Effects of the threshold function form for wavelet noise reduction with generalized cross-validation method

2004 ◽  
Vol 1268 ◽  
pp. 1238
Author(s):  
Hideaki Kubota ◽  
Nobuyoshi Tanki ◽  
Takafumi Nanjo ◽  
Kazunori Kawakami ◽  
Youichi Yamazaki ◽  
...  
Keyword(s):  
Noise Reduction ◽  
Cross Validation ◽  
Threshold Function ◽  
Function Form ◽  
Validation Method ◽  
Generalized Cross Validation

A SMOOTHING ALGORITHM FOR NONLINEAR TIME SERIES

2004 ◽  
Vol 14 (03) ◽  
pp. 1037-1051 ◽  
Author(s):  
S. A. BILLINGS ◽  
K. L. LEE
Keyword(s):  
Time Series ◽  
Noise Reduction ◽  
Cross Validation ◽  
User Interaction ◽  
Nonlinear Time Series ◽  
Smoothing Algorithm ◽  
Wavelet Thresholding ◽  
Numerical Examples ◽  
Validation Method

A new NARMA based smoothing algorithm is introduced for chaotic and nonchaotic time series. The new algorithm employs a cross-validation method to determine the smoother structure, requires very little user interaction, and can be combined with wavelet thresholding to further enhance the noise reduction. Numerical examples are included to illustrate the application of the new algorithm.

The data complexity index to construct an efficient cross-validation method

2010 ◽  
Vol 50 (1) ◽  
pp. 93-102 ◽  
Author(s):  
Der-Chiang Li ◽  
Yao-Hwei Fang ◽  
Y.M. Frank Fang
Keyword(s):  
Cross Validation ◽  
Data Complexity ◽  
Validation Method ◽  
Complexity Index

A note on generalized cross-validation with replicates

1992 ◽  
Vol 14 (4) ◽  
pp. 283-287 ◽  
Author(s):  
Chong Gu ◽  
Nancy Heckman ◽  
Grace Wahba
Keyword(s):  
Cross Validation ◽  
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.

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