Sart-Type Half-Threshold Filtering Approach for CT Reconstruction

The ℓ
₁
regularization problem has been widely used to solve the sparsity constrained problems. To enhance the sparsity constraint for better imaging performance, a promising direction is to use the ℓ
_p
norm (0 <; p <; 1) and solve the ℓ
_p
minimization problem. Very recently, Xu et al. developed an analytic solution for the ℓ
_1/2
regularization via an iterative thresholding operation, which is also referred to as half-threshold filtering. In this paper, we design a simultaneous algebraic reconstruction technique (SART)-type half-threshold filtering framework to solve the computed tomography (CT) reconstruction problem. In the medical imaging filed, the discrete gradient transform (DGT) is widely used to define the sparsity. However, the DGT is noninvertible and it cannot be applied to half-threshold filtering for CT reconstruction. To demonstrate the utility of the proposed SART-type half-threshold filtering framework, an emphasis of this paper is to construct a pseudoinverse transforms for DGT. The proposed algorithms are evaluated with numerical and physical phantom data sets. Our results show that the SART-type half-threshold filtering algorithms have great potential to improve the reconstructed image quality from few and noisy projections. They are complementary to the counterparts of the state-of-the-art soft-threshold filtering and hard-threshold filtering.