Limited-angle tomography has gained much interest in late years Nevertheless, image reconstruction from incomplete projections is a classic ill-posed issue in the field of computational imaging. In this paper, we propose a scheme based on the sparsifying operators and approximation of ℓ0-minimization. Our framework includes two main components, one for a sparsifying operator, and one for learning the scheme parameters using ℓ0-minimization from insufficient computed tomography data. Thus, the proposed scheme is capable of recovering high quality reconstructions at a range of angles and noise. Compared to the total-variation (TV) regularized reconstruction scheme, σ-u scheme and ATV (Anisotropic Total Variation) scheme, validations using Shepp-Logan phantom computed tomography data demonstrate the significant improvements in SNR and suppressed noise and artifacts.