H. Imai et al., THE FAMILY OF PARAMETRIC PROJECTION FILTERS AND ITS PROPERTIES FOR PERTURBATION, IEICE transactions on information and systems, E80D(8), 1997, pp. 788-794
A lot of optimum filters have been proposed for an image restoration p
roblem. Parametric filter, such as Parametric Wiener Filter, Parametri
c Projection Filter, or Parametric Partial Projection Filter, is often
used because it requires to calculate a generalized inverse of one op
erator. These optimum filters are formed by a degradation operator, a
covariance operator of noise, and one of original images. In practice,
these operators are estimated based on empirical knowledge. Unfortuna
tely it happens that such operators differ from the true ones. In this
paper, we show the unified formulae of inducing them to clarify their
common properties. Moreover, we investigate their properties for pert
urbation of a degradation operator. a covariance operator of noise. an
d one of original images. Some numerical examples follow to confirm th
at our description is valid.