For many years it has been true that our most powerful signal-analysis techniques are in one-dimensional space, while our most important applications are in multi-dimensional space. We have made a giant step towards overcoming this difficulty.
Recently, I noticed that a helix maps 2-D to 1-D and that convolutions and deconvolutions in one dimension are practically equivalent to their multidimensional forms. First I will explain the helical transformation. Then I will show a simple 1-D computer program and some 2-D convolutions and deconvolutions done with it.
Finally I will explain why there should be a big future for the idea of filtering in multidimensional space as though it were simply filtering on a line. The main benefit arises from recursive operations because they are very efficient at carrying information for long distances.