Method and apparatus for imaging using robust bayesian sequence reconstruction

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.

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.

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.

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.