As expected, the results of using the 2D Laplacian and 2D gradient as regularizations were far too smooth to realistically represent the ocean floor between the sparse tracks. In order to capture the texture of the ridge feature in the dense tracks, we decided to estimate a prediction-error filter on the dense region and apply it using the helix as a 2D convolutional regularization.
Rather than creating a PEF on the lower portion and comparing its application to the entire sparse data set, a simpler test would be to create the PEF on the lower dense portion of the entire merged data set and apply it to the lower sparse tracks. This would permit a very straight forward comparison: the smooth model created from all the data within the dense region compared with the model from the same region using the sparse tracks only.
By looking at the smooth model constructed from the dense tracks in Figure 4, it seems that this data has two general types of texture. There is the rough lineated texture of the spreading ridge and there is the smooth texture of the ocean plane everywhere else. To compare different prediction-error filters, I created one PEF on the rough ridge feature, one PEF on the smooth areas, and one PEF over the entire dense region.
The vertical artifacts along the southern boundary are a result of polynomial division on the helix. They could be removed by padding.
Both of the models created from PEFs estimated on the ridge, Figure 6, and over the entire template, Figure 5, seem to capture some of the lineations of the spreading ridge, although the former has slightly more continuity.
The model created from the PEF estimated on the smooth area, Figure 7, does a poor job on the ridge as expected. Further, in the smooth areas, it is only slightly better than the others. This is a not a surprise because PEFs work best at spreading linear features.