A method and system for blood flow velocity reconstruction from medical image data is disclosed. Flow system geometry of a flow conduit is generated from medical image data. The flow system velocity includes an inlet, walls, and one or more outlets of the flow conduit. A measured velocity field is extracted from the medical image data. Inlet and wall fluxes are estimated based on the measured velocity field or other external measurements. Outlet fluxes are estimated such that mass conservation is constrained based on the inlet and wall fluxes. A reconstructed velocity field is calculated by solving flux-constrained Poisson (FCP) equations that are constrained by the estimated output fluxes
