A lot of attention has been paid to sparse representation in single image super-resolution. A scheme is employed to implement the image super-resolution via sparse representation. First, the sparse representation from low-resolution input patches is sought by sparse representation algorithms. Then the corresponding high-resolution outputs are generated from them. Finally, the whole high-resolution image from patches is reconstructed. To get the sparse coefficients, an Interior Point Method (IPM) is adopted, which uses preconditioned conjugate gradients algorithm to compute the search direction. Simulation results show that our scheme outperforms the existing bicubic interpolation, Least Angle Regression(LARS) and other algorithms in both visually and qualitative evaluations. Typical Root-Mean-Square Error (RMSE) reduction of 0.29 and 0.7 is achieved over Bicubic and LARS algorithms, respectively.