This paper presents new algorithms for estimating the spatio-temporal spectrum of the signals received by a passive array. The algorithms are based on the eigenstructure of the covariance and spectral density matrices of the received signals. They allow partial correlation between the sources and thus are applicable to certain kinds of multipath problems. Simulation results that illustrate the performance of the new algorithms are presented.

Spatio-temporal spectral analysis by eigenstructure 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.

SAR imaging via modern 2-D spectral estimation methods

: This report discusses the use of modern 2-D spectral estimation algorithms for SAR imaging, and makes two principal contributions to the field of adaptive SAR imaging. First, it is a comprehensive comparison of 2-D 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. The discussion of autoregressive linear predictive techniques (ARLP), including the Tufts Kumaresan variant, is somewhat more general than appears in most of the literature, in that it allows the prediction element to be varied throughout the subaperture. This generality leads to a theoretical link between ARLP and one of Pisarenko's methods. The report also provides a theoretical analysis that predicts the impact of the adaptive sidelobe reduction (ASR) algorithm on target to clutter ratio and provides insight into order and constraint selection. Second, this work develops multi-channel variants of three related algorithms, minimum variance method (MVM), reduced rank MVM (RRMVM), and ASR to estimate both reflectivity intensity and interferometric height from polarimetric displaced-aperture interferometric data. Examples illustrate that MVM and ASR both offer significant advantages over Fourier methods for estimating both scattering intensity and interferometric height, and allow empirical comparison of the accuracies of Fourier, MVM, and- ometric height estimates.

SAR Imaging via Modern 2-D Spectral Estimation Methods. Volume 1. Imaging Methods.

Gravity and topography provide important insights regarding the degree and mechanisms of isostatic compensation. The azimuthally isotropic coherence function be- tween the Bouguer gravity anomaly and topography evolves from high to low for increasing wavenumber, a diagnostic that can be predicted for a variety of lithospheric loading models and used in inversions for flexural rigidity thereof. In this study we investigate the isostatic response of continental Australia. We consider the effects of directionally anisotropic plate strength on the coherelce. The anisotropic coherence function is calculated for regions of Australia that have distinctive geological and geophysical properties. The coherence estimation is performed by the Thomson multiple-Slepian-taper spectral analysis method extended to two-dimensional fields. Our analysis reveals the existence of flexural anisotropy in central Australia, indicative of a weaker N-S direction of lower Te. This observation is consistent with the suggestion that the parallel faults in that area act to make the lithosphere weaker in the direction perpendicular to them. It can. also be related to the N-S direction of maximum stress and possibly the presence of E-W running zones weakened due to differential sediment burial rates. We also demonstrate that the multitaper method has distinct advantages for computing the isotropic coherence function. The ability to make many independent estimates of the isostatic response that are minimally affected by spectral leakage results in a coherence that is more robust than with modified periodogram methods, particularly at low wavenumbers. Our analysis elucidates the reasons for discrepancies in previous estimates of effective elastic thickness Te of the Australian lithosphere. In isotropic inversions for Te, we obtain values that are as much as a factor of 2 less than those obtained in standard inversions of the periodogram coherence using Bouguer gravity and topography but greater than those obtained by inversions that utilize free-air rather than Bouguer gravity and ignore the presence of subsurface loads. However, owing to the low spectral power of the Australian topography, the uncertainty on any estimate of Te is substantial.

/pdf/isostatic-response-of-the-australian-lithosphere-estimation-15kp58r89n.pdf

Isostatic response of the Australian lithosphere: Estimation of effective elastic thickness and anisotropy using multitaper spectral analysis

A new method for estimating the two-dimensional (2D) exponential modes and amplitude coefficients in a Prony model is presented. This method involves two parts, each utilizing a 1D singular value decomposition-based technique, and is capable of locating frequencies anywhere in the 2D frequency plane. Simulations are shown which demonstrate the performance of the algorithm. >

Two-dimensional Prony modeling and parameter estimation

In this paper we present the results of a number of experiments that have been performed to study the properties of two-dimensional maximum entropy spectral estimates. The results presented include studies on the resolution differences for real and complex data, resolution properties of the spectral estimates, and the determination of the relative power of the sinusoids from the spectral estimates. The results also include the effects of signal-to-noise ratio, size and shape of the known autocorrelation region, and data length and initial phase of a sinusoid, on the spectral estimates. In most cases studied, the properties of two-dimensional maximum entropy spectral estimates can be viewed as simple extensions of their one-dimensional counterparts.

Properties of two-dimensional maximum entropy power spectrum estimates

A new iterative algorithm for the maximum entropy power spectrum estimation is presented in this paper. The algorithm, which is applicable to two-dimensional signals as well as one-dimensional signals, utilizes the computational efficiency of the fast Fourier transform (FFT) algorithm and has been empirically observed to solve the maximum entropy power spectrum estimation problem. Examples are shown to illustrate the performance of the new algorithm.

A new algorithm for two-dimensional maximum entropy power spectrum estimation

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Properties of two-dimensional maximum entropy power spectrum estimates

A new algorithm for two-dimensional maximum entropy power spectrum estimation