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 | Random noise attenuation using local signal-and-noise orthogonalization |  |
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For many random noise attenuation approaches, the leakage energy is not negligible. We can attempt to retrieve the leaking signal from the noise section by applying a simple nonstationary weighting operator to the initially denoised signal assuming that the leakage energy can be predicted by weighting the useful signal:
Here
is the retrieved signal,
, which denotes Hadamard (or Schur) product, and
denotes the diagonal matrix composed of an input vector. The weighting vector
can be estimated by solving the following minimzation problem:
![$\displaystyle \min_{\mathbf{w}} \parallel \overbrace{\mathbf{d} - \mathbf{P}[\m...
...mathbf{w}\circ \overbrace{\mathbf{P}[\mathbf{d}]}^{\mathbf{s}_0} \parallel_2^2,$](img17.png) |
(2) |
where
denotes the observed noisy data, and
denotes the initial random noise attenuation operator. Equation 2 uses a weighted (scaled) signal
to match the leakage energy in the initial noise section (
) in a least-squares sense. In the next section, we will introduce an approach to calculate the weighting vector
using local orthogonalization.
 |
 |
 |
 | Random noise attenuation using local signal-and-noise orthogonalization |  |
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Next: Local orthogonalization
Up: Method
Previous: Method
2015-03-25