Semisoft Generalized Total Variation Minimization for Image Reconstruction in Computed Tomography

The generalized
$l_{1}$
greedy algorithm was recently proposed and shown to outperform the standard reweighted
$l_{1}$
-minimization and
$l_{1}$
-greedy algorithms for image reconstruction in computed tomography (CT). Herein, this algorithm is extended as a semisoft generalized
$l_{1}$
greedy algorithm by adapting the wavelet technique of semisoft thresholding. The extended algorithm can also be applied to image reconstruction by incorporating it into the BCPCS framework, resulting in a semisoft generalized total variation minimization (SSGTV) algorithm for CT. Numerical tests indicate that the proposed SSGTV algorithm improves the image reconstruction for CT.