Laure Blanc-Féraud

The general purpose of my research is ill-posed inverse problems in image processing.

I have developed nonlinear regularization methods, which preserve discontinuities of the solution in order to prevent edges from smoothing during the regularization process. A class of such regularizing functions has been proposed, which correspond to half-quadratic regularization. These studies have been conducted jointly in the variational approach (minimization in BV space), and in the stochastic approach (using Markov Random Fields).

Regularization and segmentation : image segmentation models have been used to regularize inverse ill-posed problem in order to get a better compromise between smoothing and edge preserving. Thus inverse problems are explicitly stated as free discontinuity problems, by minimizing functionals with region and contour terms. Two methods have been developed

The fisrt one consists in an approximation of the functional by a sequence of elliptic functionals converging (in the Gamma-convergence sense) to the functional to be minimized. The minimium is computed by successive minimization of the functional of the sequence (see a demo for image classification).
The second one consists in explicitely writing regions and contours by using level set methods as used in active contours. For image classification application, regions and contours evolve toward an energy minimum which is a regular partition of the image according to the classes (see demo).

Parameter estimation :

In the stochastic approach , parameters of the edge preserving regularizing models (hyperparameters) have been estimated for the case of satellite image deconvolution problem. The maximum likelihood estimate is computed by using a MCMC (Monte Carlo Markov Chain) method (see demo).
Blind deconvolution consists in image deconvolution without knowing the parameters of the degradation model. This ia a great interest problem in satellite images.

Hierarchical approaches are important to obtain performing models and algorithms. I have worked on multiresolution algorithms by using wavelet transforms. More recently a deconvolution method has been proposed, using complex wavelet packets with automatic thresholding (see report).

Restoration/deconvolution

Fine structure detections

Image segmentation/classification

Applications satellite images, biological images, 2D and 3D SPECT (Single Photon Emission Tomography) reconstruction in nuclear imaging , 2D and 3D reconstruction by inverse diffraction in microwave imaging.