed techniques indicate the efficient and low-computational estimator of LP by minimizing the average output signal power at the array of antenna elements and make it possible to separate multiple scatters at a distance below the Rayleigh resolution and clean sidelobes’ phenomena in the elevation profiles. The experimental results of a dataset acquired by the TerraSAR-X sensor verify the effectiveness of the LP spectral estimator algorithm in the reconstruction of urban buildings. The estimated height of scatterers with the LP method is considerably similar to the ground-observed data.

Dynamic displacements from high-rate GNSS: Error modeling and vibration detection

Nowadays, GNSS (Global Navigation Satellite System) receivers can measure with sampling rates up to 100 Hz, and it is possible to provide displacements at a level of precision of a few millimeters. This opened an interesting field of applications, e.g. for disciplines that monitor dynamic movements, like seismology or structural health monitoring. However, the detection of smallest displacements possible requires a thorough analysis of both error types, systematic and stochastic. In view of this, this paper deals with the detection of small vibrations with amplitudes down to the sub-millimeter level, and the error modelling necessary to achieve this. The data under investigation are time series of kinematic GNSS displacement measurements. We will use parametric time series models of the ARIMA (Autoregressive Integrated Moving Average) type to characterize the GNSS errors and to do a pre-filtering based on a calibrated model. With non-parametric spectral estimation methods – namely periodograms – we can then test for the presence of harmonic processes (sinusoids) in the data. Once a sinusoid is detected, its amplitude and phase are estimated by means of harmonic regression. Subsequently, the sinusoid can be removed, and the procedure can be repeated. This algorithm is tested with data collected for a GNSS shake table experiment; it is shown that it is possible resolve and detect vibrations down to a level of tens of microns with few minutes of data being analyzed. We also highlight some theoretical considerations on minimum detectable amplitudes of vibrations for measurements of different quality and record lengths.

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.

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.

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.

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.

A novel 3-D reconstruction approach based on group sparsity of array InSAR

As an advanced technology, synthetic aperture radar tomography (Tomo SAR) provides the feasibility to solve the layover problem caused by the inherent side-view mode in SAR sensors. However, the conventional nonparametric spectral estimation methods, such as truncated singular value decomposition (TSVD), are limited by the poor elevation resolution and cannot meet the needs of practical applications. Currently, SAR 3-D imaging methods based on compressive sensing are typically used; nevertheless, classic compressive sensing algorithms such as BP and OMP still exhibitproblems such as low efficiency, weak super-resolution performance, and poor anti-interference ability. Therefore, an algorithm with high robustness and super-resolution performance is significantly demanded.In this paper, a novel array InSAR 3-D reconstruction algorithm based on group-sparsity is proposed. It is improved based on the existing compressive sensing algorithm and exhibits better super-resolution and robustness. Based on the simulation data and the actual data of the first domestic 3-D imaging experiment by an airborne array InSAR, the super-resolution ability ofthe algorithm is verified, and the 3-D imaging results of the buildings are obtained.

Bootstrap methods for long-memory processes: a review

This manuscript summarized advances in bootstrap methods for long-range dependent time series data. The stationary linear long-memory process is briefly described, which is a target process for bootstrap methodologies on time-domain and frequency-domain in this review. We illustrate time-domain bootstrap under long-range dependence, moving or non-overlapping block bootstraps, and the autoregressive-sieve bootstrap. In particular, block bootstrap methodologies need an adjustment factor for the distribution estimation of the sample mean in contrast to applications to weak dependent time processes. However, the autoregressive-sieve bootstrap does not need any other modification for application to long-memory. The frequency domain bootstrap for Whittle estimation is provided using parametric spectral density estimates because there is no current nonparametric spectral density estimation method using a kernel function for the linear long-range dependent time process.

Estimation of the energy spectrums of reflections in pulse Doppler weather radars. Part 2. Extreme performance

This is the second paper in a series of papers dedicated to the peculiarities of estimation of the continuous energy spectra of random processes of different nature, which are determined by their samples at discrete moments of time. In this paper we analyze extreme performance of the reconstruction of continuous energy spectra, in particular, the ones of interperiod fluctuations of reflections from meteorological objects in pulse Doppler weather radars under the hypothetical conditions of a priori known covariance matrix of the analyzed processes. The reasons, which cause known disadvantages of classical (nonparametric) spectral estimation (SE) methods for energy spectrums shape reconstruction, are discussed. We have considered known and suggested criteria, using which the extreme performance of classical SE methods and parametric superresolution ones has been quantitatively compared. It has been demonstrated that the extreme performance of SE methods contains important but not comprehensive information. In order to choose a SE method appropriate for operation under real-world conditions, this information should be used together with information on a corresponding method’s adaptive performance under a priori unknown statistical characteristics of input effects.

Spectral analysis of railway vehicle vertical vibration under normal operating conditions

ABSTRACTThis study focuses on railway vertical random vibration–based spectral analysis under normal operating conditions. Vibration acceleration measurements are acquired using sensors mounted on the car body, bogie frame, axle bearing, and primary suspension of an Athens Metro vehicle running without passengers on a straight track. Two distinct track segments and four speeds (50, 60, 70, 80 km/h) are considered. The analysis focuses on the 0–1000 Hz frequency range using data-based non-parametric and parametric spectral estimation methods. The results indicate good agreement of the methods, the prominence of the 5–170 Hz frequency range along with higher frequencies at around 300 Hz and in the range of 600–750 Hz on the car body and the bogie frame vibration, the relatively minor dependency of the dynamics on the track segment, but their significant dependence on train speed. Yet, resonant frequencies are affected to a lesser extent, with at least 20 of them appearing as prominent.

SINGULAR SPECTRUM DECOMPOSITION: A NEW METHOD FOR TIME SERIES DECOMPOSITION

This study introduces singular spectrum decomposition (SSD), a new adaptive method for decomposing nonlinear and nonstationary time series in narrow-banded components. The method takes its origin from singular spectrum analysis (SSA), a nonparametric spectral estimation method used for analysis and prediction of time series. Unlike SSA, SSD is a decomposition method in which the choice of fundamental parameters has been completely automated. This is achieved by focusing on the frequency content of the signal. In particular, this holds for the choice of the window length used to generate the trajectory matrix of the data and for the selection of its principal components for the reconstruction of a specific component series. Moreover, a new definition of the trajectory matrix with respect to the standard SSA allows the oscillatory content in the data to be enhanced and guarantees decrease of energy of the residual. Through the numerical examples and simulations, the SSD method is shown to be able to accurately retrieve different components concealed in the data, minimizing at the same time the generation of spurious components. Applications on time series from both the biological and the physical domain are also presented highlighting the capability of SSD to yield physically meaningful components.

Nonparametric spectral analysis with applications to seizure characterization using EEG time series

Understanding the seizure initiation process and its propagation pattern(s) is a critical task in epilepsy research. Characteristics of the pre-seizure electroencephalograms (EEGs) such as oscillating powers and high-frequency activities are believed to be indicative of the seizure onset and spread patterns. In this article, we analyze epileptic EEG time series using nonparametric spectral estimation methods to extract information on seizure-specific power and characteristic frequency [or frequency band(s)]. Because the EEGs may become nonstationary before seizure events, we develop methods for both stationary and local stationary processes. Based on penalized Whittle likelihood, we propose a direct generalized maximum likelihood (GML) and generalized approximate cross-validation (GACV) methods to estimate smoothing parameters in both smoothing spline spectrum estimation of a stationary process and smoothing spline ANOVA time-varying spectrum estimation of a locally stationary process. We also propose permutation methods to test if a locally stationary process is stationary. Extensive simulations indicate that the proposed direct methods, especially the direct GML, are stable and perform better than other existing methods. We apply the proposed methods to the intracranial electroencephalograms (IEEGs) of an epileptic patient to gain insights into the seizure generation process.

Spectral Estimation Techniques for DNA Sequence and Microarray Data Analysis

Spectral estimation techniques are widely used in modern signal processing systems. Recently, they have found important applications to the analysis of DNA data. In this paper, we review parametric and non-parametric spectral estimation methods for DNA sequence and microarray data analysis. The discrete Fourier transform (DFT) is the most commonly used technique for spectral analysis of digital signals. It can reveal the gene locations in a DNA sequence. The DFT can also be used to detect repetitive elements in a DNA sequence. The DFT produces the so-called windowing or data truncation artifacts when it is applied to a short data segment. Parametric spectral estimation methods, such as the autoregressive (AR) model, overcome this problem and can be used to obtain a high-resolution spectrum of the input signal. In this paper, we demonstrate the advantages of the AR model for the identification of protein coding regions and the detection of DNA repeats. We also review DFT and AR models and other spectral estimation techniques for the analysis of microarray time series data.

Application of empirical mode decomposition to heart rate variability analysis.

The analysis of heart rate variability, involving changes in the autonomic modulation conditions, demands specific capabilities not provided by either parametric or non-parametric spectral estimation methods. Moreover, these methods produce time-averaged power estimates over the entire length of the record. Recently, empirical mode decomposition and the associated Hilbert spectra have been proposed for non-linear and non-stationary time series. The application of these techniques to real and simulated short-term heart rate variability data under stationary and non-stationary conditions is presented. The results demonstrate the ability of empirical mode decomposition to isolate the two main components of one chirp series and three signals simulated by the integral pulse frequency modulation model, and consistently to isolate at least four main components localised in the autonomic bands of 14 real signals under controlled breathing manoeuvres. In addition, within the short time-frequency range that is recognised for heart rate variability phenomena, the Hilbert amplitude component ratio and the instantaneous frequency representation are assessed for their suitability and accuracy in time-tracking changes in amplitude and frequency in the presence of non-stationary and non-linear conditions. The frequency tracking error is found to be less than 0.22% for two simulated signals and one chirp series.