Inverse NS convolution: | (9) | |

Inverse NS combination: | (10) | |

Adjoint inverse NS convolution: | (11) | |

Adjoint inverse NS combination: | (12) | |

Table 1: Recursive formulae for non-stationary (NS) inverse operators.

As with the stationary inverse convolution described above, it is apparent that subject to numerical errors, non-stationary inverse filtering with these equations in Table 1 is the exact, analytic inverse of non-stationary filtering with the corresponding forward operator described in equations (5) through (8): they are true inverse processes. If operator represents filtering with a non-stationary causal-filter, and represents recursive inverse filtering with the same filter then

The `nhelicon` module Claerbout (1998a) implements the
non-stationary combination operator/adjoint pair, described by
equations (6) and (8), while
`npolydiv` implements the corresponding inverse operators,
described by equations (10) and (12).

10/25/1999