Imaging system performing substantially exact reconstruction and using non-traditional trajectories

A method of imaging at least a part of a region of interest (ROI) in an off-plane to a trajectory comprising:

• moving a source relative to the ROI in a trajectory, the trajectory being at least one of non-continuous or non-closed, the trajectory defining a first plane and the ROI being transected by a second plane, the second plane being off of the first plane;
• collecting data from at least one sensor as the source moves relative to the ROI;
• and
• generating a substantially exact reconstruction of the ROI based on the data collected, wherein the substantially exact reconstruction is derived from a mathematically exact transformation from data space into image space.

A method of imaging at least a part of a region of interest (ROI) in an off-plane to a trajectory comprising:

• moving a source relative to the ROI in a trajectory, the trajectory defining a first plane and the ROI being transected by a second plane, the second plane being off of the first plane;
• collecting data from at least one sensor as the source moves relative to the ROI;
• and
• generating a substantially exact reconstruction of the ROI using virtual chords based on the data collected, wherein the substantially exact reconstruction is derived from a mathematically exact transformation from data space into image space.

A system of imaging at least a part of a region of interest (ROI), the system comprising:

• at least one source for illuminating the ROI;
• at least one motor to control at least one of the source or the ROI in order to move the source relative to the ROI in a trajectory;
• at least one sensor to acquire data at least partly when the source and the ROI move relative to one another;
• and
• at least one processor configured to:
• control the motor in order to move the source relative to the ROI in a trajectory, virtual chords intersecting and filling the ROI, the virtual chords not intersecting the trajectory;
• receive data from the at least one sensor, the at least one sensor collecting the data as the source moves relative to the ROI;
• and
• generate a substantially exact reconstruction of the ROI using the virtual chords based on the data received, wherein the substantially exact reconstruction is derived from a mathematically exact transformation from data space into image space.