Conventional 2D mammography was the most effective approach to detecting early stage breast cancer in the past decades of years. Tomosynthetic breast imaging is a potentially more valuable 3D technique for breast cancer detection. The limitations of current tomosynthesis systems include a longer scanning time than a conventional digital X-ray modality and a low spatial resolution due to the movement of the single X-ray source. Dr.Otto Zhou's group proposed the concept of stationary digital breast tomosynthesis (s-DBT) using a Carbon Nano-Tube (CNT) based X-ray source array. Instead of mechanically moving a single X-ray tube, s-DBT applies a stationary X-ray source array, which generates X-ray beams from different view angles by electronically activating the individual source prepositioned at the corresponding view angle, therefore eliminating the focal spot motion blurring from sources. The scanning speed is determined only by the detector readout time and the number of sources regardless of the angular coverage spans, such that the blur from patient's motion can be reduced due to the quick scan. S-DBT is potentially a promising modality to improve the early breast cancer detection by providing decent image quality with fast scan and low radiation dose. DBT system acquires a limited number of noisy 2D projections over a limited angular range and then mathematically reconstructs a 3D breast. 3D reconstruction is faced with the challenges of cone-beam and flat-panel geometry, highly incomplete sampling and huge reconstructed volume. In this research, we investigated several representative reconstruction methods such as Filtered backprojection method (FBP), Simultaneous algebraic reconstruction technique (SART) and Maximum likelihood (ML). We also compared our proposed statistical iterative reconstruction (IR) with particular prior and computational technique to these representative methods. Of all available reconstruction methods in this research, our proposed statistical IR appears particularly promising since it provides the flexibility of accurate physical noise modeling and geometric system description. In the following chapters, we present multiple key techniques of statistical IR to tomosynthesis imaging data to demonstrate significant image quality improvement over conventional techniques. These techniques include the physical modeling with a local voxel-pair based prior with the flexibility in its parameters to fine-tune image quality, the pre-computed parameter κ incorporated with the prior to remove the data dependence and to achieve a predictable resolution property, an effective ray-driven technique to compute the forward and backprojection and an over-sampled ray-driven method to perform high resolution reconstruction with a practical region of interest (ROI) technique. In addition, to solve the estimation problem with a fast computation, we also present a semi-quantitative method to optimize the relaxation parameter in a relaxed order-subsets framework and an optimization transfer based algorithm framework which potentially allows less iterations to achieve an acceptable convergence. The phantom data is acquired with the s-DBT prototype system to assess the performance of these particular techniques and compare our proposed method to those representatives. The value of IR is demonstrated in improving the detectability of low contrast and tiny micro-calcification, in reducing cross plane artifacts, in improving resolution and lowering noise in reconstructed images. In particular, noise power spectrum analysis (NPS) indicates a superior noise spectral property of our proposed statistical IR, especially in the high frequency range. With the decent noise property, statistical IR also provides a remarkable reconstruction MTF in general and in different areas within a focus plane. Although computational load remains a significant challenge for practical development, combined with the advancing computational techniques such as graphic computing, the superior image quality provided by statistical IR will be realized to benefit the diagnostics in real clinical applications.

La tomographie à rayons X est une technologie d’imagerie en trois dimensions. Elle se base sur la transmission de rayons X à travers l’objet d’étude. Elle est non destructive mais néanmoins irradiante. Cette technique de visualisation est utilisée principalement dans trois domaines : le diagnostic médical, le contrôle non destructif (détection de défauts dans des pièces industrielles de haute performance) et la sécurité (contrôles aéroportuaires des bagages). Les récentes avancées technologiques dans le domaine des détecteurs spectrométriques de rayons X ouvrent des perspectives d’amélioration de cette technique d’imagerie dans ses divers domaines d’application. Nous avons développé une nouvelle méthode reconstruction statistique appelée MLTR-ONE-STEP qui permet de reconstruire la variabilité énergétique du coefficient linéaire d’atténuation de l’objet étudié. Cette approche est dite « one-step » car elle reconstruit directement le volume final à partir des mesures brutes issues de détecteurs spectrométriques.Les phénomènes physiques au sein du détecteur provoquent une distorsion énergétique du spectre d’atténuation qui a été prise en compte lors de la reconstruction. La méthode utilisée s’inscrit dans le cadre bayésien et maximise la log-vraisemblance du modèle tout en prenant en compte de l’a priori spatial sur le volume reconstruit. L’objectif de la méthode est l’amélioration de la qualité de l’image finale (réduction des artefacts et niveau de bruit) et la quantification des matériaux présents. Nous avons étudié dans le cadre de données simulées l’influence des paramètres de régularisation sur la reconstruction. En pratique, le détecteur de rayon X étudié classe les photons incidents en 64 canaux. Ils sont ensuite regroupés en un nombre de canaux plus faible (2 à 25) et l’influence de ce regroupement a été étudiée. La reconstruction MLTR-ONE-STEP a ensuite été testée sur des données expérimentales regroupées en 12 canaux. / X-ray spectral tomography is a 3D visualization technique. It is based on the transmission of X-rays through object matter. It is a non-destructive technology but which irradiates the studied object/patient. X-ray tomography is mainly used in three areas: medical diagnosis, non-destructive testing (detection of defects in industry devices) and airport security (luggage screening). New technological breakthroughs in X-ray photon-counting detectors provide new perspective for improving this technique in each application field. We have developed a new reconstruction method named MLTR-ONE-STEP which enables the obtention of energetic variability of the scanned object linear attenuation coefficient. This approach belongs to the “One-Step” class because it directly reconstructs the final images from raw photon-counting detector data.Physical effects inside the detector are causing spectral distortion of the energetic spectrum. This distortion is taken into account in our reconstruction through a Detector Response Matrix. The developed reconstruction method maximizes the poissonian likelihood of the measurements with a spatial regularization Tukey term. The objectives of spectral tomography are the improvement of the image quality compared to standard tomography and the quantification of materials inside the object. We have studied the influence of regularization parameters on the final result. In practice, photon-counting detector measurements are in practice sorted in 64 energy bins. Bins are then merged in a smaller number (from 2 to 25). The influence of this binning was studied on simulated data. The MLTR-ONE-STEP was then tested on real experimental data in order to prove the feasibility of such a “One-Step” reconstruction method.