To improve resolution capacity of the degraded image, a learning-based super-resolution reconstruction method via sparse representation over over-complete dictionary is introduced. Due to non-sparsest representation of signal with respect to given ill-conditioned dictionary, the suggested smoothed L0 norm sparse-representation technique over blind sparsity with continuous descending function can exhaustively exploit given specific dictionary, achieving effective sparse decomposition of low resolution image patch. Afterwards, the stable and convergent solvers are obtained from optimization of gradient steepest descent. Experimental results demonstrate that, compared to Bicubic interpolation, the Power Signal to Noise Ratio (PSNR) gain of image thrice-zoomed is close to 2 dB, and the improvement of Structural Similarity (SSIM) is almost 0.04. Moreover, the super-resolved images eliminated excessive blurring degradation and annoying edge artifacts. The proposed method can be effectively applied to resolution enhancement of degraded single-image.