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The anisotropic fractional Brownian field (AFBF) is a non-stationary Gaussian random field which has been used for the modeling of textured images. In this paper, we address the open issue of estimating the functional parameters of this field, namely the topothesy and Hurst functions. We propose an original method which fits the empirical semi-variogram of an image to the semi-variogram of a turning-band field that approximates the AFBF. Expressing the fitting criterion in terms of a separable non-linear least square criterion, we design a minimization algorithm inspired from the variable projection approach. This algorithm also includes a coarse-to-fine multigrid strategy based on approximations of functional parameters. Compared to existing methods, the new method enables to estimate both functional parameters on their whole definition domain. On simulated textures, we show that it has a low estimation error, even when the parameters are approximated with a high precision. We also apply the method to characterize mammograms and sample images with synthetic parenchymal patterns.

International audience; Image deblurring is a fundamental problem in imaging, usually solved with compu-tationally intensive optimization procedures. The goal of this paper is to provide new efficient strategies to reduce computing times for simple 1 − 2 deblurring models. We show that the minimization can be significantly accelerated by leveraging the fact that images and blur operators are compressible in the same orthogonal wavelet basis. The proposed methodology consists of three ingredients: i) a sparse approximation of the blur operator in wavelet bases, ii) a diagonal preconditioner and iii) an implementation on massively parallel architectures. Combing the three ingredients leads to acceleration factors ranging from 30 to 250 on a typical workstation. For instance, a 1024 × 1024 image can be deblurred in 0.15 seconds.

Image deblurring is a fundamental problem in imaging, usually solved with computationally intensive optimization procedures. The goal of this paper is to provide new efficient strategies to reduce computing times for simple deblurring models regularized using orthogonal wavelet transforms. We show that the minimization can be significantly accelerated by leveraging the fact that images and blur operators are compressible in the same orthogonal wavelet basis. The proposed methodology consists of three ingredients: (i) a sparse approximation of the blur operator in wavelet bases, (ii) a diagonal preconditioner and (iii) an implementation on massively parallel architectures. Combining the three ingredients leads to acceleration factors ranging from 4 to 250 on a typical workstation. For instance, a 1024 1024 image can be deblurred in 0.15 s.

Le problème de restauration d'images dégradées par des flous variables connaît un attrait croissant et touche plusieurs domaines tels que l'astronomie, la vision par ordinateur et la microscopie à feuille de lumière où les images sont de taille un milliard de pixels. Les flous variables peuvent être modélisés par des opérateurs intégraux qui associent à une image nette u, une image floue Hu. Une fois discrétisé pour être appliqué sur des images de N pixels, l'opérateur H peut être vu comme une matrice de taille N x N. Pour les applications visées, la matrice est stockée en mémoire avec un exaoctet. On voit apparaître ici les difficultés liées à ce problème de restauration des images qui sont i) le stockage de ce grand volume de données, ii) les coûts de calculs prohibitifs des produits matrice-vecteur. Ce problème souffre du fléau de la dimension. D'autre part, dans beaucoup d'applications, l'opérateur de flou n'est pas ou que partialement connu. Il y a donc deux problèmes complémentaires mais étroitement liés qui sont l'approximation et l'estimation des opérateurs de flou. Cette thèse a consisté à développer des nouveaux modèles et méthodes numériques permettant de traiter ces problèmes. The restoration of images degraded by spatially varying blurs is a problem of increasing importance. It is encountered in many applications such as astronomy, computer vision and fluorescence microscopy where images can be of size one billion pixels. Variable blurs can be modelled by linear integral operators H that map a sharp image u to its blurred version Hu. After discretization of the image on a grid of N pixels, H can be viewed as a matrix of size N x N. For targeted applications, matrices is stored with using exabytes on the memory. This simple observation illustrates the difficulties associated to this problem: i) the storage of a huge amount of data, ii) the prohibitive computation costs of matrix-vector products. This problems suffers from the challenging curse of dimensionality. In addition, in many applications, the operator is usually unknown or only partially known. There are therefore two different problems, the approximation and the estimation of blurring operators. They are intricate and have to be addressed with a global overview. Most of the work of this thesis is dedicated to the development of new models and computational methods to address those issues.

Restoring images degraded by spatially varying blur is a problem encountered in many disciplines such as astrophysics, computer vision or biomedical imaging. Blurring operators are modelled using integral operators with some regularity and decrease conditions on the kernel. Recently, we studied the approximation of these operators in wavelet bases in which operators are highly compressible. They also allow to fastly compute matrix-vector products with a complexity $O(N\epsilon^{-d/M})$ for a precision $\epsilon$ in spectral norm, where N is the number of pixels of a d-dimensional image and M describes the kernel regularity. Additionnaly, we have shown that the sparsity pattern of the matrix can be pre-defined. We exploit these results to study the estimation/reconstruction of the operator from the knwoledge of few point spread functions located at arbitrary positions in the image domain. We propose an original formulation directly in the wavelet domain and a fast algorithm.

We design an image quality measure independent of local contrast changes, which constitute simple models of illumination changes. Given two images, the algorithm provides the image closest to the first one with the component tree of the second. This problem can be cast as a specific convex program called isotonic regression. We provide a few analytic properties of the solutions to this problem. We also design a tailored first order optimization procedure together with a full complexity analysis. The proposed method turns out to be practically more efficient and reliable than the best existing algorithms based on interior point methods. The algorithm has potential applications in change detection, color image processing or image fusion. A Matlab implementation is available at http://www.math.univ-toulouse.fr/_weiss/PageCodes.html.

Image deblurring is a fundamental problem in imaging, usually solved with com-putationally intensive optimization procedures. We show that the minimization can be significantly accelerated by leveraging the fact that images and blur operators are compressible in the same orthogonal wavelet basis. The proposed methodology consists of three ingredients: i) a sparse approximation of the blur operator in wavelet bases, ii) a diagonal preconditioner and iii) an implementation on massively parallel architectures. Combing the three ingredients leads to acceleration factors ranging from 30 to 250 on a typical workstation. For instance, a 1024 x 1024 image can be deblurred in 0.15 seconds, which corresponds to real-time.

Today, Light Sheet Fluorescence Microscopy (LSFM) makes it possible to image fluorescent samples through depths of several hundreds of microns. However, LSFM also suffers from scattering, absorption and optical aberrations. Spatial variations in the refractive index inside the samples cause major changes to the light path resulting in loss of signal and contrast in the deepest regions, thus impairing in-depth imaging capability. These effects are particularly marked when inhomogeneous, complex biological samples are under study. Recently, chemical treatments have been developed to render a sample transparent by homogenizing its refractive index (RI), consequently enabling a reduction of scattering phenomena and a simplification of optical aberration patterns. One drawback of these methods is that the resulting RI of cleared samples does not match the working RI medium generally used for LSFM lenses. This RI mismatch leads to the presence of low-order aberrations and therefore to a significant degradation of image quality. In this paper, we introduce an original optical-chemical combined method based on an adaptive SPIM and a water-based clearing protocol enabling compensation for aberrations arising from RI mismatches induced by optical clearing methods and acquisition of high-resolution in-depth images of optically cleared complex thick samples such as Multi-Cellular Tumour Spheroids.