基于压缩感知的超分辨率图像重建

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。

Super-resolution image reconstruction algorithms based on compressive sensing

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.