From Newton filters, previously presented computer aided systems theor
y (CAST) tools whose basic ideas for design are inspired directly by t
he neurons of the retinal pathway, we define a new class of transforms
, the Newton transforms, using what we call Newton matrices. The prope
rties of these matrices, which are explained in this paper, make it po
ssible to define this transformation on data fields whose inverse has
the same structure as the direct transform. A parallel processing neur
on-like structure for computing these calculations is designed, and an
example of the use of this technique is on image processing and codin
g is also presented.