Recently dynamic, time-resolved three-dimensional computed tomography angiography (CTA) has been introduced to the neurological imaging community. However, the radiation dose delivered to patients in time-resolved CTA protocol is a high and potential risk associated with the ionizing radiation dose. Thus, minimizing the radiation dose is highly desirable for time-resolved CTA. In order to reduce the radiation dose delivered during dynamic, contrast-enhanced CT applications, we introduce here the CT formulation of HighlY constrained back PRojection (HYPR) imaging. We explore the radiation dose reduction approaches of both acquiring a reduced number of projections for each image and lowering the tube current used during acquisition. We then apply HYPR image reconstruction to produce image sets at a reduced patient dose and with low image noise. Numerical phantom experiments and retrospective analysis of in vivo canine studies are used to assess the accuracy and quality of HYPR reduced dose image sets and validate our approach. Experimental results demonstrated that a factor of 6-8 times radiation dose reduction is possible when the HYPR algorithm is applied to time-resolved CTA exams.