Abstract: Compressed Sensing (CS) theory can reconstruct original images from fewer measurements using the priors of the images sparse representation. The CS theory was applied into the single-image Super-Resolution (SR), and a new reconstruction algorithm based on two-step iterative shrinkage and Total Variation (TV) sparse representation was proposed. The proposed method does not need an existing training set but the single input low resolution image. A down-sampling low-pass filter was incorporated into measurement matrix to make the SR problem meet the restricted isometry property of CS theory, and the TV regularization method and a two-step iterative method with TV denoising operator were introduced to make an accurate estimate of the image's edge. The experimental results show that compared with the existing super-resolution techniques, the proposed algorithm has higher precision and better performance under different magnification level, the proposed method achieves significant improvement (about 4~6dB) in Peak Signal-to-Noise Ratio (PSNR), and the filter plays a decisive role in the reconstruction quality.

Key words: Super-Resolution (SR), Compressed Sensing (CS), Total Variation (TV), two-step iteration, restricted isometry property

摘要： 压缩感知(CS)利用图像稀疏表示的先验知识，从少量的观测值中重建出原始图像。将CS理论应用于单幅图像超分辨率(SR)，提出一种基于两步迭代收缩算法和全变分(TV)稀疏表示的图像重建方法。该方法无需任何训练集，仅需单幅低分辨率实现图像重建。算法在测量矩阵里加入下采样低通滤波器以使SR问题满足应用CS理论的有限等距性质;采用TV正则化函数，利用两步迭代法引入TV去噪算子，可以更好地重建图像边缘。实验结果证明，与已有的超分辨率方法相比，在不同的放大倍数下所提方法重建图像视觉效果更好，在峰值信噪比(PSNR)的评价指标上有显著的提高(4~6dB)，且实验证实滤波器的引入决定算法的重建质量。

关键词: 超分辨率, 压缩感知, 全变分, 两步迭代, 有限等距性质