Method and image-reconstruction apparatus for reconstructing image data

1. A method for reconstructing image data based upon measurement data from an imaging system, the method comprising:

determining initial image data based on the measurement data; and

reconstructing the image data by optimizing the initial image data, in an iterative optimization method, based on at least an edge-maintaining noise regularization term and a sparsity regularization term, the edge-maintaining noise regularization term and the sparsity regularization term being independent of one another.

2. The method as claimed in claim 1 , wherein during each iteration of the iterative optimization method, the optimizing the initial image data includes,

determining current image correction data based on the edge-maintaining noise regularization term and the sparsity regularization term,

optimizing the initial image data based on previously optimized image data and the current image correction data, and

determining whether to proceed to a next iteration of the iterative optimization method or to terminate the iterative optimization method based on the optimized initial image data and a convergence threshold.

3. The method as claimed in claim 1 , wherein the edge-maintaining noise regularization term and the sparsity regularization term form a target function to be optimized during each iteration of the iterative optimization method.

4. The method as claimed in claim 3 , wherein the target function and at least one boundary condition associated with the target function are convex functions.

5. The method as claimed in claim 1 , wherein the edge-maintaining noise regularization term and the sparsity regularization term are respectively weighted by a weighting factor during the optimizing.

6. The method as claimed in claim 5 , wherein the weighting factor of the edge-maintaining noise regularization term and the weighting factor of the sparsity regularization term are selected such that a sum of the two weighting factors is between 0 and 1.

7. The method as claimed in claim 1 , wherein the measurement data is sampled at a rate below a Nyquist limit.

8. The method as claimed in claim 5 , wherein the weighting factors are selected by a user.

9. The method as claimed in claim 5 , wherein the weighting factor of the sparsity regularization term is selected as a function of a sampling rate at which the measurement data are sampled.

10. The method as claimed in claim 9 , wherein in a sum of the weighting factor of the edge-maintaining noise regularization term and the weighting factor of the sparsity regularization term, the weighting factor of the sparsity regularization term is selected as a function of the sampling rate.

11. The method as claimed in claim 2 , wherein each iteration of the iterative optimization method includes a first stage and a second stage,

in the first stage, the determining the current image correction data includes,

determining the sparsity regularization term, and

determining sparsity based current image correction data based on at least the determined sparsity regularization term and an edge-maintaining noise regularization term corresponding to a previous iteration, wherein

the optimizing the initial image data first optimizes the initial image data based on the previously optimized image data and the sparsity based current image correction data, and

in the second stage, the determining the corresponding current image correction data includes,

determining the edge-maintaining noise regularization term based on the first optimized initial image data, and

determining noise based image correction data based on at least the determined sparsity regularization term and the determined edge-maintaining noise regularization term, wherein

the optimizing the initial image data second optimizes the initial image data based on the first optimized initial image data and the noise based image correction data.

12. The method as claimed in claim 1 , wherein the determining the initial image data determines the initial image data using a medical image acquiring system.

13. An image-reconstruction apparatus for reconstructing image data of an object, comprising:

a measurement-data interface configured to receive measurement data obtained via an imaging system;

a reconstruction unit configured to,

determine initial image data based on the measurement data, and

reconstruct the image data by optimizing the initial image data, in an iterative optimization method, based on at least an edge-maintaining noise regularization term and a sparsity regularization term, the edge-maintaining noise regularization term and the sparsity regularization term being independent of one another; and

an image-data interface configured to output the reconstructed image data.

14. A non-transitory computer readable medium including a computer program product, the computer program product comprising computer instructions, which when executed by a processor, causes the processor to perform the method as claimed in claim 1 .

15. The method as claimed in claim 2 , wherein the edge-maintaining noise regularization term and the sparsity regularization term form a target function to be optimized during each iteration of the iterative optimization method.

16. The method as claimed in claim 15 , wherein the target function and at least one boundary condition associated with the target function are convex functions.

17. The method as claimed in claim 6 , wherein the weighting factors are selected by a user.

18. The method as claimed in claim 6 , wherein the weighting factor of the sparsity regularization term is selected as a function of a sampling rate at which the measurement data are sampled.

19. The method as claimed in claim 7 , wherein the weighting factors are selected by a user.

20. The method as claimed in claim 7 , wherein the weighting factor of the sparsity regularization term is selected as a function of a sampling rate at which the measurement data are sampled.

21. The method as claimed in claim 19 , wherein in a sum of the weighting factor of the edge-maintaining noise regularization term and the weighting factor of the sparsity regularization term, the weighting factor of the sparsity regularization term is selected as a function of the sampling rate.

22. The method as claimed in claim 20 , wherein in a sum of the weighting factor of the edge-maintaining noise regularization term and the weighting factor of the sparsity regularization term, the weighting factor of the sparsity regularization term is selected as a function of the sampling rate.

23. The method as claimed in claim 2 , wherein the determining whether to proceed to the next iteration of the iterative optimization method includes,

comparing the current image correction data to the convergence threshold, and

proceeding to the next iteration if the current image correction data is less than the convergence threshold.