Seismic data restoration based on the Grassmannian rank-one update subspace estimation method

2018 ◽  
Vol 159 ◽  
pp. 731-741 ◽  
Author(s):  
Yatong Zhou ◽  
Chunying Han
2018 ◽  
Vol 12 (8) ◽  
pp. 992-999 ◽  
Author(s):  
Karthikeyan Elumalai ◽  
Shailesh Kumar ◽  
Brejesh Lall ◽  
Rakesh Kumar Patney

2012 ◽  
Vol 01 (02) ◽  
pp. 1150006 ◽  
Author(s):  
WALID HACHEM ◽  
PHILIPPE LOUBATON ◽  
XAVIER MESTRE ◽  
JAMAL NAJIM ◽  
PASCAL VALLET

In array processing, a common problem is to estimate the angles of arrival of K deterministic sources impinging on an array of M antennas, from N observations of the source signal, corrupted by Gaussian noise. In the so-called subspace methods, the problem reduces to estimate a quadratic form (called "localization function") of a certain projection matrix related to the source signal empirical covariance matrix. The estimates of the angles of arrival are then obtained by taking the K deepest local minima of the estimated localization function. Recently, a new subspace estimation method has been proposed, in the context where the number of available samples N is of the same order of magnitude than the number of sensors M. In this context, the traditional subspace methods tend to fail because they are based on the empirical covariance matrix of the observations which is a poor estimate of the source signal covariance matrix. The new subspace method is based on a consistent estimator of the localization function in the regime where M and N tend to +∞ at the same rate. However, the consistency of the angles estimator was not addressed, and the purpose of this paper is to prove this consistency in the previous asymptotic regime. For this, we prove the property that the singular values of M × N Gaussian information plus noise matrix escape from certain intervals is an event of probability decreasing at rate [Formula: see text] for all p. A regularization trick is also introduced, which allows to confine these singular values into certain intervals and to use standard tools as Poincaré inequality to characterize any moments of the estimator. These results are believed to be of independent interest.


Author(s):  
Bingxiu Li ◽  
Dian Wang ◽  
Yang Liu ◽  
Cai Liu

Sensors ◽  
2020 ◽  
Vol 20 (7) ◽  
pp. 2037
Author(s):  
Zhishuo Yan ◽  
Yi Zhang ◽  
Heng Zhang

Due to self-motion and sea waves, moving ships are typically defocused in synthetic aperture radar (SAR) images. To focus non-cooperative targets, the inverse SAR (ISAR) technique is commonly used with motion compensation. The hybrid SAR/ISAR approach allows a long coherent processing interval (CPI), in which SAR targets are processed with ISAR processing, and exploits the advantages of both SAR and ISAR to generate well-focused images of moving targets. In this paper, based on hybrid SAR/ISAR processing, we propose an improved rank-one phase estimation method (IROPE). By using an iterative two-step convergence approach in the IROPE, the proposed method achieves accurate phase error, maintains robustness to noise and performs well in estimating various phase errors. The performance of the proposed method is analyzed by comparing it with other focusing algorithms in terms of processing simulated data and real complex image data acquired by Gaofen-3 (GF-3) in spotlight mode. The results demonstrate the effectiveness of the proposed method.


Geophysics ◽  
2021 ◽  
pp. 1-50
Author(s):  
Jie Zhang ◽  
Xuehua Chen ◽  
Wei Jiang ◽  
Yunfei Liu ◽  
He Xu

Depth-domain seismic wavelet estimation is the essential foundation for depth-imaged data inversion, which is increasingly used for hydrocarbon reservoir characterization in geophysical prospecting. The seismic wavelet in the depth domain stretches with the medium velocity increase and compresses with the medium velocity decrease. The commonly used convolution model cannot be directly used to estimate depth-domain seismic wavelets due to velocity-dependent wavelet variations. We develop a separate parameter estimation method for estimating depth-domain seismic wavelets from poststack depth-domain seismic and well log data. This method is based on the velocity substitution and depth-domain generalized seismic wavelet model defined by the fractional derivative and reference wavenumber. Velocity substitution allows wavelet estimation with the convolution model in the constant-velocity depth domain. The depth-domain generalized seismic wavelet model allows for a simple workflow that estimates the depth-domain wavelet by estimating two wavelet model parameters. Additionally, this simple workflow does not need to perform searches for the optimal regularization parameter and wavelet length, which are time-consuming in least-squares-based methods. The limited numerical search ranges of the two wavelet model parameters can easily be calculated using the constant phase and peak wavenumber of the depth-domain seismic data. Our method is verified using synthetic and real seismic data and further compared with least-squares-based methods. The results indicate that the proposed method is effective and stable even for data with a low S/N.


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