System and method for iterative image reconstruction
Methods are provided for iteratively reconstructing an image signal to generate a reconstructed image signal. In one embodiment, sub-iterations of each iteration are performed on pixel or voxel subsets. The subsets may be composed of neighboring or spatially separated pixel or voxels and may extend in the z-direction. In one embodiment, an update step of the iterative reconstruction involves the direct inversion of an approximation of a Hessian matrix associated with the respective subsets. In further embodiments, non-negativity or other limitations or constraints on update values may be enforced.
1. A method for iteratively reconstructing image data, comprising the steps of:
accessing an initial image;
defining a plurality of image element subsets of the initial image, wherein some or all of the plurality of image element subsets correspond to voxels aligned in z such that they share the same (x,y) location;
iteratively generating updates to the initial image or a subsequent updated image based on the respective image element subsets, wherein at least one of the updates is generated by directly inverting a respective Hessian matrix or an approximation of a respective Hessian matrix associated with a corresponding image element subset; and
terminating the iterative generation of updates upon satisfaction of a completion criterion.
2. The method of claim 1 , wherein the image element subsets comprise one of pixel subsets or voxel subsets.
3. The method of claim 1 , wherein the approximation of the respective Hessian matrix comprises a Hessian matrix in which only a limited bandwidth is considered.
4. The method of claim 1 , wherein the approximation of the respective Hessian matrix accounts for spatial-invariance within the object domain.
5. The method of claim 1 , comprising computing the approximation of the respective Hessian matrix using a parameterized analytic function that produces an approximation of the correlation between two voxels given their locations.
6. The method of claim 1 , wherein the iteratively generated updates are limited such that the updates, when applied, do not result in updated values above a maximum or below a minimum.
7. The method of claim 1 , wherein the iteratively generated updates are limited such that the updates, when applied, do not result in negative values.
8. The method of claim 1 , comprising computing a relaxation factor for a respective iteratively generated update such that applying the update will not generate a negative value.
9. The method of claim 1 , wherein two or more of the plurality of image element subsets have image elements in common.
10. The method of claim 1 , wherein the iteratively generated updates are applied recursively such that image elements that would be updated to a negative value are set to zero and removed from the respective image element subset to generate a smaller image element subset that is updated separately.
11. One or more non-transitory machine readable media, encoding one or more routines which, when executed by a processor, perform acts comprising:
generating an initial image;
iteratively updating a plurality of image element subsets of the initial image or of a subsequent updated image, wherein one or more of the updates is generated by directly inverting an approximation of a respective Hessian matrix associated with a corresponding image element subset, and wherein some or all of the plurality of image element subsets correspond to voxels aligned in z such that they share the same (x,y) location; and
terminating the iterative generation of updates upon satisfaction of a completion criterion.
12. The one or more non-transitory machine readable media of claim 11 , wherein the one or more non-transitory machine readable media encodes a routine which, when executed by a processor, generates the approximation of the respective Hessian matrix by considering only a limited bandwidth of a corresponding complete Hessian matrix.
13. The one or more non-transitory machine readable media of claim 11 , wherein the one or more non-transitory machine readable media encodes a routine which, when executed by a processor, generates the approximation of the respective Hessian matrix by approximating a correlation between voxels of the corresponding image element subset due to space invariance between voxels within the object domain.
14. The one or more non-transitory machine readable media of claim 11 , wherein the one or more non-transitory machine readable media encodes a routine which, when executed by a processor, computes the approximation of the respective Hessian matrix using a parameterized analytic function that produces an approximation of the correlation between two voxels given their locations.
15. The one or more non-transitory machine readable media of claim 11 , wherein the iteratively generated updates are limited such that the updates, when applied, do not result in negative values.
16. The one or more non-transitory machine readable media of claim 11 , wherein the iterative updates are applied recursively such that image elements that would be updated to a negative value are set to zero and removed from the respective image element subset to generate a smaller image element subset that is updated separately.
17. A method for iteratively reconstructing image data, comprising the steps of:
accessing an initial image;
iteratively updating a plurality of image element subsets of the initial image or a subsequent updated image, wherein the iteratively generated updates are limited such that the updates, when applied, do not result in negative values, and wherein the iterative updates are applied recursively such that image elements that would be updated to a negative value are set to zero and removed from the respective image element subset to generate a smaller image element subset that is updated separately; and
terminating the iterative generation of updates upon satisfaction of a completion criterion.
18. The method of claim 17 , wherein one or more of the updates are generated by directly inverting a respective Hessian matrix associated with a corresponding image element subset or directly inverting an approximation of the respective Hessian matrix.
19. The method of claim 17 , wherein the iteratively generated updates are applied with a relaxation factor that prevents an image element from being updated to a negative value.
20. The method of claim 17 , wherein some or all of the plurality of image element subsets correspond to voxels aligned in z such that they share the same (x,y) location.