The 3D microscopic biological images are obtained by successive acquisitions of 2D images for various depths. In order to obtain an exact three-dimensional image starting from the optical cuts, it is necessary to deconvolve the stack images in order to eliminate the non specific blur at each plan and to reduce the noise. The deconvolution is a ill-posed inverse problem who needs to be regularized. The recent methods of image deconvolution in the satellite image processing tend to use at the same time a regularization by wavelets, which allows a good restoration of the average frequencies like those of textures, and a regularization by minimization of the total variation of the image, which allows a good restoration of the homogeneous zones and contours. In biological imagery, the noise which appears in the images is a Poisson noise. We recently proposed a method of 3D deconvolution combining the statistics of Poisson and the regularization by total variation.

The goal of the training course suggested is to develop a deconvolution method using a wavelet regularization. This consists in developing a 3D wavelet transform and the deconvolution algorithm adapted to the Poisson noise. The tests will be carried out on synthesized images and real images acquired by Institute Pasteur with whom we collaborate within the framework of ARC Demitri.