Next: Introduction
Approximate Shift-Invariance by Warping Shift-Variant Systems
Scott R. McNown
Optical Sciences Center, University of Arizona, Tucson AZ, 85719
Bobby R. Hunt
Electrical and Computer Engineering, University of Arizona, Tucson AZ,
85719
Abstract:
A method is presented in which a signal, degraded by a linear shift-variant
system, will undergo a warping such that the resulting warped signal will be
approximately described by a warped original signal filtered by a linear
shift-invariant system. The warping is a limited class of coordinate
transformations, for which adjacent points do not cross each other after the
transformation. This results in a signal that may appear stretched in some
places and compressed in others (and curved if the signal is two-dimensional).
The purpose of this distortion is to make the space-variant impulse response
(which can be viewed as a space-invariant impulse response which has been
warped in the original signal domain) vary as little as possible. In particular
cases, a transformation can be found which will result in no impulse response
variations. For most cases, however, the impulse response will still have some
space variance, which the warping seeks to minimize. The residual variance will
be ignored (this error must be small in order for this method to work well),
and an ``average'' impulse response in the warped domain will be assumed. This
allows for space-invariant restoration of the warped signal, with all of its
attendant advantages in speed and reduced complexity.
Keywords:
shift-invariance, space-invariance, sampling, coordinate
transformation