Shift-invariant cone-beam reconstruction outside R-lines with a disconnected source trajectory

Over the past decade, significant progress has been made in theoretically-exact and stable (TES) cone-beam reconstruction using shift-invariant filtering, provided that Tuy´s condition is satisfied. However, these algorithms only allow reconstruction at positions that lie on an R-line (an R-line is any segment of line that connects two source positions). In 2005, Pack and Noo proposed a formula that allows TES reconstruction outside R-lines using shift-invariant filtering. However, for some disconnected source trajectories, the backprojection and filtering steps for this formula are complex. In this work, we propose a new shift-invariant reconstruction formula that allows less complex TES reconstruction outside R-lines for some disconnected source trajectories. This new formula is validated using computer simulated data from a tent trajectory.