Method and apparatus for imaging using robust bayesian sequence reconstruction

1. A method for determining a sequence of energy interactions in a detector, the method comprising:

receiving a plurality of discrete energy interactions in a plurality of detector voxels;

forming a plurality of possible sequences of interaction based on said received plurality of discrete energy interactions;

for each of said plurality of possible sequences of interaction, computing an a posteriori probability, the a posteriori probability being based on a likelihood that the possible sequence of interaction is consistent with said received plurality of discrete energy interactions; and

selecting one of said formed plurality of possible sequences of interaction based on said computed a posteriori probability;

wherein said receiving a plurality of discrete energy interactions comprises receiving from the detector a plurality of signals corresponding to particular detector voxel locations and a plurality of energy measurements;

wherein said computing an a posteriori probability comprises;

for each of the plurality of detector voxels in the particular sequence, generating a distribution of multiple positions within the detector voxel;

determining a plurality of realizations by selecting at least one of the generated multiple positions for each detector voxel in the particular sequence;

for each of said determined realizations, computing an a posteriori probability; and

combining said computed a posteriori probability over all of said determined plurality of realizations to provide said computed a posteriori probability objective for the particular sequence.

2. The method of claim 1 , wherein said forming a plurality of possible sequences comprises determining all possible permutations of an order of the plurality of discrete energy interactions.

3. The method of claim 1 , wherein said computing an a posteriori probability comprises:

calculating a hypothetical energy for each of the interactions within said plurality of possible sequences of interaction;

comparing said calculated hypothetical energy to said received plurality of energy measurements.

4. The method of claim 3 , wherein said calculated hypothetical energy is computed using Compton kinematics.

5. The method of claim 3 , wherein said computing an a posteriori probability further comprises:

providing a probability for each of said plurality of possible sequences based on prior knowledge.

6. The method of claim 5 , wherein said providing a probability further comprises:

obtaining a probability distribution of possible trajectories of a photon within the detector voxels based on physics of gamma ray transport prior to receiving the energy measurements.

7. The method of claim 6 , wherein said obtaining a prior probability comprises:

computing a total cross-section for all possible trajectories based on physics of gamma ray transport;

determining an a priori distribution of said plurality of possible sequences based on said computed total cross-section.

8. The method of claim 1 , wherein said computing an a posteriori probability comprises:

calculating a hypothetical energy for each of the interactions within said plurality of possible sequences of interaction;

comparing said calculated hypothetical energy to said received plurality of energy measurements to determine a first probability;

providing a probability for each of said plurality of possible sequences based on prior knowledge to determine a second probability;

combining said determined first probability and said second probability to compute said a posteriori probability.

9. The method of claim 1 , wherein the detector comprises a detector for positron emission tomography (PET).

10. The method of claim 1 , wherein said determining a plurality of realizations of positions comprises performing a 3D sampling of distributions within the detector voxels.

11. The method of claim 10 , wherein said performing a 3D sampling comprises performing Monte Carlo integration.

12. A signal processor configured to perform the method of claim 1 .

13. A computing device configured to perform the method of claim 1 .

14. A non-transitory medium containing computer-readable instructions that when executed cause a computing device to perform the method of claim 1 .

15. An imaging system configured to perform the method of claim 1 .

16. The imaging system of claim 15 , further comprising:

at least one detector positioned to receive incoming photons from the source of incoming photons and generate a signal; and

a signal processor coupled to the at least one detector for receiving the generated signal;

said signal processor being configured to perform the method of claim 1 .

17. A method for determining a sequence of energy interactions in a detector, the method comprising:

receiving a plurality of discrete energy interactions in a plurality of detector voxels;

forming a plurality of possible sequences of interaction based on said received plurality of discrete energy interactions;

for each of said plurality of possible sequences of interaction, computing an a posteriori probability, the a posteriori probability being based on a likelihood that the possible sequence of interaction is consistent with said received plurality of discrete energy interactions; and

selecting one of said formed plurality of possible sequences of interaction based on said computed a posteriori probability;

wherein said receiving a plurality of discrete energy interactions comprises receiving from the detector a plurality of signals corresponding to particular detector voxel locations and a plurality of energy measurements;

wherein said computing an a posteriori probability comprises:

calculating a hypothetical energy for each of the interactions within said plurality of possible sequences of interaction;

comparing said calculated hypothetical energy to said received plurality of energy measurements to determine a first probability;

providing a probability for each of said plurality of possible sequences based on prior knowledge to determine a second probability;

combining said determined first probability and said second probability to compute said a posteriori probability;

wherein said combining comprises:

providing a relative weight for said determined first probability and said second probability;

combining said first probability and said second probability using said provided relative weight.

18. A method for determining an interaction path of an incoming photon received from a source of emitted photons, the method comprising:

receiving a plurality of discrete interactions of a single gamma ray photon in a plurality of detector voxels;

determining all possible sequences for the plurality of discrete interactions based on said received plurality of discrete interactions;

for each of said all possible sequences, computing an a posteriori probability objective based on a weighted likelihood of the particular sequence based on energy measurements for said received plurality of discrete interactions and a weighted a priori probability; and

selecting the sequence having the maximum computed a posteriori objective over said all possible sequences;

wherein said computing an a posteriori probability objective comprises, for each of the all possible sequences:

for each of the plurality of detector voxels in the particular sequence, generating a distribution of multiple positions within the detector voxel;

determining a plurality of realizations by selecting at least one of the generated multiple positions for each detector voxel in the particular sequence;

for each of said determined realizations, computing an a posteriori probability; and

combining said computed a posteriori probability over all of said determined plurality of realizations to provide said computed a posteriori probability objective for the particular sequence.

19. The method of claim 18 , further comprising:

selecting a first interaction based on said selected sequence.

20. The method of claim 19 , further comprising:

determining a line of response (LOR) of the incoming photon based on said selecting a first interaction.

21. The method of claim 19 , further comprising:

determining a direction for the incoming photon based on said selected sequence.

22. The method of claim 18 , further comprising:

selecting a first and second interaction using said selected sequence; and

determining whether to accept or reject an event based on said selecting.

23. The method of claim 18 , further comprising:

imaging a subject using said selected sequence.

24. A system for determining an interaction path of an incoming photon received from a source of emitted photons, the system comprising:

detector means for receiving a plurality of discrete interactions of a single gamma ray photon in a plurality of detector voxels;

means for computing an a posteriori probability objective for all possible sequences for the plurality of discrete interactions using a weighted likelihood of multiple distributed paths of the particular sequence based on energy measurements for the received plurality of discrete interactions and a weighted a priori probability of multiple distributed paths of the particular sequence; and

means for selecting the sequence having the maximum computed a posteriori probability objective over all possible sequences;

wherein said means for computing an a posteriori probability comprises:

means for calculating a hypothetical energy for each of the interactions within said plurality of possible sequences of interaction;

means for comparing said calculated hypothetical energy to said received plurality of energy measurements to determine a first probability;

means for providing a probability for each of said plurality of possible sequences based on prior knowledge to determine a second probability;

means for combining said determined first probability and said second probability to compute said a posteriori probability;

wherein said means for computing an a posteriori probability comprises;

means for generating, for each of the plurality of detector voxels in the particular sequence, a distribution of multiple positions within the detector voxel;

means for determining a plurality of realizations by selecting at least one of the generated multiple positions for each detector voxel in the particular sequence;

means for computing, for each of said determined realizations, an a posteriori probability; and

means for combining said computed a posteriori probability over all of said determined plurality of realizations to provide said computed a posteriori probability objective for the particular sequence.

25. A method for determining a sequence of energy interactions in a detector, the method comprising:

receiving a plurality of discrete energy interactions in a plurality of detector voxels;

forming a plurality of possible sequences of interaction based on said received plurality of discrete energy interactions;

for each of said plurality of possible sequences of interaction, computing an a posteriori probability comprising an a priori probability based on physics of energy transport;

selecting one of said formed plurality of possible sequences of interaction based on said computed a posteriori probability;

wherein said computing an a posteriori probability comprises;

for each of the plurality of detector voxels in the particular sequence, generating a distribution of multiple positions within the detector voxel;

determining a plurality of realizations by selecting at least one of the generated multiple positions for each detector voxel in the particular sequence;

for each of said determined realizations, computing an a posteriori probability; and

combining said computed a posteriori probability over all of said determined plurality of realizations to provide said computed a posteriori probability objective for the particular sequence.