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中文摘要：
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.
英文摘要：
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 nonsmooth 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.
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