Separation of geometric system response matrix for three-dimensional image reconstruction
An image-reconstruction method in which interactions with particular crystal pairs are detected and a trans-axial component of a geometric system response matrix is retrieved from a storage medium. This component provides an estimate of an axial component of the geometric system response matrix. At least in part on the basis of the axial component and the trans-axial component, an annihilation site distribution of annihilations most likely to have resulted in the interaction with the particular crystal pair is estimated.
1. In a PET scanner, a method for enabling three-dimensional image reconstruction, the method comprising:
storing unconditional data indicating a likelihood that an annihilation occurring at a particular annihilation site will cause illumination of a crystal pair having a crystal from a first crystal column and a crystal from a second crystal column.
2. The method of claim 1 , further comprising:
determining conditional data providing an estimate of a likelihood that an annihilation occuring at a particular annihilatian site will cause illumination of a particular crystal pair, given that an annihilation occurring at that annihilation site has caused illumination of some crystal pair from the first and second crystal columns.
3. The method of claim 2 , further comprising:
detecting illumination of illuminated crystal pairs;
retrieving the unconditional data; and
at least in part on the basis of the unconditional data and the conditional data, determining an annihilation site distribution most likely to have caused the detected illumination of the illuminated crystal pairs.
4. The method of claim 3 , wherein determining an annihilation site comprises:
multiplying a conditional matrix, which incorporates the conditional data, by an unconditional matrix, which incorporates the unconditional data,
the unconditional matrix and the conditional matrix each having
a first dimension that corresponds to crystal pairs and
second dimension that corresponds to annihilation sites.
5. The method of claim 1 , wherein determining conditional data comprises determining a ratio between a first distance and a second distance,
the first distance being obtained from a distance between a particular annihilation site and one of the crystals from a crystal pair, and
the second distance being obtained from a distance between the crystals of the crystal pair.
6. A computer-readable medium having encoded thereon software for enabling three-dimensional image reconstruction, the software comprising instructions for:
storing unconditional data indicating a likelihood that an annihilation occuring at a particular annihilation site will cause illumination of a crystal pair having a crystal from a first crystal column and a crystal from a second crystal column.
7. The computer-readable medium of claim 6 , wherein the software further comprises instructions for:
determining conditional data that provides an estimate of a likelihood that an annihilation occurring at a particular annihilation site will cause illumination of a particular crystal pair, given that an annihilation occuring at that annihilation site has caused illumination of some crystal pair from the first and second crystal columns.
8. The computer-readable medium of claim 7 , wherein the software further comprises instructions for:
detecting illumination of illuminated crystal pairs;
retrieving the unconditional data; and
at least in part on the basis of the unconditional data and the conditional data, determining an annihilation site distribution most likely to have caused the detected illumination of the illuminated crystal pairs.
9. The computer-readable medium of claim 8 , wherein the instructions for determining an annihilation site comprise instructions for:
multiplying a conditional matrix, which incorporates the conditional data, by an unconditional matrix, which incorporates the unconditional data,
the unconditional matrix and the conditional matrix each having
a first dimension that corresponds to crystal pairs and
a second dimension that corresponds to annihilation sites.
10. The computer-readable medium of claim 7 , wherein the instructions for determining conditional data comprise instructions for determining a ratio between a first distance and a second distance,
the first distance being obtained from a distance between a particular annihilation site and one of the crystals from a crystal pair, and
the second distance being obtained from a distance between the crystals of the crystal pair.