Notes on Deconvolution
The MR/1 Approach to Deconvolution
- Detection of signal, and hence of noise, provides a very effective
way to regularize the solution.
- There is no need to guess or estimate any regularizing parameter.
- In fact, convergence is usually very rapid (a few iterations only).
- In such regularization through noise removal (and the use of
variance stabilization if called for), the image so treated is the
discrepancy image between given input image and the approximation to this
at any iteration (the "residual image").
So variance stabilization does not alter the
basic nature of the inverse problem.
- The future: software for maximum entropy deconvolution is nearing
completion and will be part of the MR/2 package, due for release around
mid-1999. Multiscale entropy and noise modeling is used in this method.
- For various examples, evaluation, and to read further:
- Chapter 3 of JL Starck, F Murtagh and A Bijaoui, Image and Data
Analysis: the Multiscale Approach", Cambridge University Press, 1998.
- A Bijaoui, JL Starck and F Murtagh, "Restauration des images
multi-échelles par l'algorithme à trous", Traitement du
Signal, 11, 229-243, 1994.
- JL Starck and A Bijaoui, "Filtering and deconvolution by the
wavelet transform", Signal Processing, 35, 195-211, 1994.
- JL Starck and F Murtagh, "Image restoration with noise suppression
using the wavelet transform", Astronomy and Astrophysics, 288, 343-348,
- F Murtagh, JL Starck and A Bijaoui, "Image restoration with noise
suppression using a multiresolution support", Astronomy and Astrophysics
Supplement Series, 112, 179-189, 1995.
- JL Starck and E Pantin, "Multiscale maximum entropy image restoration",
Vistas in Astronomy, 40, 1-6, 1996.