Exact filtered backprojection reconstruction for dynamic pitch helical cone beam computed tomography

We present an exact filtered backprojection reconstruction formula for helical cone beam computed tomography in which the pitch of the helix varies with time. We prove that the resulting algorithm, which is functionally identical to the constant pitch case, provides exact reconstruction provided that the projection of the helix onto the detector forms convex boundaries and that PI lines are unique. Furthermore, we demonstrate that both of these conditions are satisfied provided the sum of the translational velocity and the derivative of the translational acceleration does not change sign. As a special case, we show that gantry tilt can also be handled by our dynamic pitch formula. Simulation results demonstrate the resulting algorithm.