Epigraphical Projection for Solving Least Squares Anscombe Transformed Constrained Optimization Problems
Epigraphical Projection for Solving Least Squares Anscombe Transformed Constrained Optimization Problems
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DOI：
10.1007/978-3-642-38267-3_11
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发表时间：
2013-06
期刊：
影响因子：
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通讯作者：
S. Harizanov;J. Pesquet;G. Steidl
中科院分区：
文献类型：
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作者：
S. Harizanov;J. Pesquet;G. Steidl
本文研究了受不可逆或病态线性变换和泊松噪声污染的图像的恢复问题。泊松数据通常出现在成像过程中，其中通过对颗粒进行计数来获得图像，光子，撞击图像支撑。通过使用Anscombe变换，泊松噪声可以近似为具有零均值和单位方差的加性高斯噪声。然后，Anscombe变换的损坏的图像和原始图像之间的最小二乘差可以通过观察的数量来估计。我们使用这些信息，考虑Anscombe变换约束模型来恢复图像。相对于相应的惩罚方法的优点在于存在一个简单的模型参数估计。我们解决了约束最小化问题，通过应用原始-对偶算法与投影到上图的凸函数相关的Anscombe变换。我们表明，这种epigraphical投影可以有效地计算牛顿的方法与适当的初始化。数值例子表明，我们的方法，特别是其密切的行为与theI-发散约束模型的良好性能。
This paper deals with the restoration of images corrupted by a non-invertible or ill-conditioned linear transform and Poisson noise. Poisson data typically occur in imaging processes where the images are obtained by counting particles, e.g., photons, that hit the image support. By using the Anscombe transform, the Poisson noise can be approximated by an additive Gaussian noise with zero mean and unit variance. Then, the least squares difference between the Anscombe transformed corrupted image and the original image can be estimated by the number of observations. We use this information by considering an Anscombe transformed constrained model to restore the image. The advantage with respect to corresponding penalized approaches lies in the existence of a simple model for parameter estimation. We solve the constrained minimization problem by applying a primal-dual algorithm together with a projection onto the epigraph of a convex function related to the Anscombe transform. We show that this epigraphical projection can be efficiently computed by Newton’s methods with an appropriate initialization. Numerical examples demonstrate the good performance of our approach, in particular, its close behaviour with respect to theI-divergence constrained model.