摘要： 基于图像在Shearlet变换下的稀疏表示，建立Shearlet域稀疏性正则化的图像复原凸变分模型。通过目标函数中的正则化项刻画理想图像在Shearlet下的稀疏性先验。引入目标函数的代理函数，设计图像复原凸变分问题的迭代收缩求解方法。在迭代收缩求解过程中，利用系数间的相关性，引入双变量收缩函数，以减少迭代次数，提高收敛速度。仿真实验结果表明，与迭代阈值收缩算法和双步迭代收缩算法相比，该算法在主观视觉质量和峰值信噪比方面都有较大的改善，并具有更快的收敛速度。

关键词: 图像复原, 正则化, Shearlet变换, 迭代收缩, 稀疏表示, 代理函数

Abstract: Based on the sparse representation of image in Shearlet transform, a sparsity regularized convex variational model is presented to recover the degraded images. The regularization term of objective function constrains the ideal image to have a sparse representation in Shearlet domain. Using the surrogate function of objective function, an iterative shrinkage method is deduced to solve convex variational of image restoration. The bivariate shrinkage function is used to decrease the iterations and improve the convergence rate. Simulation experimental results demonstrate that, compared with iterative threshold shrinkage algorithm and two-step iterative shrinkage algorithm, the algorithm is improved greatly in the subjective visual quality and Peak Signal to Noise Ratio (PSNR), and has faster convergence speed.

Key words: image restoration, regularization, Shearlet transform, iterative shrinkage, sparse representation, surrogate function

中图分类号: 

• TP301.6