Texture synthesis and prediction error filtering |

To fill ``holes'' in collected data, we have the familiar SEP formulation
(Claerbout, 1998a):

[5] is the ``data matching'' goal, which states that the model must match the known data , while [6] is the ``model smoothness'' goal, where is an arbitrary roughening operator. To combat slow convergence, Claerbout (1998a) preconditions with the inverse of the convolutional operator (multidimensional

The operator effectively maps vectors in model space into a smaller-dimension ``known data space'', so it has a nonempty nullspace. Missing points in model space are completely unconstrained by , so our choice of wholly determines the behavior of the missing model points, i.e., their

tree-hole-filled
Clockwise from top left:
Data with hole, impulse response of ``inverse PEF'' (deconvolution of the PEF
estimated from the data and a spike), data in-filled using
regularization, data in-filled using preconditioned PEF regularization.
Figure 10. |
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Texture synthesis and prediction error filtering |

2013-03-03