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The panel on the left shows bathymetry (water depth) measurements
above the mid-ocean ridge in the Pacific.
The measurements were taken by a side-scan sonar hanging off the bottom of
a ship.
The vessel's path did not cover the entire image area and
consequently we attempt to estimate the missing data.
The masking operator
extracts the known data,
from the total data set
.
The solution in the center panel
minimizes the output of the Laplace operator applied to
the data ,
,
under the constraint that
the known data does not change,
.
The solution in the right panel
uses a two stage prediction-error technique.
First,
we minimize the convolution
to estimate the prediction-error filter
.
Next, we replace the Laplacian in the earlier formulation
by the prediction-error filter and solve again for the missing data.
The missing data estimation
is easily built from a combination of
the objects shown in the deconvolution example,
a specialized prediction-error filter class,
and the mask operator
.