Ill-posed inverse problems have wide applications in many fields such as oceanography, signal processing, machine learning, biomedical imaging, remote sensing, geophysics, and others. In this dissertation, we address the problem of solving unstable operator equations with iteratively regularized Newton-type algorithms. Important practical questions such as selection of regularization parameters, construction of generating (filtering) functions based on a priori information available for different models, algorithms for stopping rules and error estimates are investigated with equal attention given to theoretical study and numerical experiments.

Le sujet de cette thèse concerne le codage et la restauration d'image dans le contexte de l'imagerie satellite. En dépit des récents développements en restauration et compression embarquée d'images, de nombreux artéfacts apparaissent dans la reconstruction de l'image. L'objectif de cette thèse est d'améliorer la qualité de l'image finale en étudiant la structure optimale de décodage et de restauration en fonction des caractéristiques des processus d'acquisition et de compression. Plus globalement, le but de cette thèse est de proposer une méthode efficace permettant de résoudre le problème de décodage-déconvolution-débruitage optimal dans un objectif d'optimisation globale de la chaîne compression/restauration. Le manuscrit est organisé en trois parties. La première partie est une introduction générale à la problématique traitée dans ce travail. Nous présentons un état de l'art des techniques de restauration et de compression pour l'imagerie satellite et nous décrivons la chaîne de traitement actuellement utilisée par le Centre National d'Etudes Spatiales (CNES) qui servira de référence tout au long de ce manuscrit. La deuxième partie concerne l'optimisation globale de la chaîne e d'imagerie satellite. Nous proposons une approche pour estimer la distorsion théorique de la chaîne complète et développons, dans trois configurations différentes de codage/restauration, un algorithme pour réaliser la minimisation. Notre deuxième contribution met également l'accent sur l'étude la chaîne globale mais est plus ciblée sur l'optimisation de la qualité visuelle de l'image finale. Nous présentons des méthodes numériques permettant d'améliorer la qualité de l'image reconstruite et nous proposons une nouvelle chaîne image basée sur les résultats d'évaluation de qualité de ces techniques. La dernière partie de la thèse introduit une chaîne d'imagerie satellite basée sur une nouvelle théorie de l'échantillonnage. Cette technique d'échantillonnage est intéressante dans le domaine du satellitaire car elle permet de transférer toutes les difficultés au décodeur qui se situe au sol. Nous rappelons les principaux résultats théoriques de cette technique d'échantillonnage et nous présentons une chaîne image construite à partir de cette méthode. Nous proposons un algorithme permettant de résoudre le problème de reconstruction et nous concluons cette partie en comparant les résultats obtenus avec cette chaîne et celle utilisée actuellement par le CNES. / The subject of this work is image coding and restoration in the context of satellite imaging. Regardless of recent developments in image restoration techniques and embedded compression algorithms, the reconstructed image still suffers from coding artifacts making its quality evaluation difficult. The objective of the thesis is to improve the quality of the final image with the study of the optimal structure of decoding and restoration regarding to the properties of the acquisition and compression processes. More essentially, the aim of this work is to propose a reliable technique to address the optimal decoding-deconvolution-denoising problem in the objective of global optimization of the compression/restoration chain. The thesis is organized in three parts. The first part is a general introduction to the problematic addressed in this work. We then review a state-of-the-art of restoration and compression techniques for satellite imaging and we describe the current imaging chain used by the French Space Agency as this is the focus of the thesis. The second part is concerned with the global optimization of the satellite imaging chain. We propose an approach to estimate the theoretical distortion of the complete chain and we present, for three different configurations of coding/restoration, an algorithm to perform its minimization. Our second contribution is also focused on the study of the global chain but is more aimed to optimize the visual quality of the final image. We present numerical methods to improve the quality of the reconstructed image and we propose a novel imaging chain based on the image quality assessment results of these techniques. The last part of the thesis introduces a satellite imaging chain based on a new sampling approach. This approach is interesting in the context of satellite imaging as it allows transferring all the difficulties to the on-ground decoder. We recall the main theoretical results of this sampling technique and we present a satellite imaging chain based on this framework. We propose an algorithm to solve the reconstruction problem and we conclude by comparing the proposed chain to the one currently used by the CNES.

Neste trabalho técnicas de restauração de imagens aplicadas à filtragem de imagens médicas foram estudadas. Considera-se uma abordagem recursiva de filtragem e suas diversas implementações em duas dimensões. A implementação utilizada neste trabalho foi a do filtro de Kalman de atualização reduzida (RUKF). Na implementação do filtro de Kalman de atualização reduzida um quarto de plano (QP) foi tomado como região de suporte e um modelo autoregressivo bidimensional (AR 2-D) foi utilizado como modelo de imagem. Os parâmetros do modelo AR 2-D e a variância do ruído foram encontrados através de uma implementação do algoritmo de Levinson para duas dimensões baseada no algoritmo de Levinson em configuração multicanal. A ordem do modelo AR 2-D foi determinada pelo critério de informação de Akaike (AIC). Para análise de resultados o filtro de Kalman de atualização reduzida foi aplicado em uma imagem planar, considerada invariante no espaço e com ruído ele observação não estacionário, e os resultados comparados àqueles obtidos com o filtro de Wiener. / In this work image restoration techniques for the filtering of medicai images are studied. Emphasis is given to the recursive approach to image restoration and its different implementations are described. The implementation used in the restoration procedure is the reduced update Kalman filter (RUKF). In the implementation of the reduced update Kalman filter a quarter plane is adopted as the region of support and a 2-D autoregressive (AR) model is used as the image model. The parameters of the 2-D AR model and the variance of the driving noise are found by a 2-D implementation of the Levinson algorithm. The model order of the 2-D AR model is determined by the Akaike information criterion (AIC). For the analysis of the results, the reduced update Kalman filter is applied to a space invariant plane image with nonstationary noise. The results are compared to the results of the Wiener filter.

<p>This report adresses the problem of software correction of spatially variant blur in digital images. The problem arises when the camera optics contains flaws, when the scene contains multiple moving objects with different relative motion or the camera itself is i.e. rotated. Compensation through deconvolving is impossible due to the shift-variance in the PSF hence alternative methods are required. There are a number of suggested methods published. This report evaluates two methods</p>

sA very fruitful approach to the solution of image segmentation andssurface reconstruction tasks is their formulation as estimationsproblems via the use of Markov random field models and Bayes theory.sHowever, the Maximuma Posteriori (MAP) estimate, which is the one mostsfrequently used, is suboptimal in these cases. We show that forssegmentation problems the optimal Bayesian estimator is the maximizersof the posterior marginals, while for reconstruction tasks, thesthreshold posterior mean has the best possible performance. We presentsefficient distributed algorithms for approximating these estimates insthe general case. Based on these results, we develop a maximumslikelihood that leads to a parameter-free distributed algorithm forsrestoring piecewise constant images. To illustrate these ideas, thesreconstruction of binary patterns is discussed in detail.

This report adresses the problem of software correction of spatially variant blur in digital images. The problem arises when the camera optics contains flaws, when the scene contains multiple moving objects with different relative motion or the camera itself is i.e. rotated. Compensation through deconvolving is impossible due to the shift-variance in the PSF hence alternative methods are required. There are a number of suggested methods published. This report evaluates two methods

No description available.

Multiframe image superresolution has been an active research area for many years. In this approach image processing techniques are used to combine multiple low-resolution (LR) images capturing different views of an object. These multiple images are generally under-sampled, degraded by optical and pixel blurs, and corrupted by measurement noise. We exploit diversities in the imaging channels, namely, the number of cameras, magnification, position, and rotation, to undo degradations. Using an iterative back-projection (IBP) algorithm we quantify the improvements in image fidelity gained by using multiple frames compared to single frame, and discuss effects of system parameters on the reconstruction fidelity. As an example, for a system in which the pixel size is matched to optical blur size at a moderate detector noise, we can reduce the reconstruction root-mean-square-error by 570% by using 16 cameras and a large amount of diversity in deployment.We develop a new technique for superresolving binary imagery by incorporating finite-alphabet prior knowledge. We employ a message-passing based algorithm called two-dimensional distributed data detection (2D4) to estimate the object pixel likelihoods. We present a novel complexity-reduction technique that makes the algorithm suitable even for channels with support size as large as 5x5 object pixels. We compare the performance and complexity of 2D4 with that of IBP. In an imaging system with an optical blur spot matched to pixel size, and four 2x2 undersampled LR images, the reconstruction error for 2D4 is 300 times smaller than that for IBP at a signal-to-noise ratio of 38dB.We also present a transform-domain superresolution algorithm to efficiently incorporate sparsity as a form of prior knowledge. The prior knowledge that the object is sparse in some domain is incorporated in two ways: first we use the popular L1 norm as the regularization operator. Secondly we model wavelet coefficients of natural objects using generalized Gaussian densities. The model parameters are learned from a set of training objects and the regularization operator is derived from these parameters. We compare the results from our algorithms with an expectation-maximization (EM) algorithm for L1 norm minimization and also with the linear minimum mean squared error (LMMSE) estimator.

The subject of this work is image coding and restoration in the context of satellite imaging. Regardless of recent developments in image restoration techniques and embedded compression algorithms, the reconstructed image still suffers from coding artifacts making its quality evaluation difficult. The objective of the thesis is to improve the quality of the final image with the study of the optimal structure of decoding and restoration regarding to the properties of the acquisition and compression processes. More essentially, the aim of this work is to propose a reliable technique to address the optimal decoding-deconvolution-denoising problem in the objective of global optimization of the compression/restoration chain. The thesis is organized in three parts. The first part is a general introduction to the problematic addressed in this work. We then review a state-of-the-art of restoration and compression techniques for satellite imaging and we describe the current imaging chain used by the French Space Agency as this is the focus of the thesis. The second part is concerned with the global optimization of the satellite imaging chain. We propose an approach to estimate the theoretical distortion of the complete chain and we present, for three different configurations of coding/restoration, an algorithm to perform its minimization. Our second contribution is also focused on the study of the global chain but is more aimed to optimize the visual quality of the final image. We present numerical methods to improve the quality of the reconstructed image and we propose a novel imaging chain based on the image quality assessment results of these techniques. The last part of the thesis introduces a satellite imaging chain based on a new sampling approach. This approach is interesting in the context of satellite imaging as it allows transferring all the difficulties to the on-ground decoder. We recall the main theoretical results of this sampling technique and we present a satellite imaging chain based on this framework. We propose an algorithm to solve the reconstruction problem and we conclude by comparing the proposed chain to the one currently used by the CNES.

Neste trabalho técnicas de restauração de imagens aplicadas à filtragem de imagens médicas foram estudadas. Considera-se uma abordagem recursiva de filtragem e suas diversas implementações em duas dimensões. A implementação utilizada neste trabalho foi a do filtro de Kalman de atualização reduzida (RUKF). Na implementação do filtro de Kalman de atualização reduzida um quarto de plano (QP) foi tomado como região de suporte e um modelo autoregressivo bidimensional (AR 2-D) foi utilizado como modelo de imagem. Os parâmetros do modelo AR 2-D e a variância do ruído foram encontrados através de uma implementação do algoritmo de Levinson para duas dimensões baseada no algoritmo de Levinson em configuração multicanal. A ordem do modelo AR 2-D foi determinada pelo critério de informação de Akaike (AIC). Para análise de resultados o filtro de Kalman de atualização reduzida foi aplicado em uma imagem planar, considerada invariante no espaço e com ruído ele observação não estacionário, e os resultados comparados àqueles obtidos com o filtro de Wiener. / In this work image restoration techniques for the filtering of medicai images are studied. Emphasis is given to the recursive approach to image restoration and its different implementations are described. The implementation used in the restoration procedure is the reduced update Kalman filter (RUKF). In the implementation of the reduced update Kalman filter a quarter plane is adopted as the region of support and a 2-D autoregressive (AR) model is used as the image model. The parameters of the 2-D AR model and the variance of the driving noise are found by a 2-D implementation of the Levinson algorithm. The model order of the 2-D AR model is determined by the Akaike information criterion (AIC). For the analysis of the results, the reduced update Kalman filter is applied to a space invariant plane image with nonstationary noise. The results are compared to the results of the Wiener filter.