为改善单帧降质图像的分辨率水平，提出了一种新的基于稀疏表示的学习法超分辨率图像重构方法。针对信号在既定的欠定超完备字典下的非稀疏性问题，采用光滑的递减函数逼近 L0范数以避免对稀疏度先验的依赖，从而实现待重构图像块的有效稀疏表示，同时通过梯度下降的迭代优化获得稳定的收敛解。与双立方插值相比，图像的三倍超分辨实验显示，图像峰值信噪比 (PSNR)提高 2 dB，框架相似性 (SSIM)改善 0.04，重构图像剔除了更多的模糊退化及边缘伪迹。该方法适于单帧降质图像的超分辨率增强。

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.