Activity-dependent, spatially-varying regularization parameter design for regularized image reconstruction
A method and apparatus is provided to iteratively reconstruct an image from gamma-ray emission data by optimizing an objective function with a spatially-varying regularization term. The image is reconstructed using a regularization term that varies spatially based on an activity-level map to spatially vary the regularization term in the objective function. For example, more smoothing (or less edge-preserving) can be imposed where the activity is lower. The activity-level map can be used to calculate a spatially-varying smoothing parameter and/or spatially-varying edge-preserving parameter. The smoothing parameter can be a regularization parameter β that scales/weights the regularization term relative to a data fidelity term of the objective function, and the regularization parameter β can depend on a sensitivity parameter. The edge-preserving parameter β can control the shape of a potential function that is applied as a penalty in the regularization term of the objective function.
1. An apparatus, comprising:
circuitry configured to
obtain emission data representing detection events of gamma rays at a plurality of detector elements,
reconstruct, using the obtained emission data, a first image of a radioactivity level and generate an activity weighting map based on the radioactivity level, and
reconstruct, using the obtained emission data and the activity weighting map, a second image of the radioactivity level, the reconstruction of the second image being performed using an iterative-reconstruction method in which an objective function is optimized, the objective function including a regularization term that uses the activity weighting map and the objective function including a data fidelity term, wherein
the objective function is defined by a difference between the data fidelity term and a product of the regularization term and a regularization parameter, and
the regularization parameter is set in accordance with a radioactivity level of each location in the activity weighting map, and provides a relative weight between the data fidelity term and the regularization term, and has a property of increasing a degree of smoothing with respect to the second image along with an increase of the value of the regularization parameter, and a property of reducing both a noise level and a resolution.
2. The apparatus according to claim 1 , wherein the circuitry is further configured to reconstruct the second image using the objective function including the regularization term, wherein the regularization term includes one or more spatial-varying edge-preserving parameters determined from the activity weighting map.
3. The apparatus according to claim 1 , wherein the circuitry is further configured to reconstruct the second image using the objective function including the regularization term, wherein the regularization term includes one or more spatial-varying smoothing parameters determined from the activity weighting map.
4. The apparatus according to claim 2 , wherein the circuitry is further configured to reconstruct the second image using the objective function including the regularization term, wherein the regularization term includes one or more spatial-varying smoothing parameters determined from the activity weighting map.
5. The apparatus according to claim 1 , wherein the circuitry is further configured to reconstruct the first image using an iterative-reconstruction method that is a same iterative-reconstruction method used to reconstruct the second image, except during reconstruction of the first image a predetermined parameter is used in the regularization term instead of the activity weighting map, which is used during reconstruction of the second image.
6. The apparatus according to claim 5 , wherein the circuitry is further configured to reconstruct the first image by performing a predetermined number of iterations of the iterative-reconstruction method.
7. The apparatus according to claim 5 , wherein the circuitry is further configured to
update the activity weighting map based on the second image, and
repeat reconstructing the second image of the radioactivity level using the updated activity weighting map.
8. The apparatus according to claim 1 , wherein
in the reconstruction of the second image, the iterative-reconstruction method is an ordered-subset expectation maximization (OSEM) method, which is iteratively repeated until a predetermined stopping criteria is reached, and
the reconstruction of the first image is performed using the OSEM method until another predetermined stopping criteria is reached, the another predetermined stopping criteria including one or more of a predetermined maximum number of iterations and a convergence criterion.
9. The apparatus according to claim 1 , wherein the circuitry is further configured to reconstruct the second image using the regularization term that includes a regularization parameter determined from the activity weighting map, the regularization parameter being a multiplicative factor that scales the regularization term.
10. The apparatus according to claim 9 , wherein the circuitry is further configured to reconstruct the second image using the regularization parameter, wherein the regularization parameter is calculated using a sensitivity parameter that depends on a geometry of the detector elements with respect to voxels of the second image.
11. The apparatus according to claim 1 , wherein the circuitry is further configured to reconstruct the second image using the objective function that includes the regularization term, wherein the regularization term includes an edge-preserving potential function that has a shape based on the activity weighting map.
12. The apparatus according to claim 1 , wherein the circuitry is further configured to
segment the activity weighting map according to types of organs represented therein, and
reconstruct the second image, wherein the regularization term depends on the segmentation of the activity weighting map.
13. The apparatus according to claim 1 , wherein the circuitry is further configured to reconstruct the second image, wherein a spatially varying type of the regularization term depends on the activity weighting map.
14. A method, comprising:
obtaining emission data representing detection events of gamma rays at a plurality of detector elements,
reconstructing, using the obtained emission data, a first image of a radioactivity level and an activity weighting map based on the radioactivity level, and
reconstructing, using the obtained emission data and the activity weighting map, a second image of the radioactivity level, the reconstruction of the second image being performed using an iterative-reconstruction method in which an objective function is optimized, the objective function including a regularization term that uses the activity weighting map and the objective function including a data fidelity term, wherein
the objective function is defined by a difference between the data fidelity term and a product of the regularization term and a regularization parameter, and
the regularization parameter is set in accordance with a radioactivity level of each location in the activity weighting map, and provides a relative weight between the data fidelity term and the regularization term, and has a property of increasing a degree of smoothing with respect to the second image along with an increase of the value of the regularization parameter, and a property of reducing both a noise level and a resolution.
15. The method according to claim 14 , wherein the reconstructing of the second image further includes that the regularization term includes one or more of (i) a spatial-varying smoothing parameter determined from the activity weighting map and (ii) a spatial-varying edge-preserving parameter determined from.
16. The method according to claim 14 , further includes
updating the activity weighting map based on the second image, and
repeating the reconstructing of the second image based on the updated activity weighting map.
17. The method according to claim 14 , wherein
in the reconstructing of the second image, the iterative-reconstruction method is an ordered-subset expectation maximization (OSEM) method, which is iteratively repeated until a predetermined stopping criteria is reached, and
the reconstructing of the first image is performed using the OSEM method until another predetermined stopping criteria is reached, the another predetermined stopping criteria including one or more of a predetermined maximum number of iterations and a convergence criterion.
18. The apparatus according to claim 1 , wherein
the reconstructing of the second image is performed using a regularization parameter in the regularization term,
the regularization parameter is calculated using one or more of the activity weighting map and a sensitivity parameter,
the regularization parameter is a multiplicative factor that scales the regularization term, and,
when the regularization parameter is calculated using the sensitivity parameter, the sensitivity parameter depends on a geometry of the detector elements with respect to voxels of the second image.
19. The method according to claim 14 , wherein the reconstructing of the first image is performed by
initializing the first image using a filtered back-projection methods, and
performing a predetermined number of iterations of an iterative reconstruction method starting with the initialized first image to generate the first image.
20. A non-transitory computer-readable storage medium including executable instructions, which when executed by circuitry, cause the circuitry to perform the method according to claim 14 .