A General-Thresholding Solution for lp(0 <; p <; 1) Regularized CT Reconstruction

It is well known that l
₁
minimization can be used to recover sufficiently sparse unknown signals in the compressive sensing field. The l p regularization method, a generalized version between the well-known l
₁
regularization and the l
₀
regularization, has been proposed for a sparser solution. In this paper, we derive several quasi-analytic thresholding representations for the l
_p
(0 <; p <; 1) regularization. The derived representations are exact matches for the well-known soft-threshold filtering for the l
₁
regularization and the hard-threshold filtering for the l
₀
regularization. The error bounds of the approximate general formulas are analyzed. The general-threshold representation formulas are incorporated into an iterative thresholding framework for a fast solution of an l p regularized computed tomography (CT) reconstruction. A series of simulated and realistic data experiments are conducted to evaluate the performance of the proposed general-threshold filtering algorithm for CT reconstruction, and it is also compared with the well-known re-weighted approach. Compared with the re-weighted algorithm, the proposed general-threshold filtering algorithm can substantially reduce the necessary view number for an accurate reconstruction of the Shepp-Logan phantom. In addition, the proposed general-threshold filtering algorithm performs well in terms of image quality, reconstruction accuracy, convergence speed, and sensitivity to parameters.