**38.
Rounded Hartley Transform: A quasi-involution
**

A
new multiplicative-free transform derived from discrete Hartley transform
(DHT) is introduced: The Rouded Hartley Transform RHT.

Investigations on the properties of the RHT lead us to the concept of matrix
weak-inversion.

Using new constructs, we show that RHT is not exactly involutionary like
the DHT, but exhibits a quasi-involutionary property,

a definition derived from periodicity of matrices. Thus, instead of the actual
inverse transform, the RHT can be roughly viewed as

an involutionary transform, allowing the use of direct (multiplication-free)
to evaluate the inverse transform.

A fast algorithm to compute the RHT is presented. This algorithm held embedded
properties. We also extended RHT to the two-dimensional case.

This allows us to perform a preliminary analysis on the effects of RHT on
images.

Despite some signal to noise ratio loss, the RHT can be very interesting
for applications involving image monitoring associated with

decision making, such as military applications or medical imaging.

** **