Iterative algorithm for proton ct image reconstruction

A non-transitory computer readable medium, the computer readable medium including instructions that, when executed, perform a method of iteratively reconstructing a proton (pCT) image, the method comprising:

• determining an A matrix comprising a plurality of chord lengths, the plurality of chord lengths corresponding to one or more proton trajectories through one or more voxels;
• determining a b vector including one or more water equivalent path length (WEPL) values, the one or more WEPL values corresponding to one or more protons;
• determining a x vector including one or more relative stopping power (RSP) values, the RSP values corresponding to the one or more voxels;
• determining a proton deviation vector based on the A matrix, the b vector, and the x vector, wherein the proton deviation vector comprises one or more deviations, the one or more deviations corresponding to the one or more protons;
• determining a voxel deviation vector comprising one or more entries, the one or more entries corresponding to weighted averages of the one or more deviations of the one or more protons going through the one or more voxels;
• determining a relaxation parameter;
• updating the x vector based on the voxel deviation vector and the relaxation parameter;
• and
• repeating the steps of determining the proton deviation vector to updating the x vector until a stopping criterion is reached.

A system for 3D proton imaging of an object, the system comprising:

• a source for generating a pencil beam of protons;
• a scanning element for steering the pencil beam of protons;
• a plurality of tracking detectors for generating photons, the photons corresponding to the pencil beam of protons interacting with the object;
• a residual range detector;
• and
• a computing system for receiving signals from the plurality of tracking detectors and the residual range detector, the computing system configured to:
• determine an A matrix comprising a plurality of chord lengths, the plurality of chord lengths corresponding to one or more proton trajectories through one or more voxels;
• determine a b vector including one or more water equivalent path length (WEPL) values, the one or more WEPL values corresponding to the pencil beam of protons;
• determine a x vector including one or more relative stopping power (RSP) values, the RSP values corresponding to the one or more voxels;
• determine a proton deviation vector based on the A matrix, the b vector, and the x vector, wherein the proton deviation vector comprises one or more deviations, the one or more deviations corresponding to the pencil beam of protons;
• determine a voxel deviation vector comprising one or more entries, the one or more entries corresponding to weighted averages of the one or more deviations of the pencil beam of protons going through the one or more voxels;
• determine a relaxation parameter;
• update the x vector based on the voxel deviation vector and the relaxation parameter;
• and
• repeat the steps of determining the proton deviation vector to updating the x vector until a stopping criterion is reached.