Ordered subset scheme in spectral CT

1. An apparatus to perform a spectral computed tomography (CT) ordered subsets (OS) reconstruction method using two sets of projection data having a different number of views, the apparatus comprising:

a processing circuit configured to

obtain a first set of projection data that includes single-energy CT data for a first number of views;

obtain a second set of projection data that includes spectral CT data for a second number of views, wherein the second number is smaller than the first number;

partition the first set of projection data into N equal-sized subsets of projection data;

include the second set of projection data in each of the N subsets of projection data to generate N expanded subsets of projection data; and

perform OS reconstruction with the N expanded subsets of projection data to generate a reconstructed CT image.

2. The apparatus of claim 1 , wherein the processing circuit is further configured to:

perform data domain decomposition on the second set of projection data to obtain measured basis line integrals; and

initialize basis images.

3. The apparatus of claim 2 , wherein, in performing OS reconstruction, the processing circuit is further configured to:

reproject the basis images to obtain first basis line integrals, and reproject the basis images to obtain second basis line integrals;

perform beam hardening correction on the first set of projection data to generate corrected data;

update the basis images with a difference of the measured basis line integrals and the first basis line integrals and a difference of the corrected data and combined second basis line integrals; and

repeat the reprojecting, performing, and updating steps for the second number of views and for each of the N subsets.

4. The apparatus of claim 3 , wherein the processing circuit is further configured to:

repeat the reprojecting, performing, updating steps, and repeating steps until predetermined convergence criteria is met.

5. The apparatus of claim 1 , wherein, in performing the partitioning, the processing circuit is further configured to partition the first set of projection data into N subsets of projection data,

wherein N is set to be equal to the first number divided by the second number.

6. A spectral computed tomography (CT) ordered subsets (OS) reconstruction method using two sets of projection data having a different number of views, the method comprising:

obtaining a first set of projection data that includes single-energy CT data for a first number of views;

obtaining a second set of projection data that includes spectral CT data for a second number of views, wherein the second number is smaller than the first number;

partitioning the first set of projection data into N equal-sized subsets of projection data;

including the second set of projection data in each of the N subsets of projection data to generate N expanded subsets of projection data; and

performing OS reconstruction with the N expanded subsets of projection data to generate a reconstructed CT image.

7. The method of claim 6 , further comprising:

performing data domain decomposition on the second set of projection data to obtain measured basis line integrals; and

initializing basis images.

8. The method of claim 7 , wherein the step of performing OS reconstruction comprises:

reprojecting the basis images to obtain first basis line integrals, and reprojecting the basis images to obtain second basis line integrals;

performing beam hardening correction on the first set of projection data to generate corrected data;

updating the basis images with a difference of the measured basis line integrals and the first basis line integrals and a difference of the corrected data and combined second basis line integrals; and

repeating the reprojecting, performing, and updating steps for the second number of views and for each of the N subsets.

9. The method of claim 8 , further comprising:

repeating the reprojecting, performing, updating steps, and repeating steps until predetermined convergence criteria is met.

10. The method of claim 6 , wherein the partitioning step comprises partitioning the first set of projection data into N subsets of projection data, wherein N is set to be equal to the first number divided by the second number.

11. The method of claim 8 , wherein the updating step comprises:

calculating a diagonal denominator matrix D n for each of the N subsets as Diag{D n }=NA t n W n A n 1, wherein A n is a projector matrix, W n is a weighting matrix, t represents transpose, and 1 is a vector of ones.

12. The method of claim 11 , further comprising calculating a global matrix D as

D

ii

=

max

n

⁢

D

n

,

ii

.

13. The method of claim 8 , wherein the updating step comprises:

calculating a diagonal denominator matrix D as Diag{D}=A t W ˜ A1, wherein A is a projector matrix, t represents transpose, and 1 is a vector of ones, and W ˜ is a statistical weighting matrix that is calculated as W ˜ i =I i exp(−g ˜ i ) where I i is a flux for ray i and g ˜ i is a shadow-corrected attenuation.