Abstract: The key challenge of transform based shrinkage denoising is to find the optimal threshold value. Aiming at the Shearlet based shrinkage denoising, optimal threshold selection method based particle swarm optimization is proposed. Generalized cross validation for optimal threshold is derived in Shearlet domain. Using the generalized cross validation as fitness function, the optimal threshold associated with Shearlet scale and direction is adaptively determined by particle swarm optimization. The threshold selection method does not rely on any prior knowledges, is an adaptive method. Simulation results show that the optimal threshold can reduce the noise effectively, achieve the more satisfied visual quality.

Key words: shrikage denoising, Shearlet transform, particle swarm optimization, generalized cross validation

摘要： 选取最佳的收缩阈值是变换域收缩去噪的关键。针对Shearlet变换域图像收缩去噪的阈值选取问题，提出了基于粒子群优化的最佳阈值选取算法。建立了Shearlet变换域最佳阈值选取的广义交叉验证准则；以广义交叉验证准则为适应值函数，利用粒子群优化算法自适应地确定出与Shearlet尺度和方向匹配的最佳阈值。算法不依赖任何的先验知识，实现Shearlet变换域图像自适应去噪。仿真结果表明，最佳阈值能够更有效地去除噪声，获得更好的视觉效果。

关键词: 收缩去噪, Shearlet变换, 粒子群优化, 广义交叉验证