Splitting-based statistical X-ray CT image reconstruction with blind gain correction

Abstract

Variational methods are useful for solving ill-posed inverse imaging problems by minimizing a cost function with a data fidelity term and a regularization term. For statistical X-ray computed tomography (CT) image reconstruction, penalized weighted least-squares (PWLS) criteria with edge-preserving regularization can improve quality of the reconstructed image compared to traditional filtered back-projection (FBP) reconstruction. Nevertheless, the huge dynamic range of the statistical weights used in PWLS image reconstruction leads to a highly shift-variant local impulse response, making effective preconditioning difficult. To overcome this problem, iterative algorithms based on variable splitting were proposed recently. However, existing splitting-based iterative algorithms do not consider the (unknown) gain fluctuations that can occur between views. This paper proposes a new variational formulation for splitting-based iterative algorithms where the unknown gain parameter vector and the image are estimated jointly with just simple changes to the original algorithms. Simulations show that the proposed algorithm greatly reduces the shading artifacts caused by gain fluctuations yet with almost unchanged computational complexity per iteration.