Semi soft 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.