System and method for image reconstruction
View Patent ↗A system and method for image reconstruction is disclosed. The method divides iterative image reconstruction into two stages, in the image and Radon space, respectively. In the first stage, filtered back projection and adaptive filtering in the image space are combined to generate a refined reconstructed image of a sinogram residue. This reconstructed image represents an update direction in the image space. In the second stage, the update direction is transformed to the Radon space, and a step size is determined to minimize a difference between the sinogram residue and a Radon transform of the refined reconstructed image of the sinogram residue in the Radon space. These stages are repeated iteratively until the solution converges.
1. A method for reconstructing an image from a sinogram, comprising:
(a) generating, by a processor, in image space an artifact-reduced reconstructed image of a current sinogram residue;
(b) minimizing, by a processor, in Radon space a difference between the current sinogram residue and a Radon transform of the artifact-reduced reconstructed image of the current sinogram residue to calculate a next sinogram residue; and
(c) generating, by a processor, a final reconstruction result from at least one artifact-reduced reconstructed image generated at step (a) when the next sonogram residue converges.
2. The method of claim 1 , further comprising:
repeating steps (a) and (b) iteratively using the next sinogram residue as the current sinogram residue until the next sinogram residue converges.
3. The method of claim 2 , wherein step (c) comprises:
combining the artifact-reduced reconstructed images generated at each iteration of step (a).
4. The method of claim 2 , wherein for a first iteration of steps (a) and (b), the current sinogram residue is an entire sinogram.
5. The method of claim 1 , wherein step (a) comprises:
enforcing prior knowledge constraints on the artifact-reduce reconstructed image in image space.
6. The method of claim 1 , wherein step (a) comprises:
reconstructing an image of the current sinogram residue using filtering back projection; and
generating the artifact-reduced reconstructed image of the current sinogram residue by adaptively bilateral filtering the image reconstructed using filtering back projection to regularize the image based on prior constraints.
7. The method of claim 1 , wherein step (b) comprises:
determining an update direction by calculating a radon transform of the artifact-reduced reconstructed image of the current sinogram residue,
determining a step size based on the update direction to minimize the difference between the current sinogram residue and the Radon transform of the artifact-reduced reconstructed image of the current sinogram residue; and
calculating the next sinogram residue by subtracting a product of the update direction and the step size from the current sinogram residue.
8. The method of claim 7 , wherein step (c) comprises:
weighting the artifact-reduced reconstructed image of the current sinogram residue by the step size determined for the current residue.
9. The method of claim 1 , wherein the artifact-reduced reconstructed image of the current sinogram residue is an update direction in the image space.
10. The method of claim 1 , wherein the sinogram comprises projection measurements from a computed tomography scan.
11. A non-transitory computer readable medium storing computer program instructions for performing a method of reconstructing an image from a sinogram, the computer program instructions defining steps comprising:
(a) generating in image space an artifact-reduced reconstructed image of a current sinogram residue;
(b) minimizing in Radon space a difference between the current sinogram residue and a Radon transform of the artifact-reduced reconstructed image of the current sinogram residue to calculate a next sinogram residue; and
(c) generating a final reconstruction result from at least one artifact-reduced reconstructed image generated at step (a) when the next sonogram residue converges.
12. The computer readable medium of claim 11 , further comprising computer program instructions defining the step of:
repeating steps (a) and (b) iteratively using the next sinogram residue as the current sinogram residue until the next sinogram residue converges.
13. The computer readable medium of claim 12 , wherein the computer program instructions defining step (c) comprise computer program instructions defining the step of:
combining the artifact-reduced reconstructed images generated at each iteration of step (a).
14. The computer readable medium of claim 12 , wherein for a first iteration of steps (a) and (b), the current sinogram residue is an entire sinogram.
15. The computer readable medium of claim 11 , wherein the computer program instructions defining step (a) comprise computer program instructions defining the step of:
enforcing prior knowledge constraints on the artifact-reduce reconstructed image in image space.
16. The computer readable medium of claim 11 , wherein the computer program instructions defining step (a) comprise computer program instructions defining the steps of:
reconstructing an image of the current sinogram residue using filtering back projection; and
generating the artifact-reduced reconstructed image of the current sinogram residue by adaptively bilateral filtering the image reconstructed using filtering back projection to regularize the image based on prior constraints.
17. The computer readable medium of claim 11 , wherein the computer program instructions defining step (b) comprise computer program instructions defining the steps of:
determining an update direction by calculating a radon transform of the artifact-reduced reconstructed image of the current sinogram residue,
determining a step size based on the update direction to minimize the difference between the current sinogram residue and the Radon transform of the artifact-reduced reconstructed image of the current sinogram residue; and
calculating the next sinogram residue by subtracting a product of the update direction and the step size from the current sinogram residue.
18. The computer readable medium of claim 17 , wherein the computer program instructions defining step (c) comprise computer program instructions defining the step of:
weighting the artifact-reduced reconstructed image of the current sinogram residue by the step size determined for the current residue.
19. An apparatus for reconstructing an image from a sinogram, comprising:
means for generating in image space an artifact-reduced reconstructed image of a current sinogram residue;
means for minimizing in Radon space a difference between the current sinogram residue and a Radon transform of the artifact-reduced reconstructed image of the current sinogram residue to calculate a next sinogram residue; and
means for generating a reconstruction result from at least one artifact-reduced reconstructed image when the next sonogram residue converges.
20. The apparatus of claim 19 , wherein the current sinogram residue is an entire sinogram.
21. The apparatus of claim 19 , wherein said means for generating a reconstruction result comprises:
means for artifact-reduced reconstructive images generated from multiple sinogram residues.
22. The apparatus of claim 19 , wherein said means for generating in image space an artifact-reduced reconstructed image of a current sinogram residue comprises:
means for enforcing prior knowledge constraints on the artifact-reduce reconstructed image in image space.
23. The apparatus of claim 19 , wherein said means for generating in image space an artifact-reduced reconstructed image of a current sinogram residue comprises:
means for reconstructing an image of the current sinogram residue using filtering back projection; and
means for adaptively bilateral filtering the image reconstructed using filtering back projection to regularize the image based on prior constraints tot generate the artifact-reduced reconstructed image of the current sinogram residue.
24. The apparatus of claim 19 , wherein said means for minimizing in Radon space a difference between the current sinogram residue and a Radon transform of the artifact-reduced reconstructed image of the current sinogram residue comprises:
means for calculating a radon transform of the artifact-reduced reconstructed image of the current sinogram residue to determine an update direction in the Radon space,
means for determining a step size based on the update direction to minimize the difference between the current sinogram residue and the Radon transform of the artifact-reduced reconstructed image of the current sinogram residue; and
means for calculating the next sinogram residue by subtracting a product of the update direction and the step size from the current sinogram residue.
25. The apparatus of claim 24 , wherein said means for generating a reconstruction result comprises:
means for weighting the artifact-reduced reconstructed image of the current sinogram residue by said step size; and
means for adding said multiplication result to a previous reconstruction result.
26. The apparatus of claim 19 , wherein said means for generating in image space an artifact-reduced reconstructed image of a current sinogram residue comprises:
means for determining an update direction in the image space.