Method and apparatus for acceleration of iterative reconstruction of a computed tomography image

Patent metadata

Field	Value
Publication number	US-11087508-B2
Application number	US-201816206922-A
Country	US
Kind code	B2
Filing date	Nov 30, 2018
Priority date	Nov 30, 2018
Publication date	Aug 10, 2021
Grant date	Aug 10, 2021

Abstract

A method and apparatus is provided to reconstruct a computed tomography image using iterative reconstruction (IR) that is accelerated using various combinations of ordered subsets, conjugate gradient, preconditioning, resetting/restarting, and/or gradient approximation techniques. For example, when restarting criteria are satisfied the IR algorithm can be reset by setting conjugate-gradient parameters to initial values and/or by changing the number of ordered subsets. The IR algorithm can be accelerated by approximately calculating the gradients, by using a diagonal or Fourier preconditioner, and by selectively updating the preconditioner based on the regularization function. The update direction and step size can be calculated using the preconditioner and a surrogate function, which is not necessarily separable.

First claim

The invention claimed is:

1. An apparatus, comprising:
circuitry configured to
obtain projection data representing an intensity of X-ray radiation detected at a plurality of detector elements, the X-ray radiation being detected after having been transmitted through an image volume, and the projection data being partitioned into a plurality of subsets,
initialize an image, the image representing X-ray attenuation within the image volume that is reconstructed from the projection data,
iteratively update the image using a conjugate gradient of an objective function applied to respective subsets of the plurality of subsets, the objective function including a data fidelity term and a regularization term,
check whether a restart criterion is satisfied, the restart criterion being based on the updated image,
reset conjugate gradient parameters for iteratively updating the image when the restart criterion is satisfied, and
control a display to display the updated image.

2. The apparatus according to claim 1 , wherein the circuitry is further configured to iteratively update the image using the conjugate gradient by
calculating a data-fidelity gradient with respect to the data fidelity term of the objective function of a given subset, and calculating a regularization gradient with respective to the regularization term of the objective function of the given subset to generate an update direction,
calculating a step size based on (i) first terms derived from the data fidelity term of the objective function of the given subset and (ii) second terms derived from the regularization term of the objective function of the given subset, and
calculating the updated image of a next iteration of the iteratively updating the image by summing the updated image of a current iteration with a product of the step size and the update direction.

3. The apparatus according to claim 2 , wherein the circuitry is further configured to iteratively update the image using a conjugate gradient by calculating the update direction using a diagonal preconditioner and a conjugate-gradient term γ n .

4. The apparatus according to claim 3 , wherein the conjugate-gradient term γ n is calculated using one of a Fletcher-Reeves formula, a Polak-Ribiere-Polyak formula, and Hestenes-Stiefel formula.

5. The apparatus according to claim 2 , wherein calculating the data-fidelity gradient is accelerated by at least one of:
using as the data-fidelity gradient an approximation calculated by back projecting a difference between projection data of the given subset and a forward projection of the image,
using as the data-fidelity gradient an approximation calculated using a surrogate function,
omitting, from the calculation of the objective function gradient, the regularization gradient for a predetermined number of iterations, and then using data-fidelity gradient in the calculation of the objective function gradient during subsequent iterations, and
approximating the data-fidelity gradient using a reduced number of views for predetermined iterations, and then during other iterations using all views of the given subset to calculate the data-fidelity gradient.

6. The apparatus according to claim 2 , wherein the circuitry is further configured to iteratively update the image using a conjugate gradient using a diagonal preconditioner, wherein
the diagonal preconditioner is at least one of (a) an inverse of a diagonal matrix that is obtained as a parabolic surrogate for the objective function, and
(b) a Fourier preconditioner.

7. The apparatus according to claim 1 , wherein the circuitry is further configured to, after completing a complete iteration by iteratively updating the image for all respective subsets of the plurality of subsets, repeating another complete iteration by again iteratively updating the image for all the respective subsets, until a convergence criterion is satisfied.

8. The apparatus according to claim 3 , wherein the circuitry configured to check whether the restart criterion is satisfied comprises circuitry configured to check whether plural restart criteria are satisfied, wherein the plural restart criteria include at least two of:
a condition of a value of the objective function at completion of a previous complete iteration of updating the image for all the respective subsets is less than a value of the objective function at completion of a current complete iteration of updating the image for all the respective subsets,
a condition of a value of the objective function at completion of a previous iteration of updating the image for a given subset is less than a value of the objective function at completion of a predefined number of iterations of updating the image for the predefined number of subsets, and
a condition that a convergence rate of one or more iterations of updating the image slows below a predefined threshold.

9. The apparatus according to claim 1 , wherein the circuitry is further configured to reset the conjugate gradient parameters for iteratively updating the image by at least one of:
setting a conjugate-gradient term γ n to zero, and
partitioning the projection data into another plurality of subsets, which replaces the plurality of subsets, a number of subsets in the another plurality of subsets being different from a number of subsets in the plurality of subsets.

10. The apparatus according to claim 1 , wherein the restart criterion comprises a condition of a value of the objective function at completion of a previous complete iteration of updating the image for all the respective subsets is less than a value of the objective function at completion of a current complete iteration of updating the image for all the respective subsets.

11. The apparatus according to claim 1 , wherein the restart criterion comprises a condition of a value of the objective function at completion of a previous iteration of updating the image for a given subset is less than a value of the objective function at completion of a predefined number of iterations of updating the image for the predefined number of subsets.

12. The apparatus according to claim 1 , wherein the restart criterion comprises a condition that a convergence rate of one or more iterations of updating the image slows below a predefined threshold.

13. An apparatus, comprising:
an X-ray source to radiate X-rays;
a plurality of detector elements, each configured to
detect the X-ray radiation emanating from the X-ray source, the detected X-ray radiation having been transmitted through an image volume, and
generate projection data representing an intensity of the X-ray radiation detected at the plurality of detector elements, the projection data being partitioned into a plurality of subsets; and

processing circuitry configured to
partition the projection data into a plurality of subsets,
initialize an image, the image representing X-ray attenuation within the image volume that is reconstructed from the projection data,
iteratively update the image using a conjugate gradient of an objective function applied to respective subsets of the plurality of subsets, the objective function including a data fidelity term and a regularization term,
check whether a restart criterion is satisfied, the restart criterion being based on the updated image,
reset conjugate gradient parameters for iteratively updating the image when the restart criterion are satisfied, and
control a display to display the updated image.

14. A method, comprising:
obtaining projection data representing an intensity of X-ray radiation detected at a plurality of detector elements after the X-ray radiation has be

Assignees

• Canon Medical Systems Corp
• The Univ Of Central Florida Research Foundation Inc

Inventors

• Katsevich Alexander
• Yu Zhou
• Shi Daxin

Classifications

• G06T12/20 Primary

  Inverse problem, i.e. transformations from projection space into object space · CPC title

• G06T2211/424

  Iterative · CPC title

• G06T11/006 Primary

  Physics · mapped topic