Blind Deconvolution Using Generalized Cross-Validation Approach to Regularization Parameter Estimation

2011 ◽  
Vol 20 (3) ◽  
pp. 670-680 ◽  
Author(s):  
Haiyong Liao ◽  
Michael K Ng
Keyword(s):  
Parameter Estimation ◽  
Cross Validation ◽  
Blind Deconvolution ◽  
Regularization Parameter ◽  
Generalized Cross Validation

Automatic blind deconvolution with Toeplitz-structured sparse total least squares

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. V345-V357 ◽  
Author(s):  
Nasser Kazemi
Keyword(s):  
Least Squares ◽  
Cross Validation ◽  
Blind Deconvolution ◽  
Real Data ◽  
Total Least Squares ◽  
Data Matrix ◽  
Seismic Survey ◽  
Structural Constraints ◽  
Generalized Cross Validation ◽  
Free Data

Given the noise-corrupted seismic recordings, blind deconvolution simultaneously solves for the reflectivity series and the wavelet. Blind deconvolution can be formulated as a fully perturbed linear regression model and solved by the total least-squares (TLS) algorithm. However, this algorithm performs poorly when the data matrix is a structured matrix and ill-conditioned. In blind deconvolution, the data matrix has a Toeplitz structure and is ill-conditioned. Accordingly, we develop a fully automatic single-channel blind-deconvolution algorithm to improve the performance of the TLS method. The proposed algorithm, called Toeplitz-structured sparse TLS, has no assumptions about the phase of the wavelet. However, it assumes that the reflectivity series is sparse. In addition, to reduce the model space and the number of unknowns, the algorithm benefits from the structural constraints on the data matrix. Our algorithm is an alternating minimization method and uses a generalized cross validation function to define the optimum regularization parameter automatically. Because the generalized cross validation function does not require any prior information about the noise level of the data, our approach is suitable for real-world applications. We validate the proposed technique using synthetic examples. In noise-free data, we achieve a near-optimal recovery of the wavelet and the reflectivity series. For noise-corrupted data with a moderate signal-to-noise ratio (S/N), we found that the algorithm successfully accounts for the noise in its model, resulting in a satisfactory performance. However, the results deteriorate as the S/N and the sparsity level of the data are decreased. We also successfully apply the algorithm to real data. The real-data examples come from 2D and 3D data sets of the Teapot Dome seismic survey.

scholarly journals Iteratively Reweighted Blind Deconvolution With Adaptive Regularization Parameter Estimation

IEEE Access ◽  
2017 ◽  
Vol 5 ◽  
pp. 11959-11973 ◽  
Author(s):  
Houzhang Fang ◽  
Yi Chang ◽  
Gang Zhou ◽  
Lizhen Deng
Keyword(s):  
Parameter Estimation ◽  
Blind Deconvolution ◽  
Regularization Parameter ◽  
Adaptive Regularization

On generalized cross validation for stable parameter selection in disease models

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Alexandra Smirnova ◽  
Maia Martcheva ◽  
Hui Liu
Keyword(s):  
Inverse Problem ◽  
Operator Equation ◽  
Recovery Rate ◽  
Cross Validation ◽  
Regularization Parameter ◽  
Parameter Selection ◽  
Time Dependent ◽  
Disease Models ◽  
Generalized Cross Validation ◽  
Irregular Operator

AbstractIn this paper we study advantages and limitations of the Generalized Cross Validation (GCV) approach for selecting a regularization parameter in the case of a partially stochastic linear irregular operator equation. The research has been motivated by an inverse problem in epidemiology, where the goal was to reconstruct a time dependent treatment recovery rate for

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