去除医学、天文图像中的泊松噪声是一个重要问题,基于图像在过完备字典下的稀疏表示,在Bayesian-MAP框架下建立了稀疏性正则化的图像泊松去噪凸变分模型,采用负log的泊松似然函数作为模型的数据保真项,模型中非光滑的正则项约束图像表示系数的稀疏性,并附加非负性约束,保证去噪图像的非负性.基于分裂Bregman方法,提出了数值求解该模型的多步迭代快速算法,通过引入辅助变量与Bregman距离可将原问题转化为两个简单子问题的迭代求解,降低了计算复杂性.实验结果验证了本文模型与数值算法的有效性.

The removal of Poisson noise is essential in medical and astronomical imaging.In the framework of Bayesian-MAP estimation,a sparsity regularized convex functional model is proposed to denoise Poisson noisy image in terms of the sparse representation of the underlying image in an over-complete dictionary.The negative-log Poisson likelihood functional is used for data fidelity term and non-smooth regularization term constrains the sparse representations of the underlying image over the dictionary.An additional term is also added in the functional to ensure the non-negative of the denoised image.Based on the Split Bergman iteration method,a multi-step fast iterative algorithm is proposed to solve the above model numerically.By introducing an intermediate variable and Bergman distance,the original problem is transformed into solving two simple sub-problems iteratively,thus the computational complexity is decreased rapidly.Experimental results demonstrate the effectiveness of our recovery model and the numerical iteration algorithm.