Reconstruction of dynamic multi-dimensional image data

1. A method of reconstructing a multi-dimensional data set representing a dynamic sample at a series of reconstruction instants, the multi-dimensional data set comprising a static component and a dynamic component, the method comprising:

acquiring a plurality of projection images of the dynamic sample;

reconstructing the static component of the multi-dimensional data set from the acquired projection images;

acquiring a further plurality of projection images of the dynamic sample; and

reconstructing the dynamic component of the multi-dimensional data set at each reconstruction instant from the further plurality of acquired projection images using a priori information about the dynamic sample,

the multi-dimensional data set being the sum of the static component and the dynamic component at each reconstruction instant.

2. A method according to claim 1 , wherein the second reconstructing comprises:

updating a current estimate of the dynamic component using the further plurality of projection images; and

correcting the updated estimate of the dynamic component using the a priori information about the dynamic sample.

3. A method according to claim 2 , further comprising:

determining whether stagnation has occurred, and

repeating, depending on the determination, the updating and correcting steps on the corrected updated estimate.

4. A method according to claim 3 , further comprising:

composition correcting, depending on the determination, the corrected estimate of the dynamic component; and

determining whether the updating, correcting, and composition correcting have had a significant effect on the estimate of the dynamic component.

5. A method according to claim 4 , further comprising repeating, based on the second determining, the updating, correcting, and stagnation determining.

6. A method according to claim 4 , wherein the composition correcting comprises setting the corrected estimate to zero everywhere that the absolute value of the corrected estimate is less than a noise threshold.

7. A method according to claim 6 , wherein the composition correcting comprises setting the corrected estimate to a value that preserves the average value of the corrected estimate everywhere that the absolute value of the corrected estimate is greater than or equal to than a noise threshold.

8. A method according to claim 2 , wherein the correcting comprises:

encouraging spatial localisation of the changes in the updated estimate between acquisition instants of the further plurality of projection images.

9. A method according to claim 8 , wherein the encouraging comprises setting the updated estimate to zero outside a spatial support region that is the complement of the spatial support region of the reconstructed static component of the multi-dimensional data set.

10. A method according to claim 2 , wherein the updating comprises:

projecting the current estimate of the dynamic component at a plurality of viewing angles to form a plurality of projections;

forming difference images from the projections and the further plurality of projection images;

normalising the difference images by the projected path length through the sample;

backprojecting the normalised difference images; and

adding the backprojection to the current estimate of the dynamic component.

11. A method according to claim 10 , wherein the forming comprises:

subtracting static contrast images of the static component of the dynamic sample from the further plurality of projection images to form dynamic contrast images of the dynamic sample; and

subtracting the projections from the dynamic contrast images.

12. A method according to claim 1 , wherein the dynamic sample is a geological specimen extracted from a geological formation.

13. A method according to claim 12 , further comprising determining, using the reconstructed multi-dimensional data set, one or more physical properties of the geological formation.

14. A method according to claim 13 , further comprising extracting oil from the geological formation using the determined physical properties of the geological formation.

15. A method of reconstructing a series of multi-dimensional images representing a dynamic sample at a series of reconstruction instants from a set of projection images of the dynamic sample acquired at a plurality of acquisition instants and corresponding viewing angles, the method comprising, at each reconstruction instant:

projecting a current estimate of the multi-dimensional image at the reconstruction instant at the viewing angles to form a plurality of projections;

forming difference images from the projections and from a sequence of the projection images, wherein the sequence comprises consecutive projection images, acquired at acquisition instants surrounding the reconstruction instant;

normalising the difference images by the projected path length through the dynamic sample;

backprojecting the normalised difference images; and

adding the backprojection to the current estimate of the multi-dimensional image at the reconstruction instant.

16. A method according to claim 15 , wherein successive reconstruction instants are separated by half the time to acquire the projection images at viewing angles making up a complete revolution of the sample.

17. A method according to claim 15 , wherein the sequence comprises projection images acquired at viewing angles making up a complete revolution of the sample.

18. A method according to claim 15 , wherein the sequence comprises projection images acquired at acquisition instants symmetrically surrounding the reconstruction instant.

19. A non-transitory medium comprising computer program code, which when executed by a computer device, cause the computing device to perform a method of reconstructing a multi-dimensional data set representing a dynamic sample at a series of reconstruction instants, the multi-dimensional data set comprising a static component and a dynamic component, the computer program code comprising:

code for acquiring a plurality of projection images the dynamic sample;

code for reconstructing the static component of the multi-dimensional data set from the projection images;

code for acquiring a further plurality of projection images of the dynamic sample; and

code for reconstructing the dynamic component of the multi-dimensional data set at each reconstruction instant from the further plurality of projection images using a priori information about the dynamic sample, the multi-dimensional data set being the sum of the static component and the dynamic component at each reconstruction instant.

20. A non-transitory medium comprising computer program code, which when executed by a computing device, cause the computing device to perform a method of reconstructing a series of multi-dimensional images representing a dynamic sample at a series of reconstruction instants from a set of projection images of the dynamic sample acquired at a plurality of acquisition instants and corresponding viewing angles, the computer program code comprising:

code for projecting, at each reconstruction instant, a current estimate of the multi-dimensional image at the reconstruction instant at the viewing angles to form a plurality of projections;

code for forming difference images from the projections and from a sequence of the projection images, wherein the sequence comprises consecutive projection images, acquired at acquisition instants surrounding the reconstruction instant;

code for normalising the difference images by the projected path length through the dynamic sample;

code for backprojecting the normalised difference images; and

code for adding the backprojection to the current estimate of the multi-dimensional image at the reconstruction instant.