In this work, we investigate optimization-based image reconstruction from few-view (i.e. less than ten views) projections of sparse objects such as coronary-artery specimens. Using optimization programs as a guide, we formulate constraint programs as reconstruction programs and develop algorithms to reconstruct images through solving the reconstruction programs. Characterization studies are carried out for elucidating the algorithm properties of 'convergence' (relative to designed solutions) and 'utility' (relative to desired solutions) by using simulated few-view data calculated from a discrete FORBILD coronary-artery phantom, and real few-view data acquired from a human coronary-artery specimen. Study results suggest that carefully designed reconstruction programs and algorithms can yield accurate reconstructions of sparse images from few-view projections.