 |
 |
 |
 | Seismic data interpolation using nonlinear shaping regularization |  |
![[pdf]](icons/pdf.png) |
Next: Comparison with the traditional
Up: Theory
Previous: Connection with projection onto
Using the definition of equation 9, we define a new shaping operator as:
![$\displaystyle \mathbf{S}'=\mathbf{L}(\mathbf{S}[\mathbf{d}'_n],\mathbf{S}[\mathbf{d}'_{n-1}]),$](img49.png) |
(12) |
where
is a new version of the commonly defined
shown in equation 6 and
denotes a linear combination operator. This new shaping operation apply a biased combination between the current model and the previous model, thus is thought to be faster.
Substituting
in equation 6 with
in equation 12, and combined with equation 10, we get a faster version of shaping regularization:
![$\displaystyle \mathbf{d}_{n+1} = \mathbf{L}(\mathbf{S}[\mathbf{d}'_n],\mathbf{S}[\mathbf{d}'_{n-1}]).$](img52.png) |
(13) |
The linear combination operator
can be defined as
 |
(14) |
where
.
 |
 |
 |
 | Seismic data interpolation using nonlinear shaping regularization |  |
![[pdf]](icons/pdf.png) |
Next: Comparison with the traditional
Up: Theory
Previous: Connection with projection onto
2015-11-24