Edge preserving penalized reconstruction for step-and-shoot and motion compensated positron emission tomography (PET) studies

1. A non-transitory computer-readable medium storing instructions readable and executable by a workstation including at least one electronic processor to perform an imaging method, the method comprising:

receiving imaging data on a frame by frame basis for frames along an axial direction with neighboring frames overlapping along the axial direction wherein the frames include at least a volume (k) and a succeeding volume (k+1) at least partially overlapping the volume (k) along the axial direction; and

generating an image of the volume (k) using an iterative image reconstruction process in which an iteration of the iterative image reconstruction process includes:

computing a local penalty function for suppressing noise over the volume (k), wherein the local penalty function depends on the total coincidence counts passing through the voxel being penalized, and the value of the local penalty function is reduced in an overlap region by an amount compensating for the total coincidence counts passing through the voxel being penalized in the succeeding volume k+1; and

generating an update image of the volume (k) using imaging data from the volume (k) and further using the local penalty function.

2. The non-transitory computer-readable medium of claim 1 , wherein the penalty function depends upon γ i =γ 0 √{square root over (λ i,k n ·C i,k )}

where γ is an edge preservation parameter of the local penalty function, i indexes a voxel, λ i,k n is the value of the voxel i in the iterative reconstruction of the volume k specifically in the update image n of that iterative reconstruction n; C i,k is the count of coincidence events in the dataset for bed position of volume k whose LORs pass through the voxel i.

3. The non-transitory computer-readable medium of claim 2 , wherein the PET imaging device is a time-of-flight imaging device, and

the penalty function depends upon γ i =γ 0 √{square root over (λ i,k n ·Σ v=1 C i,k w v )} where γ is an edge preservation parameter of the local penalty function, i indexes a voxel, λ i,k n is the value of the voxel i in the iterative reconstruction of the volume k specifically in the update image n of that iterative reconstruction n; C i,k is the count of coincidence events in the dataset for bed position of volume k whose LORs pass through the voxel i; and the index v runs over the C i,k coincidence counts of the dataset for bed position k whose LORs pass through the voxel i, and w v is the time-of-flight probability that the count indexed by v originated in the voxel i.

4. The non-transitory computer-readable medium of claim 1 , wherein the reconstructing includes:

reconstructing the volume (k) of the imaging data separately from the other volumes (k) of the imaging data into a reconstructed image.

5. The non-transitory computer-readable medium of claim 1 , wherein the reconstructing includes:

combining the number of counts from the volumes (k) in the imaging data into a total volume; and

reconstructing the total volume into a reconstructed image.

6. The non-transitory computer-readable medium of claim 5 , wherein the local penalty function depends upon γ i,k joint =√{square root over (λ i,k n ·(s i,k +s i,k+1 ))}

where γ is an edge preservation parameter of the local penalty function, i indexes a voxel, λ i,k n is the value of the voxel i in the iterative reconstruction of the volume k specifically in the update image n of that iterative reconstruction n, s i,k is the geometric sensitivity of the PET imaging device for voxel i when acquiring data on the volume k and s i,k+1 is the geometric sensitivity of the PET imaging device for voxel i when acquiring data on the volume k+1.

7. The non-transitory computer-readable medium of claim 1 , wherein the reducing of the value of the local penalty function in the overlap region is scaled based on a ratio of respective acquisition times for the volume (k) and the succeeding volume k+1.

8. An imaging system, comprising:

a positron emission tomography (PET) imaging device; and

at least one electronic processor programmed to:

receive imaging data on a frame by frame basis for frames along an axial direction with neighboring frames overlapping along the axial direction wherein the frames include at least a volume (k) and a succeeding volume (k+1) at least partially overlapping the volume (k) along the axial direction; and

generate an image of the volume (k) using an iterative image reconstruction process in which an iteration of the iterative image reconstruction process includes:

computing a local penalty function for suppressing noise over the volume (k) including reducing the value of the local penalty function in an overlap region, the local penalty function depending on the total coincidence counts passing through the voxel being penalized, and the value of the local penalty function is reduced in the overlap region by an amount compensating for the total coincidence counts passing through the voxel being penalized in the succeeding volume k+1;

generating an update image of the volume (k) using imaging data from the volume (k) and further using the local penalty function;

wherein γ is an edge preservation parameter of the local penalty function, i indexes a voxel, λ i,k n is the value of the voxel i in the iterative reconstruction of the volume k specifically in the update image n of that iterative reconstruction n, and the local penalty function depends upon one of:

(i) γ i =γ 0 √{square root over (λ i,k n ·C i,k )} where C i,k is the count of coincidence events in the dataset for bed position of volume k whose LORs pass through the voxel i, or

(ii) γ i,k joint =√{square root over (λ i,k n ·(s i,k +s i,k+1 ))} where s i,k is the geometric sensitivity of the PET imaging device for voxel i when acquiring data on the volume k and s i,k+1 is the geometric sensitivity of the PET imaging device for voxel i when acquiring data on the volume k+1; and

wherein the reconstructing includes combining the number of counts from the volumes (k) in the imaging data into a total volume, and reconstructing the total volume into a reconstructed image.

9. The system of claim 8 , wherein the local penalty function depends upon γ i =γ 0 √{square root over (λ i,k n ·C i,k )}.

10. The system of claim 9 , wherein the PET imaging device is a time-of-flight imaging device, and

the local penalty function depends upon γ i =γ 0 √{square root over (λ i,k n ·Σ v=1 C i,k w v )} where the index v runs over the C i,k coincidence counts of the dataset for bed position k whose LORs pass through the voxel i, and w v is the time-of-flight probability that the count indexed by v originated in the voxel i.

11. The system of claim 8 , wherein the local penalty function depends upon γ i,k joint =√{square root over (λ i,k n ·(s i,k +s i,k+1 ))}.

12. The system of claim 8 , wherein the reducing of the value of the local penalty function in the overlap region is scaled based on a ratio of respective acquisition times for the volume (k) and the succeeding volume k+1.

13. An imaging method performed on imaging data on a frame by frame basis for frames along an axial direction with neighboring frames overlapping along the axial direction wherein the frames include at least a volume (k) and a succeeding volume (k+1) at least partially overlapping the volume (k) along the axial direction, the method comprising:

generating an image of the volume (k) using an iterative image reconstruction process in which an iteration of the iterative image reconstruction process includes:

computing a local penalty function for suppressing noise over the volume (k) including reducing the value of the local penalty function in an overlap region, the local penalty function depends on local geometric sensitivity of the PET imaging device and the value of the local penalty function is reduced in the overlap region by an amount compensating for loss of geometric sensitivity due to axial truncation of the volume (k);

generating an update image of the volume (k) using imaging data from the volume (k) and further using the local penalty function;

wherein the reconstructing includes:

reconstructing the volume (k) of the imaging data separately from the other volumes (k) of the imaging data into a reconstructed image;

wherein the local penalty function depends upon γ i,k joint =√{square root over (λ i,k n ·(s i,k +s i,k+1 ))}

where γ is an edge preservation parameter of the local penalty function, i indexes a voxel, λ i,k n is the value of the voxel i in the iterative reconstruction of the volume k specifically in the update image n of that iterative reconstruction n, s i,k is the geometric sensitivity of the PET imaging device for voxel i when acquiring data on the volume k and s i,k+1 is the geometric sensitivity of the PET imaging device for voxel i when acquiring data on the volume k+1.

14. The imaging method of claim 13 , wherein the reducing of the value of the local penalty function in the overlap region is scaled based on a ratio of respective acquisition times for the volume (k) and the succeeding volume k+1.

15. An imaging method performed on imaging data on a frame by frame basis for frames along an axial direction with neighboring frames overlapping along the axial direction wherein the frames include at least a volume (k) and a succeeding volume (k+1) at least partially overlapping the volume (k) along the axial direction, the method comprising:

generating an image of the volume (k) using an iterative image reconstruction process in which an iteration of the iterative image reconstruction process includes:

adjusting the imaging data with respiratory gating using two or more gate phases and motion detected in the gate phases according to γ i,j joint =γ 0 √{square root over (f i,k (s i +s i+Δr ))} where γ is an edge preservation parameter, i is a voxel, f is a greyscale value of the voxel, s is a geometric sensitivity passing through the voxel, and Δ r is a motion vector between two gate phases ϕ k and ϕk+1;

computing a local penalty function for suppressing noise over the volume (k) including reducing the value of the local penalty function in an overlap region;

generating an update image of the volume (k) using imaging data from the volume (k) and further using the local penalty function.