|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).