The goal in medical x-ray imaging is to obtain the image quality requiredfor a given detection task, while ensuring that the patient dose is kept as lowas reasonably achievable. The two most common strategies for dose reductionare: optimizing incident x-ray beams and utilizing energy informationof transmitted beams with new detector techniques (spectral imaging). Inthis thesis, dose optimization schemes were investigated in two x-ray imagingsystems: digital mammography and computed tomography (CT). In digital mammography, the usefulness of anti-scatter grids was investigatedas a function of breast thickness with varying geometries and experimentalconditions. The general conclusion is that keeping the grid is optimalfor breasts thicker than 5 cm, whereas the dose can be reduced without a gridfor thinner breasts. A photon-counting silicon-strip detector developed for spectral mammographywas characterized using synchrotron radiation. Energy resolution, ΔE/Ein, was measured to vary between 0.11-0.23 in the energy range 15-40 keV, which is better than the energy resolution of 0.12-0.35 measured inthe state-of-the-art photon-counting mammography system. Pulse pileup hasshown little effect on energy resolution. In CT, the performance of a segmented silicon-strip detector developedfor spectral CT was evaluated and a theoretical comparison was made withthe state-of-the-art CT detector for some clinically relevant imaging tasks.The results indicate that the proposed photon-counting silicon CT detector issuperior to the state-of-the-art CT detector, especially for high-contrast andhigh-resolution imaging tasks. The beam quality was optimized for the proposed photon-counting spectralCT detector in two head imaging cases: non-enhanced imaging and Kedgeimaging. For non-enhanced imaging, a 120-kVp spectrum filtered by 2half value layer (HVL) copper (Z = 29) provides the best performance. Wheniodine is used in K-edge imaging, the optimal filter is 2 HVL iodine (Z = 53)and the optimal kVps are 60-75 kVp. In the case of gadolinium imaging, theradiation dose can be minimized at 120 kVp filtered by 2 HVL thulium (Z =69). / <p>QC 20160401</p>