稀疏性正则化的图像Laplace去噪及PR算子分裂算法

Sparsity regularized image Laplace denosing based on Peaceman Rachford operator splitting algorithm

在Bayesian-MAP框架下,建立了针对Laplace噪声的稀疏性正则化图像去噪凸变分模型,模型采用L1范数作为数据保真项,非光滑的正则项约束图像在过完备字典下表示系数的稀疏性。进一步基于Peaceman-Rachford算子分裂算法,提出了数值求解该非光滑模型的多步迭代快速算法,通过引入保真项与稀疏性正则项的邻近算子,可将原问题转换为两个简单子问题的迭代求解,降低了计算复杂性。实验结果验证了模型与数值算法的有效性,本算法在摄像自动报靶系统中得到了应用。

Adopting Bayesian-MAP estimation framework,this paper proposed a sparsity regularized non-smooth convex functional model to denosie Laplace noisy image.The L1 norm was used for data fidelity term and non-smooth regularization term constrains the sparse representation of the underlying image over the overcomplete dictionary.Inspired form the Peaceman-Rachford operator splitting method,proposed a multi-step fast iterative algorithm to solve the non-smooth model above numerically.By introducing the proximal operators of fidelity term and regularization term,the original problem was transformed into solving two simple sub-problems iteratively,thus decreased the computational complexity rapidly.Experimental results demonstrate the effectiveness of our recovery model and numerical iteration algorithm.This algorithm has been applied to automatic target-reading system based on video processing.