Issue |
EAS Publications Series
Volume 59, 2013
New Concepts in Imaging: Optical and Statistical Models
|
|
---|---|---|
Page(s) | 265 - 301 | |
Section | Statistical Models in Signal and Image Processing | |
DOI | https://doi.org/10.1051/eas/1359013 | |
Published online | 13 March 2013 |
D. Mary, C. Theys and C. Aime (eds)
EAS Publications Series, 59 (2013) 265-301
Introduction to the Restoration of Astrophysical Images by Multiscale Transforms and Bayesian Methods
University of Nice Sophia Antipolis, UMR CNRS 6202,
OCA, BP. 4229,
06304
Nice Cedex 04,
France
The image restoration is today an important part of the astrophysical data analysis. The denoising and the deblurring can be efficiently performed using multiscale transforms. The multiresolution analysis constitutes the fundamental pillar for these transforms. The discrete wavelet transform is introduced from the theory of the approximation by translated functions. The continuous wavelet transform carries out a generalization of multiscale representations from translated and dilated wavelets. The à trous algorithm furnishes its discrete redundant transform. The image denoising is first considered without any hypothesis on the signal distribution, on the basis of the a contrario detection. Different softening functions are introduced. The introduction of a regularization constraint may improve the results. The application of Bayesian methods leads to an automated adaptation of the softening function to the signal distribution. The MAP principle leads to the basis pursuit, a sparse decomposition on redundant dictionaries. Nevertheless the posterior expectation minimizes, scale per scale, the quadratic error. The proposed deconvolution algorithm is based on a coupling of the wavelet denoising with an iterative inversion algorithm. The different methods are illustrated by numerical experiments on a simulated image similar to images of the deep sky. A white Gaussian stationary noise was added with three levels. In the conclusion different important connected problems are tackled.
© EAS, EDP Sciences 2013