Image Poisson Denoising Using Sparse Representations

SUN Yu-bao; WEI Zhi-hui; WU Min; XIAO Liang; FEI Xuan

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Image Poisson Denoising Using Sparse Representations

更新时间：2025-07-16

- Image Poisson Denoising Using Sparse Representations
- Acta Electronica Sinica Vol. 39, Issue 2, Pages: 285-290(2011)
- 作者机构：
  
  1. 南京理工大学计算机科学与技术学院, 模式识别与智能系统实验室,江苏,南京,210094
  2. 总参谋部第六十研究所,江苏,南京,210016
  3. 南京理工大学计算机科学与技术学院模式识别与智能系统实验室,江苏,南京,210094
  4. 总参谋部第六十研究所,江苏,南京,210016
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP391
- Published：2011
- 稿件说明：
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SUN Yu-bao, WEI Zhi-hui, WU Min, et al. Image Poisson Denoising Using Sparse Representations[J]. Acta Electronica Sinica, 2011, 39(2): 285-290.
DOI：

SUN Yu-bao, WEI Zhi-hui, WU Min, et al. Image Poisson Denoising Using Sparse Representations[J]. Acta Electronica Sinica, 2011, 39(2): 285-290. DOI：

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.

Abstract

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.

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