Definition of LOMOPLAN in 3-D

Three-dimensional LOMOPLAN is somewhat like multiple passes of two-dimensional LOMOPLAN; i.e., we first LOMOPLAN the (t,x)-plane for each y, and then we LOMOPLAN the (t,y)-plane for each x. Actually, 3-D LOMOPLAN is a little more complicated than this. Each LOMOPLAN filter is designed on all the data in a small (t,x,y) volume.

I began from my earlier two-dimensional code and made the obvious extensions to three dimensions. For example, converting subroutine icaf2() to the 3-D version icaf3() gives a subroutine that convolves a volume over a volume to get a volume. When we need a 2-D filter, we pick a3=1 and with it, subroutine icaf3() convolves the planar filter throughout the input volume and thus gives an output volume. When we want a monoplane filter orthogonally oriented, we take a2=1 but a3=2.

To put the LOcal in LOMOPLAN we use subcubes (bricks). Recall that we can do 2-D LOMOPLAN with the prediction-error subroutine lopef2() . To do 3-D LOMOPLAN we need to make two calls to subroutine lopef3(), one for the x-axis in-line planar filters and one for the y-axis crossline filters. That is what I will try next time I install this book on a computer with a bigger memory.