Iterative methods have become a hot topic of research in computed tomography (CT) imaging because of their capacity to resolve the reconstruction problem from a limited number of projections. This allows the possibility of reducing radiation exposure on patients during the data acquisition. However, the complexity of the data still makes the reconstruction process time-consuming, especially for 3D cases. The reconstruction time and the high radiation dose imposed on patients are the two major drawbacks in CT. To resolve them effectively we adapted the method for sparse linear equations and sparse least squares (LSQR) with soft threshold filtering (STF) and the fast iterative shrinkage-thresholding algorithm (FISTA) to computed tomography reconstruction. While STF technique helps to preserve the edge data structure of the object, FISTA accelerates the convergence of the solution and improves the image quality further. The efficiency and feasibility of the proposed method are demonstrated using numerical calculations.