Plane waves in three dimensions

Mono-plane deconvolution

The coefficients of a 2-D monoplane annihilator filter are defined to be the same as those of a 2-D PEF of spatial order unity; in other words, those defined by either (1) or (2).

The filter can be lengthened in time but not in space. The choice of exactly two columns is a choice to have an analytic form that can exactly destroy a single plane, but cannot destroy two. Applied to two signals that are statistically independent, the filter (2) reduces to the well-known prediction-error filter in the left column and zeros in the right column. If the filter coefficients were extended in both directions on $t$ and to the right on $x$ , the two-dimensional spectrum of the input would be flattened.