Iterative image reconstruction methods based on conventional total variation (TV) for computed tomography imaging may have limitations for specific applications or situations, such as images with non-sparse gradient parts, complicated textures, or severely contaminated data sets. For these cases, encoders in optimization programs with only TV-based terms may not be sufficient for high-precision image reconstruction. Here, we incorporate a new regularization method, which is based on a block matching local SVD operator, in the reconstruction program. In addition, we develop the corresponding algorithm, which is based on projection onto convex sets and the alternating direction method of multipliers. Theoretically, the proposed method indicates improved sparse representations for complicated textures. Necessary description and discussion on the design of the proposed algorithm are provided. Preliminary results obtained using the simulation data set and the real CT projection verify the capabilities of the proposed algorithm.