Figure 2

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 .

3/8/1999