In the CGLS algorithm, vector multiplications are required in Equations (12) and (14), which are Kp and [K.
2 makes it possible to run CGLS using the blockwised matrix [K.
In the following experiments, 3-D problems are solved using blockwised CGLS methods to validate its performance.
In order to demonstrate the performance of the CGLS method, a 3D sensitivity map is necessary and a large grid number was chosen: 81 x 81 x 81.
1 was used in both cases for the matrix free CGLS inversion.
For time comparison, the same CGLS algorithm was executed with 25 iterations using parallel computing and serial streaming computing respectively.
This is due to the regularisation effect mainly from the CGLS iterations and the penalty term [R.
The images were also reconstructed by the blockwised CGLS method with the same size of the sensitivity map (81 x 81 x 81).
The number of CGLS iterations used to reconstruct the images was 25.
In this section, two experiments are performed to demonstrate the advantage of using parallel CGLS computing for image reconstruction.
The results shown in Table 1 indicate the time required to complete 25 CGLS iteration for one reconstructed image.
Now we divide the sensitivity matrix K into two segments only, then measure the computational time for a single reconstructed image (25 CGLS iterations) again.