Applications of plane-wave destruction filters

Application examples

In this section, I examine the performance of the finite-difference plane-destruction filters on several test applications. The general framework for applying these filters consists of the two steps:

1. Estimate the dominant local slope (or a set of local slopes) from the data. This step follows the least-squares optimization embedded in equations (14) or (16). Thanks to the general regularization technique of equations (15 ) and (17-18), locally smooth slope estimates are obtained without any need for breaking the data into local windows. Of course, local windows can be employed for other purposes (parallelization, memory management, etc.) Selecting appropriate initial values for the local slopes can speed up the computation and steer it towards desirable results. It is easy to incorporate additional constraints on the local slope values.
2. Using the estimated slope, apply non-stationary plane-wave destruction filters for the particular application purposes. In the fault detection application, we simply look at the output of plane-wave destruction. In the interpolation application, the filters are used to constrain the missing data. In the noise attenuation application, they characterize the coherent signal and noise components in the data.

A description of these particular applications follows next.

Applications of plane-wave destruction filters