Since the temporal resolution of a CT scanner is mainly limited by the rotation speed of the CT gantry, we are motivated to remove any mechanical rotation and achieve a completely stationary architecture. For fast cardiac imaging, in particular, we propose a “Trinity” CT architecture with three linear/curvilinear x-ray source arrays, each paired with an opposing 2D detector array. In this proposed design, the x-ray source arrays and associated detector arrays are arranged in a hexagon around the object to be scanned. Data collected in this geometry are truncated to various degrees and, to perform image reconstruction, an iterative algorithm is developed and implemented in the compressed-sensing framework. Numerical simulation suggests that this system architecture yields good quality reconstructions over a large field of view, with even better quality within smaller interior regions of interest. Relevant issues are also discussed for further research.