Fast statistical imaging reconstruction via denoised ordered-subset statistically-penalized algebraic reconstruction technique

1. A method for reconstructing an image of a subject using a medical imaging system, the steps of the method comprising:

a) acquiring data from the subject using the medical imaging system;

b) reconstructing an image of the subject from the acquired data using an iterative statistical image reconstruction that is decomposed to include in each iteration an image reconstruction step without regularization and a denoising step that includes regularization.

2. The method as recited in claim 1 , wherein the image reconstruction step includes establishing a cost function to minimize, selecting an estimate of the image, evaluating the cost function for the estimate, and producing an updated estimate by adding a step value to the estimate.

3. The method as recited in claim 2 , wherein the step value is calculated by:

producing synthesized data by applying a system matrix to the estimate;

producing difference data by calculating a difference between the synthesized data and the acquired data;

producing noise-weighted data by applying a noise-weighting matrix to the difference data, the noise weighting matrix including an estimate of noise; and

producing the step value by applying a transpose of the system matrix to the noise-weighted data.

4. The method as recited in claim 1 , wherein the denoising step includes using a regularizer to denoise the image reconstructed in the image reconstruction step.

5. The method as recited in claim 4 , wherein the regularizer is at least one of a total variation function, an absolute value function, a quadratic function, a general power function, an indicator function, a Huber function, a q-GGMRF function, and a Fair potential.

6. The method as recited in claim 4 , wherein the regularizer is a PICCS function that includes a term that sparsifies the image using a prior image of the subject.

7. The method as recited in claim 1 , further comprising homogenizing noise in the image reconstructed in step b) by:

i) forming a denoised image by denoising the image reconstructed in step b);

ii) combining the denoised image and the image reconstructed in step b).

8. The method as recited in claim 7 , wherein combining the denoised image and the image reconstructed instep b) further includes performing a weighted combination.

9. The method as recited in claim 7 , wherein forming the denoised image includes applying a low-pass filter to the image reconstructed in step b).

10. The method as recited in claim 7 , wherein forming the denoised image further includes selecting the denoised image as a prior image and updating the denoised image using an iterative minimization that includes a term that sparsifies an estimate of the updated denoised image using the prior image.

11. The method as recited in claim 1 , wherein step b) includes reconstructing the image of the subject from ordered subsets of the data acquired in step a).

12. The method as recited in claim 11 , wherein the medical imaging system comprises a tomographic medical imaging system and step b) includes reconstructing the image of the subject from ordered subsets of acquired data that are ordered by view angles.

13. The method as recited in claim 12 , wherein a union of the ordered subsets of acquired data encompasses the data acquired in step a).

14. A method for reconstructing an image of a subject using a medical imaging system, the steps of the method comprising:

a) acquiring data from the subject using the medical imaging system;

b) reconstructing an image of the subject from the acquired data by iteratively minimizing a cost function such that during each iteration an estimate of the image is updated using a step value that is calculated by weighting a derivative of the cost function by a matrix that accounts for noise in the acquired data.

15. The method as recited in claim 14 , wherein the matrix that accounts for noise in the acquired data is a diagonal matrix that includes values based on noise variances of the acquired data.

16. The method as recited in claim 15 , wherein the diagonal matrix includes values that are inverses of the noise variances of the acquired data.

17. The method as recited in claim 14 , wherein the cost function minimized in step b) computes a sum-of-squares of differences between the acquired data and a forward projection of an estimate of the image to be reconstructed.

18. The method as recited in claim 14 , wherein step b) includes reconstructing the image of the subject from ordered subsets of the data acquired in step a).

19. A method for reconstructing an image of a subject, the steps of the method comprising:

acquiring data from a subject using a medical imaging system; and

iteratively reconstructing an image of the subject from the acquired data by:

i) establishing a cost function to minimize;

ii) selecting an estimate of the image;

iii) evaluating the cost function for the estimate;

iv) producing an updated estimate by adding a step value to the estimate, the step value being calculated by:

producing synthesized data by applying a system matrix to the estimate;

producing difference data by calculating a difference between the synthesized data and the acquired data;

producing noise-weighted data by applying a noise-weighting matrix to the difference data, the noise weighting matrix including an estimate of noise;

producing the step value by applying a transpose of the system matrix to the noise-weighted data;

v) evaluating a stopping criterion; and

vi) storing the updated estimate as the image of the subject when the stopping criterion is satisfied and when the stopping criterion is not satisfied, storing the updated estimate as the estimate and repeating steps iii)-v).