A REWEIGHTED l2 METHOD FOR IMAGE RESTORATION WITH POISSON AND MIXED POISSON-GAUSSIAN NOISE
A REWEIGHTED l2 METHOD FOR IMAGE RESTORATION WITH POISSON AND MIXED POISSON-GAUSSIAN NOISE
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DOI：
10.3934/ipi.2015.9.875
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发表时间：
2015-08-01
影响因子：
1.3
通讯作者：
Zhang, Xiaoqun
中科院分区：
文献类型：
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作者：
Li, Jia;Shen, Zuowei;Zhang, Xiaoqun
本文研究了泊松噪声相关图像复原问题变分模型中的加权l（2）保真度。采用泊松噪声统计量的高斯近似来推导加权l（2）保真度。与传统的加权l（2）逼近不同，本文提出了一种基于小波框架的稀疏正则化加权l（2）逼近。基于[21]中介绍的分裂Bregman算法，所提出的数值格式由三个简单的子问题组成，涉及二次最小化、软收缩和矩阵向量乘法。与通常的最小二乘近似泊松噪声，我们动态更新的基础噪声方差从以前的估计。所提出的算法的解决方案被证明是通过最小化Kullback-Leibler发散保真度相同的正则化。这种重新加权的l（2）公式可以很容易地推广到混合泊松-高斯噪声的情况。最后，通过去噪和去模糊的例子，证明了该算法的效率和质量相比，其他泊松噪声去除方法。此外，混合泊松-高斯噪声测试进行模拟和真实的数字图像的性能进一步说明所提出的方法。
We study weighted l(2) fidelity in variational models for Poisson noise related image restoration problems. Gaussian approximation to Poisson noise statistic is adopted to deduce weighted l(2) fidelity. Different from the traditional weighted l(2) approximation, we propose a reweighted l(2) fidelity with sparse regularization by wavelet frame. Based on the split Bregman algorithm introduced in [21], the proposed numerical scheme is composed of three easy subproblems that involve quadratic minimization, soft shrinkage and matrix vector multiplications. Unlike usual least square approximation of Poisson noise, we dynamically update the underlying noise variance from previous estimate. The solution of the proposed algorithm is shown to be the same as the one obtained by minimizing Kullback-Leibler divergence fidelity with the same regularization. This reweighted l(2) formulation can be easily extended to mixed Poisson-Gaussian noise case. Finally, the efficiency and quality of the proposed algorithm compared to other Poisson noise removal methods are demonstrated through denoising and deblurring examples. Moreover, mixed Poisson-Gaussian noise tests are performed on both simulated and real digital images for further illustration of the performance of the proposed method.