Accurate 3D detector response compensation in SPECT using multigrid iterative reconstruction methods

We investigated the use of multigrid iterative reconstruction methods to compensate for 3D collimator-detector response. The methods were evaluated in terms of reduction in processing time and effectiveness in the compensation as compared with using the single grid scheme. A phantom consisting of four Gaussian-shaped objects with different sizes was used in the investigation. Noise-free projection data that modeled the spatially variant collimator-detector response were simulated and collapsed down to different projection matrix sizes. They were reconstructed using the iterative WLS-CG reconstruction algorithm that includes an accurate model of the collimator-detector response. In the single grid reconstruction scheme, the 3D reconstructed image grid was fixed throughout the iterations. In the multigrid scheme, the voxel size of the reconstructed image grid was large at early iterations and decreased with increasing number of iterations. The FWHM values of the reconstructed Gaussian-shaped objects in the radial, tangential and longitudinal directions, as well as the normalized mean square errors over regions covering of the objects were determined. The results indicate that the multigrid scheme allows significantly faster rate of resolution recovery as compared to using a single grid for large to medium size objects and for partial resolution recovery for small objects. Small effect was found by changing the grid size at different iteration numbers. However, advantage of the multigrid method is minimal for complete resolution recovery of small objects where small image grid size and large number of iterations are required.