The first half of this talk will focus on the initiatives by the Ariana project in providing image processing tools that aid in solving inverse
problems arising in Earth observation and cartography. Some of these problems are related to cartographic updating, land management, and
agriculture. For such problems, even in the rare instance when the existence and uniqueness of the solution is guaranteed, the solution is
unstable due to the perturbing effects of observation noise. We use two broad classes of techniques to attack these problems: probabilistic models
combined with stochastic algorithms, and variational models combined with deterministic algorithms. In addition to applying these techniques to
specific cases, the project advances these techniques more generally, through innovative modeling and theoretical analysis, and a comparative
study of the two classes. The Bayesian methodology is followed as far as possible and probabilistic models are used for two purposes: to describe
the class of images to be expected from any given scene, and to describe prior knowledge about the scene in the absence of the current data. Some
of the probabilistic models used are Markov Random Fields (MRF) for texture segmentation, wavelets that sparsely represent the image data for
denoising and deconvolution. The use of variational models is mostly to regularize the inverse problems. Attention is focused on the use of such
models for image segmentation, in particular texture segmentation; on the theoretical study of the models and their associated algorithms, in
particular level set methods; and on the incorporation of prior geometric information concerning the regions sought using higher-order active
contour energies. Another interesting problem studied is how to estimate the parameters that appear in the models. For probabilistic models, the
problem is easily framed, but is not necessarily easy to solve, particularly in the case when it is necessary to extract simultaneously
from the data both the information of interest and the parameters. We shall provide some applications examples from image restoration and
denoising, multicamera reconstruction and super resolution, extraction of various complex structures in a scene, 3D modeling, segmentation and
classification, and information mining and retrieval from remote sensing image databases.

The second half of this talk will address a specific issue related to restoration of fluorescence Confocal Laser Scanning Microscope (CLSM)
images with parametric estimation of the acquisition system’s Point Spread Function (PSF). The CLSM is an optical fluorescence microscope that scans
a specimen in 3D and uses a pinhole to reject most of the out-of-focus light. However, the quality of the image suffers from two primary physical
limitations. The first is due to the diffraction-limited nature of the optical system and the second is due to the reduced amount of light
detected by the photomultiplier tube (PMT). These limitations cause blur and photon counting noise respectively. The images can hence benefit from
post-processing restoration methods based on deconvolution. An efficient method for parametric blind image deconvolution involves the simultaneous
estimation of the specimen 3D distribution of fluorescent sources and the microscope PSF. By using a model for the microscope image acquisition
physical process, we reduce the number of free parameters describing the PSF and introduce constraints. The parameters of the PSF may vary during
the course of experimentation, and so they have to be estimated directly from the observation data. We also introduce a priori knowledge of the
specimen that permits stabilization of the estimation process and favors the convergence. Experiments on simulated data show that the PSF could be
estimated with a higher degree of accuracy and those done on real data show very good deconvolution results in comparison to the theoretical
microscope PSF model.