Radiation therapy (RT) is commonly used to treat patients with lung cancer. One of the limitations of RT is that irradiation of the surrounding healthy lung tissues during RT may cause damage to the lungs. Radiation-induced pulmonary toxicity may be mitigated by minimizing doses to high-function lung tissues, which we refer to as functional avoidance RT. Lung function can be computed by image registration of treatment planning four-dimensional computed tomography (4DCT), which we refer to as CT ventilation imaging. However, the accuracy of functional avoidance RT is limited by lung function imaging accuracy and artifacts in 4DCT. The goal of this dissertation is to improve the accuracy of functional avoidance RT by overcoming those two limitations. A common method for estimating lung ventilation uses image registration to align the peak exhale and inhale 3DCT images. This approach called the 2-phase local expansion ratio is limited because it assumes no out-of-phase lung ventilation and may underestimate local lung ventilation. Out-of-phase ventilation occurs when regions of the lung reach their maximum (minimum) local volume in a phase other than the peak of inhalation (end of exhalation). This dissertation presents a new method called the N-phase local expansion ratio for detecting and characterizing locations of the lung that experience out-of-phase ventilation. The N-phase LER measure uses all 4DCT phases instead of two peak phases to estimate lung ventilation. Results show that out-of-phase breathing was common in the lungs and that the spatial distribution of out-of-phase ventilation varied from subject to subject. On average, 49% of the out-of-phase regions were mislabeled as low-function by the 2-phase LER. 4DCT and Xenon-enhanced CT (Xe-CT) of four sheep were used to evaluate the accuracy of 2-phase LER and N-phase LER. Results show that the N-phase LER measure was more correlated with the Xe-CT than the 2-phase LER measure. These results suggest that it may be better to use all 4DCT phases instead of the two peak phases to estimate lung function. The accuracy of functional avoidance RT may also be improved by reducing the impact of artifacts in 4DCT. In this dissertation, we propose a a geodesic density regression (GDR) algorithm to correct artifacts in one breathing phase by using artifact-free data in corresponding regions of the other breathing phases. Local tissue density change associated with CT intensity change during respiration is accommodated in the GDR algorithm. Binary artifact masks are used to exclude regions of artifacts from the regression, i.e., the GDR algorithm only uses artifact-free data. The GDR algorithm estimates an artifact-free CT template image and its time flow through a respiratory cycle. Evaluation of the GDR algorithm was performed using both 2D CT time-series images with simulated known motion artifacts and treatment planning 4DCT with real motion artifacts. The 2D results show that there is no significant difference (p-value = 0.95) between GDR regression of artifact data using artifact masks and regression of artifact-free data. In contrast, significant errors (p-value = 0.005) were present in the estimated Jacobian images when artifact masks were not used. We also demonstrated the effectiveness of the GDR algorithm for removing real duplication, misalignment, and interpolation artifacts in 4DCT. Overall this dissertation proposes methods that have the potential to improve functional avoidance RT by accommodating out-of-phase ventilation, and removing motion artifacts in 4DCT using geodesic image regression.