Artifacts are unwanted effects in tomographic images that do not reflect the nature of the object. Their widespread occurrence makes their reduction and if possible removal an important subject in the development of tomographic image reconstruction algorithms. Limited angle artifacts are caused by the limited angular measurements, constraining the available tomographic information. This thesis focuses on reducing these artifacts via image reconstruction in two cases of incomplete measurements from: (1) the gaps left after the removal of high density objects such as dental fillings, screws and implants in computed tomography (CT) and (2) partial ring scanner configurations in positron emission tomography (PET). In order to include knowledge about the measurement and noise, prior terms were used within the reconstruction methods. Careful consideration was given to the trade-off between image blurring and noise reduction upon reconstruction of low-dose measurements.Development of reconstruction methods is an incremental process starting with testing on simple phantoms towards more clinically relevant ones by modeling the respective physical processes involved. In this work, phantoms were constructed to ensure that the proposed reconstruction methods addressed to the limited angle problem. The reconstructed images were assessed qualitatively and quantitatively in terms of noise reduction, edge sharpness and contrast recovery.Maximum a posteriori (MAP) estimation with median root prior (MRP) was selected for the reconstruction of limited angle measurements. MAP with MRP successfully reduced the artifacts caused by limited angle data in various datasets, tested with the reconstruction of both list-mode and projection data. In all cases, its performance was found to be superior to conventional reconstruction methods such as total-variation (TV) prior, maximum likelihood expectation maximization (MLEM) and filtered backprojection (FBP). MAP with MRP was also more robust with respect to parameter selection than MAP with TV prior.This thesis demonstrates the wide-range applicability of MAP with MRP in medical tomography, especially in low-dose imaging. Furthermore, we emphasize the importance of developing and testing reconstruction methods with application-specific phantoms, together with the properties and limitations of the measurements in mind
