Image Restoration Models Based on Dyadic Hardy Space and Dyadic Bounded Mean Oscillation Space
Image Restoration Models Based on Dyadic Hardy Space and Dyadic Bounded Mean Oscillation Space
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基于二进Hardy空间和二进有界平均振荡空间的图像恢复模型
DOI：
10.1109/access.2019.2936711
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发表时间：
2019
期刊：
影响因子：
3.9
通讯作者：
Mo Xutao
中科院分区：
文献类型：
--
作者：
Zhang Tao;Mo Xutao
纹理广泛存在于各种图像中，在医学图像诊断、遥感等领域发挥着重要作用。然而，纹理区域的图像在恢复过程中容易出现劣化现象。本文将二进Hardy空间<inline-formula> < text -math符号="LaTeX">$H_{d}^{1}$ </ text -math></inline-formula>和二进有界平均振荡（BMO）空间应用于纹理保持图像恢复模型。我们提出了一个<inline-formula> < text -math符号="LaTeX">$H_{d}^{1}$ </ text -math></inline-formula>正则化最小化模型从噪声数据中提取纹理。在该模型中，采用<inline-formula> < text -math notation="LaTeX">$H^{1}_{d}$ </ text -math></inline-formula>范数作为正则化器，根据正则化参数强制噪声局部方差低于一定水平的先验。本文还分析了该模型的数学性质，指出了<inline-formula> < text -math符号="LaTeX">$H^{1}_{d}$ </ text -math></inline-formula>正则化器控制局部方差的机理。对于模型的数值解，我们基于并进Hardy空间和并进BMO空间的小波特征将其转化为小波域，并采用固定迭代算法求解。将全变分（TV）正则化方法和基于帧的正则化方法相结合，提出了一种边缘和纹理保持的两层正则化模型，并在分割Bregman框架中进行了分析和求解。最后，我们在图像上展示了各种数值结果，以证明我们的方法的潜力。
Texture is widely existed in various images and plays an important role in many area such as medical image diagnosis, remote sensing, etc. However, the image in texture regions is tend to be deteriorated during restoration process. In this paper, we apply the dyadic Hardy space <inline-formula> <tex-math notation="LaTeX">$H_{d}^{1}$ </tex-math></inline-formula> and dyadic Bounded Mean Oscillation (BMO) space in the texture preserving image restoration model. We propose a <inline-formula> <tex-math notation="LaTeX">$H_{d}^{1}$ </tex-math></inline-formula> regularized minimization model to extract texture from noisy data. In this model, <inline-formula> <tex-math notation="LaTeX">$H^{1}_{d}$ </tex-math></inline-formula> norm is taken as regularizer to enforce the prior that the local variance of the noise is below certain level depending on the regularization parameter. We also analyze the mathematical properties of this model which indicate the mechanism of <inline-formula> <tex-math notation="LaTeX">$H^{1}_{d}$ </tex-math></inline-formula> regularizer to control the local variance. For the numerical solution of the model, we transform it into wavelet domain based on the wavelet characterization of dyadic Hardy space and dyadic BMO space, and solve it by the fixed iteration algorithm. Combing the total variation (TV) regularization method and frame based regularization method, a two-layers regularization model is proposed for edge and texture preserving, and then analyzed and solved in the frame of split Bregman method. Finally, we present various numerical results on images to demonstrate the potential of our methods.
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