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

作者：Miao Chuang^*; Yu Hengyong

来源：IEEE Transactions on Image Processing, 2015, 24(12): 5455-5468.

DOI：10.1109/TIP.2015.2468175

• Compressive sensing
• sparsity
• l(p) regularization
• thresholding representation
• least square

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 reweighted approach. Compared with the reweighted 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.

• 出版日期2015-12