Superiorization of Preconditioned Conjugate Gradient Algorithms for Tomographic Image Reconstruction
For the field of tomographic image reconstruction, this work offers a fast method to improve image quality over least-squares solutions, though it is an incremental combination of existing techniques.
The paper examines Superiorized Preconditioned Conjugate Gradient (SupPCG) algorithms for tomographic image reconstruction, showing that they produce high-quality reconstructions in remarkably short time compared to standard PCG.
Properties of Superiorized Preconditioned Conjugate Gradient (SupPCG) algorithms in image reconstruction from projections are examined. Least squares (LS) is usually chosen for measuring data-inconsistency in these inverse problems. Preconditioned Conjugate Gradient algorithms are fast methods for finding an LS solution. However, for ill-posed problems, such as image reconstruction, an LS solution may not provide good image quality. This can be taken care of by superiorization. A superiorized algorithm leads to images with the value of a secondary criterion (a merit function such as the total variation) improved as compared to images with similar data-inconsistency obtained by the algorithm without superiorization. Numerical experimentation shows that SupPCG can lead to high-quality reconstructions within a remarkably short time. A theoretical analysis is also provided.