R^{(n)}(x,y) = I(x,y) - P(x,y) * O^{(n)}(x,y) |
(14.111) |

By using the *à trous* wavelet transform algorithm, *R*^{(n)}
can be defined by the sum of its *n*_{p} wavelet planes and the last smooth
plane (see equation 14.33).

The wavelet coefficients provide a mechanism to extract from the residuals
at each iteration only the significant structures. A large part of
these residuals are generally statistically non significant.
The significant residual is:

(14.113) |

*N*_{j} is the standard deviation of the noise at scale *j*, and
is
a function which is defined by:

(14.114) |

The standard deviation of the noise *N*_{j} is estimated from the
standard deviation of the noise in the image. This
is done from the study of noise variation in the wavelet space,
with the hypothesis of a white Gaussian noise.

We now show how the iterative deconvolution algorithms can be modified in order to take into account only the significant structure at each scale.

- Regularization of Van Cittert's algorithm
- Regularization of the one-step gradient method
- Regularization of Lucy's algorithm
- Convergence