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中文摘要：
生物医学、天文等成像系统通常会受到泊松噪声的干扰,基于图像在过完备字典下的稀疏表示,在贝叶斯最大后验概率估计框架下,建立了针对泊松噪声的稀疏性正则化图像恢复凸变分模型,采用负log的泊松似然函数作为数据保真项,模型中非光滑的正则项约束图像表示系数的稀疏性,并附加恢复图像的非负性约束.进一步,基于分裂Bregman方法,提出了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,大幅度降低了计算复杂性.实验结果验证了本文模型与数值算法的有效性.
英文摘要：
Astronomical and biomedical imaging instruments are often corrupted by Poisson noise. Using the sparse representation of the underlying image in an over-complete dictionary,a sparsity regularized convex functional model is proposed to deconvolve the Poisson noisy image in the Bayesian-MAP estimate framework. The negative-log Poisson likelihood functional is used as the data fidelity term,and the non-smooth regularization term is used to constrain the sparse image representation over the dictionary. An additional term is also added to ensure the positivity of the restored image. Inspired form the split Bergman iteration method,a multi-step fast iterative algorithm is proposed to numerically solve the above model. By introducing an intermediate variable and Bergman distance,the original problem is transformed into solving two simple sub-problems iteratively,thus computational complexity is decreased greatly. Experimental results demonstrate the effiectiveness of our recovery model and numerical algorithm.
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