Abstract: The orthogonal wavelet fails to provide an optimal sparse representation for images that contain texture details due to limited direction, and the current regularization method is singleness. In this paper, it proposes a compressed sensing reconstruction algorithm based on Shearlet sparse representation and compound regularizers, the algorithm uses Shearlet for image sparse representation, and the problem is solved by alternating minimization algorithm. The experimental results indicate that the visual quality and PSNR of reconstructed image is improved by proposed algorithm compared with single total variation regularizer method and wavelet transform.

Key words: compressive sampling, Shearlet transform, regularizer

摘要： 针对图像压缩采样中正交小波变换方向有限和单一正则化的问题，提出了一种基于Shearlet的双正则化图像压缩采样恢复算法。该算法用Shearlet作为图像的稀疏表示，用交替最小化对联合正则化模型进行求解。实验结果表明，该算法恢复的图像与单一的全变分正则化方法和小波变换相比有更好的视觉效果，更高的峰值信噪比。

关键词: 压缩采样, 剪切波变换, 正则化