If we use an iterative deconvolution algorithm, such as Van Cittert's or
Lucy's one, we define 
, the error at iteration n:
By using the à trous wavelet transform algorithm, 
can be defined by the sum of its 
wavelet planes and the last smooth
plane (see equation 
).
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:
is the standard deviation of the noise at scale j, and 
is
a function which is defined by:
The standard deviation of the noise 
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.
