Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise
Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise
复制标题
DOI：
10.3389/fcomp.2023.1131317
复制
发表时间：
2023-01
期刊：
影响因子：
--
通讯作者：
Kevin Bui;Yifei Lou;Fredrick Park;J. Xin
中科院分区：
文献类型：
--
作者：
Kevin Bui;Yifei Lou;Fredrick Park;J. Xin
在本文中，我们的目标是分割图像退化的模糊和泊松噪声。我们采用平滑和阈值（SaT）分割框架，找到一个分段平滑的解决方案，然后通过k均值聚类分割图像。特别是对于图像平滑步骤，我们用最大后验（MAP）项代替Mumford-Shah模型中高斯噪声的最小二乘保真度来处理泊松噪声，并将各向异性和各向同性总变差（AITV）的加权差作为正则化来促进图像梯度的稀疏性。对于这样一个非凸模型，我们开发了一个特定的分裂方案，并利用一个邻近算子应用交替方向乘子法（ADMM）。收敛性分析，以验证ADMM计划的有效性。各种分割方案（灰度/彩色和多相）的数值实验表明，我们提出的方法优于一些分割方法，包括原来的SaT。
In this paper, we aim to segment an image degraded by blur and Poisson noise. We adopt a smoothing-and-thresholding (SaT) segmentation framework that finds a piecewise-smooth solution, followed by k-means clustering to segment the image. Specifically for the image smoothing step, we replace the least-squares fidelity for Gaussian noise in the Mumford-Shah model with a maximum posterior (MAP) term to deal with Poisson noise and we incorporate the weighted difference of anisotropic and isotropic total variation (AITV) as a regularization to promote the sparsity of image gradients. For such a nonconvex model, we develop a specific splitting scheme and utilize a proximal operator to apply the alternating direction method of multipliers (ADMM). Convergence analysis is provided to validate the efficacy of the ADMM scheme. Numerical experiments on various segmentation scenarios (grayscale/color and multiphase) showcase that our proposed method outperforms a number of segmentation methods, including the original SaT.