Multi-dimensional Capon spectral estimation using discrete Zhang neural networks

The minimum variance spectral estimator, also known as the Capon spectral estimator, is a high resolution spectral estimator used extensively in practice. In this paper, we derive a novel implementation of a very computationally demanding matched filter-bank based a spectral estimator, namely the multi-dimensional Capon spectral estimator. To avoid the direct computation of the inverse covariance matrix used to estimate the Capon spectrum which can be computationally very expensive, particularly when the dimension of the matrix is large, we propose to use the discrete Zhang neural network for the online covariance matrix inversion. The computational complexity of the proposed algorithm for one-dimensional (1-D), as well as for two-dimensional (2-D) and three-dimensional (3-D) data sequences is lower when a parallel implementation is used.     

Enhanced autoregressive moving average spectral estimation appliedto the measurement of Doppler spectral width

The measurement of clear-air turbulence with a Doppler radar is investigated. An autoregressive moving average (ARMA) model is proposed to improve the Doppler spectral width estimates. An iterative algorithm that has its origin in system identification is used for the estimation of the ARMA parameters. By taking advantage of a priori knowledge of the correlation matrix, which arises in the derivation of the governing equations of the ARMA parameters, the ARMA spectral estimate can be improved. This improvement is shown in terms of bias and variance of the spectral width estimate     

Estimation of spectral parameters of correlated signals in wavefields

The statistical properties of a known method to estimate the spectral matrix of signals in a wavefield are investigated assuming the output of an array of sensors is observed. Because the wave parameters, for example bearings and ranges, of the sources are usually unknown, a suitable technique for estimating them separately is reported. Assuming the wave parameters, conditions for the identifiability of the signal spectral parameters are derived. Optimal properties of the estimate for the spectral matrix of signals are shown, for example, minimum variance unbiasedness for normally distributed data. A numerical experiment demonstrates some properties of the estimates of all parameters, for example, the estimates of signal spectral powers and bearings are significantly correlated for sources close together.     

Spatial spectral estimation using multiple beam antennas

The processing simplifications which result in using a multiple beam antenna (MBA) as a spatial sensor for performing spectral estimation are considered. Sources are presumed to be located over a two-dimensional field of view characterized by the two angular coordinatesthetaandphi. The MBA configuration consists of an aperture (usually either a reflector or lens) illuminated by a collection of feeds located in its focal plane (see Fig. 1), followed by a switch network for selecting the outputs of any desired feed port. Using the MBA as the spatial sensor for performing spectral estimation, as contrasted to the array antenna configuration, has a distinct advantage: for a given collection of source wavefronts incident on the aperture, a crude estimate of each source position is obtained simply by monitoring the power output of each feed port. This is to be contrasted to the array configuration, where the average output power of each element port is the same, so long as the wavefronts incident on the aperture emanate from uncorrelated sources. As shall be developed further, this initial crude estimate of source location can be used to develop refined estimates using processing algorithms which significantly reduce processing requirements when compared to those required using a comparable array when the number of anticipated sources existing over the field of view (FOV) is large. Finally, since the spectral estimate of the source location is essentially an "open-loop" estimate, involving a priori measured quantities such as the antenna port radiation patterns, we consider the effects of measurement errors on the estimate. The results are normalized so as to be generally applicable to both the array antenna configuration as well as for the MBA.     

On the performance advantage of multitaper spectral analysis

The performance advantage of multitaper spectral analysis is quantified relative to weighted overlapped segment averaging (WOSA). To make the comparison of these two nonparametric spectral estimators, theoretical performance measures are derived in terms of leakage, variance, and resolution. The methods are then compared by evaluating each measure in turn, while requiring the other two measures to be equal. The results show that multitaper analysis always performs better than WOSA. For example, given the same leakage and resolution, multitaper analysis can have three-quarters to one-half the variance of WOSA. Given the same resolution and variance, multitaper analysis can exhibit a 10-20-dB leakage advantage over WOSA. These and other results provide compelling evidence for greater use of multitaper analysis in situations for which a nonparametric spectral estimator is appropriate     

Quantifying errors in spectral estimates of HRV due to beat replacement and resampling

Spectral estimates of heart rate variability (HRV) often involve the use of techniques such as the fast Fourier transform (FFT), which require an evenly sampled time series. HRV is calculated from the variations in the beat-to-beat (RR) interval timing of the cardiac cycle which are inherently irregularly spaced in time. In order to produce an evenly sampled time series prior to FFT-based spectral estimation, linear or cubic spline resampling is usually employed. In this paper, by using a realistic artificial RR interval generator, interpolation and resampling is shown to result in consistent over-estimations of the power spectral density (PSD) compared with the theoretical solution. The Lomb-Scargle (LS) periodogram, a more appropriate spectral estimation technique for unevenly sampled time series that uses only the original data, is shown to provide a superior PSD estimate. Ectopy removal or replacement is shown to be essential regardless of the spectral estimation technique. Resampling and phantom beat replacement is shown to decrease the accuracy of PSD estimation, even at low levels of ectopy or artefact. A linear relationship between the frequency of ectopy/artefact and the error (mean and variance) of the PSD estimate is demonstrated. Comparisons of PSD estimation techniques performed on real RR interval data during minimally active segments (sleep) demonstrate that the LS periodogram provides a less noisy spectral estimate of HRV.     

Smoothed nonparametric spectral estimation via cepsturm thresholding - Introduction of a method for smoothed nonparametric spectral estimation

Cepstrum thresholding is shown to be an effective, automatic way of obtaining a smoothed nonparametric estimate of the spectrum of a stationary signal. In the process of introducing the cepstrum thresholding-based spectral estimator, we discuss a number of results on the cepstrum of a stationary signal, which might also be of interest to researchers in spectral analysis and allied topics, such as speech processing     

Autoregressive spectral estimation of fetal breathing movement

Fetal breathing movement (FBM) in utero may be an indicator of fetal health. This paper provides a second-by-second estimate of FBM rate. In the absence of a statistical model for the fetal breathing movement, block data structured autoregressive spectral estimation is used. The optimum tapered Burg algorithm provides a minimum variance breathing rate estimate from a short block of data. The data were recorded using a PVDF (PolyVinyliDeneFluoride) transducer which picks up maternal abdominal wall movements. A peak tracking algorithm is used to extract the fetal breathing rate. Results from these signals are presented in graphical form. Further analysis of the fetal breathing rate has revealed periodicities, similar to that observed in the fetal heart rate.     

Adaptive image coding using spectral classification

We present a new classification scheme, dubbed spectral classification, which uses the spectral characteristics of the image blocks to classify them into one of a finite number of classes. A vector quantizer with an appropriate distortion measure is designed to perform the classification operation. The application of the proposed spectral classification scheme is then demonstrated in the context of adaptive image coding. It is shown that the spectral classifier outperforms gain-based classifiers while requiring a lower computational complexity.     

Two-dimensional strip spectral correlation algorithm to fast estimation of 2D-cyclic spectral function for texture analysis

This paper presents a new affective scheme to estimate the two-dimensional cyclic spectral function of a texture as a two-dimensional signal. Recently, considering textures as cyclostationary signals, several algorithms have been introduced to utilize the more discriminant features of hidden periodicity for texture analysis, such as one-dimensional strip spectral correlation analysis (1D-SSCA), one-dimensional FFT-accumulated method, and direct frequency smoothing method. Although the reported results of these algorithms are proper, all of them suffer a drawback: they sweep texture images row by row and column by column and analyze them as one-dimensional signals, and hence lose the relationships between neighboring pixels. In this paper a new efficient extended algorithm namely two-dimensional SSCA is proposed to estimate the two-dimensional cyclic spectral function for two-dimensional signals. This algorithm is fast respect to other cyclic spectral function estimators and is based on 1D-SSCA algorithm. The effectiveness of the proposed algorithm is evaluated on three well-known databases. The experimental results illustrate that the proposed scheme is computationally efficient, generates flexible features and improves correct classification rate, in comparison with other studies in this field.     

High-resolution spectral analysis using multiple-interval adaptive prediction

The problem of adaptively detecting two sinusoids corrupted by noise is considered, with emphasis on resolution properties. The approach is to form a spectral estimate from the coefficients of a Δ-step-ahead adaptive predictor. A theoretical analysis reveals that attention to the choice of the prediction horizon Δ gives a distinct improvement in the spectral estimate and in the resolution of the signals. The theoretical results are illustrated with numerical examples. Comparisons with previously suggested techniques are also made.     

Data-adaptive evolutionary spectral estimation

We present a novel data-adaptive estimator for the evolutionary spectrum of nonstationary signals. We model the signal at a frequency of interest as a sinusoid with a time-varying amplitude, which is accurately represented by an orthonormal basis expansion. We then compute a minimum mean-squared error estimate of this amplitude and use it to estimate the time-varying spectrum at that frequency, all while minimizing the interference from the signal components at other frequencies. Repeating the process over all frequencies, we obtain a power distribution that is consistent with the Wold-Cramer evolutionary spectrum and reduces to Capon's (1969) method for the stationary case. Our estimator possesses desirable properties in terms of time-frequency resolution and positivity and is robust in the spectral estimation of noisy nonstationary data. We also propose a new estimator for the autocorrelation of nonstationary signals. This autocorrelation estimate is needed in the data-adaptive spectral estimation. We illustrate the performance of our estimator using simulation examples and compare it with the recently presented evolutionary periodogram and the bilinear time-frequency distribution with exponential kernels     

On the Design of Classifiers for Crop Inventories

Crop proportion estimators that use classifications of satellite data to correct, in an additive way, a given estimate acquired from ground observations are discussed. A linear version of these estimators is optimal, in terms of minimum variance, when the regression of the ground observations onto the satellite observations is linear. When this regression is not linear, but the reverse regression (satellite observations onto ground observations) is linear, the estimator is suboptimal but still has certain appealing variance properties. In this paper we derive expressions for those regressions which relate the intercepts and slopes to conditional classification probabilities. These expressions are then used to discuss the question of classifier designs that can lead to low-variance crop proportion estimates. Variance expressions for these estimates in terms of classifier omission and commission errors are also derived.     

Cumulant-based LP method for two-dimensional spectral estimation

A cumulant-based linear prediction (CBLP) method for two-dimensional (2-D) spectral estimation is presented. The main idea of the method is to compute the coefficients of two different single-quadrant prediction filters by applying the LP theory to a selected 2-D fourth-order mixed cumulant slice of the noisy signal. These coefficients are employed in formulating two different autoregressive spectral models. Both spectral models are combined to obtain the desired spectral estimate. The effectiveness of the proposed CBLP method is demonstrated through computer simulation     

Noncooperative target classification using hierarchical modeling ofhigh-range resolution radar signatures

The classification of high-range resolution (HRR) radar signatures using multiscale features is considered. We present a hierarchical autoregressive moving average (ARMA) model for modeling HRR radar signals at multiple scales and use spectral features extracted from the model for classifying radar signatures. First, we show that the radar signal at a different scale obeys an ARMA process if it is an ARMA process at the observed scale. Then, an algorithm to estimate model parameters and power spectral density function at different scales using model parameters at the observed scale is presented. A feature set composed of spectral peaks is extracted from the estimated spectral density function using multiscale ARMA models. For HRR radar signature classification, multispectral features extracted from five different scales are used, and a minimum distance classifier with multiple prototypes is used to classify HRR data. The multiscale classifier is applied to two HRR radar data sets. Each data set contains 2500 test samples and 2500 training samples in five classes. For both data sets, about 95% of the radar returns are correctly classified     

Efficient time-recursive implementation of matched filterbank spectral estimators

In this paper, we present a computationally efficient sliding window time updating of the Capon and amplitude and phase estimation (APES) matched filterbank spectral estimators based on the time-variant displacement structure of the data covariance matrix. The presented algorithm forms a natural extension of the most computationally efficient algorithm to date, and offers a significant computational gain as compared to the computational complexity associated with the batch re-evaluation of the spectral estimates for each time-update. Furthermore, through simulations, the algorithm is found to be numerically superior to the time-updated spectral estimate formed from directly updating the data covariance matrix.     

SAR imaging via modern 2-D spectral estimation methods

Discusses the use of modern 2D spectral estimation algorithms for synthetic aperture radar (SAR) imaging. The motivation for applying power spectrum estimation methods to SAR imaging is to improve resolution, remove sidelobe artifacts, and reduce speckle compared to what is possible with conventional Fourier transform SAR imaging techniques. This paper makes two principal contributions to the field of adaptive SAR imaging. First, it is a comprehensive comparison of 2D spectral estimation methods for SAR imaging. It provides a synopsis of the algorithms available, discusses their relative merits for SAR imaging, and illustrates their performance on simulated and collected SAR imagery. Some of the algorithms presented or their derivations are new, as are some of the insights into or analyses of the algorithms. Second, this work develops multichannel variants of four related algorithms, minimum variance method (MVM), reduced-rank MVM (RRMVM), adaptive sidelobe reduction (ASR) and space variant apodization (SVA) to estimate both reflectivity intensity and interferometric height from polarimetric displaced-aperture interferometric data. All of these interferometric variants are new. In the interferometric contest, adaptive spectral estimation can improve the height estimates through a combination of adaptive nulling and averaging. Examples illustrate that MVM, ASR, and SVA offer significant advantages over Fourier methods for estimating both scattering intensity and interferometric height, and allow empirical comparison of the accuracies of Fourier, MVM, ASR, and SVA interferometric height estimates.     

A spectral matching approach for parameter and spectral estimationof nonstationary rational processes

The parameter and spectral estimation problems of nonstationary signals are considered. The nonstationary signals are modeled as rational processes with time-varying parameters. The spectral matching approach, which was introduced by Friedlander and Porat (1984), is generalized to the nonstationary case and two new estimators, namely, the time-varying spectral matching estimator (TVSME) and the time-frequency spectral matching estimator (TFSME) are proposed. The proposed methods estimate the parameters of the time-varying rational model by fitting the parametric spectrum expression to an estimated time-frequency distribution of the signal. An approximate statistical analysis is given for both methods along with computer simulation results, illustrating the performance of the proposed estimators