Approximate Shift-Invariance by Warping Shift-Variant Systems

Scott R. McNown Bobby R. Hunt

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.

Pages 181-187

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