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Examples

In this section, we use two synthetic examples and two field data examples to test the denoising performance of the proposed DSD based thresholding. In order to numerically test the performance, and to quantify the comparison for all the examples, we simulate noisy data by adding Gaussian white noise.

We apply the following simple model for synthesizing noisy data with Gaussian white noise:

$\displaystyle \mathbf{u} = \mathbf{d} + \epsilon(\sigma),$ (10)

where $ \mathbf{u}$ denotes the simulated noisy seismic data, $ \mathbf{d}$ denotes the clean data, and $ \epsilon(\sigma)$ denotes a Gaussian white noise with zero mean and standard deviation $ \sigma$ . The clean data is recovered by applying a simple thresholding operator in the DSD domain.

In order to numerically test the denoising performance, we define the criterion for comparison as signal-to-noise ratio (SNR):

$\displaystyle SNR=10\log_{10}\frac{\Arrowvert \mathbf{d} \Arrowvert_2^2}{\Arrowvert \mathbf{d}-\hat{\mathbf{d}}\Arrowvert_2^2},$ (11)

where $ \hat{\mathbf{d}}$ is the denoised signal.



Subsections
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Next: Synthetic examples Up: Chen & Ma & Previous: Seislet transform based DSD

2016-02-27