Adaptive subtraction

The goal of adaptive subtraction is to estimate the non-stationary filters ${\bf f}$ that minimize the objective function  

$$g({\bf f})=\Vert{\bf Pf}-{\bf d}\Vert^2 ,$$ (71)

where ${\bf P}$ represents the non-stationary convolution with the multiple model obtained with SRMP (i.e., Chapter ) and ${\bf d}$ are the input data. These filters are estimated in a least-squares sense for one shot gather at a time. Note that in practice, a regularization term is usually added in equation () to enforce smoothness between filters. This strategy is similar to the one used in Chapter . The residual vector ${\bf Pf}-{\bf d}$ contains the estimated primaries.