Figure 6

The set of test data shown in Figure is a superposition of three functions like plane waves. One plane wave looks like low-frequency horizontal layers. Notice that the various layers vary in strength with depth. The second wave is dipping about down to the right and its waveform is perfectly sinusoidal. The third wave dips down to the left and its waveform is bandpassed random noise like the horizontal beds. These waves will be handled differently by different processing schemes, so I hope you can identify all three. If you have difficulty, view the figure at a grazing angle from various directions.

Later we will make use of the dense data region, but first let be the east-west PE operator and be the north-south operator and let the signal or image be .The fitting residuals are

(19) |

Figure shows the result of using a single one-dimensional PEF along either the vertical or the horizontal axis.

Figure 7

Figure compares the use of a pair of 1-D PEFs versus a single 2-D PEF (which needs the ``cheat'' corner in Figure .

Figure 8

Studying Figure we conclude (what theory predicts) that

- These waves are predictable with a pair of 1-D filters:
- Horizontal (or vertical) plane-wave with random waveform
- Dipping plane-wave with a sinusoidal waveform

- These waves are predictable with a single 2-D filter:
- both of the above
- Dipping plane-wave with a random waveform

4/27/2004