Abstract
Computed tomography (CT) plays a key role in modern medical system, whether it be for diagnosis
or therapy. As an increased risk of cancer development is associated with exposure to radiation,
reducing radiation exposure in CT becomes an essential issue. Based on the compressive sensing
(CS) theory, iterative based method with total variation (TV) minimization is proven to be a
powerful framework for few-view tomographic image reconstruction. Multigrid method is an
iterative method for solving both linear and nonlinear systems, especially when the system contains
a huge number of components. In medical imaging, image background is often defined by zero
intensity, thus attaining spatial support of the image, which is helpful for iterative reconstruction. In
the proposed method, the image support is not considered as a priori knowledge. Rather, it evolves
during the reconstruction process. Based on the CS framework, we proposed a multigrid method
with adaptive spatial support constraint. The simultaneous algebraic reconstruction (SART) with TV
minimization is implemented for comparison purpose. The numerical result shows: 1. Multigrid
method has better performance while less than 60 views of projection data were used, 2. Spatial
support highly improves the CS reconstruction, and 3. When few views of projection data were
measured, our method performs better than the SART+TV method with spatial support constraint.
